Research ArticleMultiple Hidden Markov Model forPathological Vessel Segmentation

Xin Hu 1 Deqiong Ding2 and Dianhui Chu 1

1School of Computer Science and Technology Harbin Institute of Technology at Weihai Weihai 264209 China2School of Computer Science and Technology Harbin Institute of Technology Harbin 150001 China

Correspondence should be addressed to Xin Hu hithuxinhiteducn and Dianhui Chu chudhhiteducn

Received 27 June 2018 Revised 12 September 2018 Accepted 28 November 2018 Published 10 December 2018

Academic Editor Kwang Gi Kim

Copyright copy 2018 Xin Hu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

One of the obstacles that prevent the accurate delineation of vessel boundaries is the presence of pathologies which results inobscure boundaries and vessel-like structures Targeting this limitation we present a novel segmentationmethod based onmultipleHidden Markov Models This method works with a vessel axis + cross-section model which constrains the classifier around thevessel The vessel axis constraint gives our method the potential to be both physiologically accurate and computationally effectiveFocusing on pathological vessels we reap the benefits of the redundant information embedded in multiple vessel-specific featuresand the good statistical properties comingwith HiddenMarkovModel to cover the widest possible spectrumof complex situationsThe performance of our method is evaluated on synthetic complex-structured datasets where we achieve a 91 high overlap ratioWe also validate the proposedmethod on a real challenging case segmentation of pathological abdominal arteriesThe performanceof our method is promising since our method yields better results than two state-of-the-art methods on both synthetic datasetsand real clinical datasets

1 Introduction

Automatic vessel segmentation in three-dimensional (3-D)medical computed tomography (CT) images plays a fun-damental role in many clinical fields study of anatomicalstructure [1] quantification of vascular diseases (stenosisocclusion and calcification) for clinical diagnosis [2] surgeryplanning [3] and patient-specific flow simulations [1] Vesselsegmentation can help clinical workers to have an intuitiveimpression of vessels and blood supply Based on the vesselsegmentation clinical workers can also establish the patientsrsquoresponse to treatment and determine the stage of diseasesto further plan a minimally invasive surgery All theseapplications ask for a competent segmentation techniquewhich has the capability of segmenting vessels accurately notonly for normal vessels but also for vessels with the presenceof pathologies

In recent years many methods [1ndash3] have been proposedto segment vessels with the presence of pathologies Thesemethods can be roughly classified into three categories (a)feature based segmentation approaches [4 5] which have

been proven to be efficient in detecting vessels at differentscales (b) tracking based segmentation approaches [6ndash8]which have the capability to be robust against noise and (c)model based approaches [9ndash12] which resolve subsequenttwo-dimensional (2-D) slices of vessels using tubular shapepriors

By targeting the curvilinear structures the feature basedsegmentation approaches are efficient in identifying vesselsfrom other tissues [5 13ndash18] They have several commondetection procedures firstly assuming that vessels haveidentifiable curvilinear structures and then calculating theeigenvalues of the Hessian matrix to traverse the whole 3-Dimage at different scales by convolving with 3-D Gaussianfilters The standard deviation of the Gaussian filter definesthe detecting scale Third a response function based on theseeigenvalues is constructed which can detect the curvilinearstructures locally at a certain scale Since the curvilinearstructures signed to vessels are significantly different fromother tissues the feature based segmentation approaches canrecognize vessels from other nonvessel structures such asplanar structure blob noise or no structure The response

HindawiBioMed Research InternationalVolume 2018 Article ID 9868215 14 pageshttpsdoiorg10115520189868215

2 BioMed Research International

consisting of eigenvalues can represent the local struc-ture when it comes to its maximum over different scales[5 16]

However the feature based segmentation approaches donot produce direct vessel segmentation they output re-sponses instead of segmentation As a result their resultscan be used in structure analysis where many researchersconsider it as the advantage of the feature based segmentationapproaches [19 20] especially in combining the trackingbased segmentation approaches Based on the responses ofthe feature based segmentation approaches the trackingbased segmentation approaches resolve subsequent two-dimensional (2-D) slices of vessels by using the tubular shapepriors [19 20] Based on the tubular shape structure Tyrrellet al [21] propose another 3-D structure 3-D cylindroidalsuperellipsoids combining with the local regional statisticsmethod This tracking methodology extracts topologicalinformation frommicrovasculature networks

The tracking based segmentation approaches are shownto be robust against noise [19ndash21] However the shape priorsthey use are too exclusive [22] which lead to false detectionwith the complex vessel boundaries Targeting at this chal-lenge the statistical mixture models have been proposed [22ndash24]They combine the statistical mixture models with expec-tation-maximization algorithm to detect complex vesselboundaries However these approaches ask for an accurateparametrical estimation or nonparametric modeling As aresult they all rely on the second-order derivative informa-tion which is associated with the principal curvatures ofimage intensities They suffer from sensitivity caused by localdeformations which are considered as pathologies in thiswork

In the past decade after many sophisticated vascularsegmentation algorithms have been proposed there are stillseveral challenges remaining unsolved such as detectingvessel radius with the presence of pathologies (stenosis andocclusion) delineating vessel accurately with low contrastvessel boundary and distinguishing vessels from vessel-like tissues All these challenges are caused by pathologiesespecially by the vessel calcification As far as we knowthe accurate delineation of pathological vessel is valuable inclinical fields However the proposed challenges may leadto false segmentation which makes the vessel segmentationuseless For further information several good reviews can befound in [1ndash3]

Addressing these unsolved challenges we propose aMultiple Hidden Markov Model (MHMM) for pathologicalvessels by taking the advantages of the redundant informa-tion embedded in multiple vessel-specific features and thegood statistical properties coming with the Hidden MarkovModel (HMM) As we target at pathological vessels theshape complexity of obscure vessel boundary may not becaptured by one single existing vessel-specific feature Thuswe dig the redundant information embedded in multiplevessel features automatically by usingmultipleHMMs and tryto combine multiple vessel features optimally by employingthe good statistical properties of HMM Different from mostof the other researchers we build the MHMM to describe thetransition course from the inner vessel to the outside of vessel

By doing so the MHMM has the capability to delineate theobscure vessel boundaries accurately

This paper is organized as follows Section 2 introducesthe proposed method MHMM Section 21 details the train-ing samples and the testing samples we use in this work Themultiscale vessel-specific feature set is followed in Section 22Then we present the details of training a single HMM inSection 23 The MHMM combining multiple vessel featureswith multiple HMMs is given in Section 24 The evalua-tion datasets the evaluation methods and the experimentalresults are shown in Section 3 In Section 4 we discussthe advantages and disadvantages of our method possibleimprovements and future work Finally we conclude thepaper in Section 5

2 Method

This paper describes a Multiple Hidden Markov Model(MHMM) for abdominal artery with the presence of patholo-gies which takes two advantages (1) the redundant infor-mation included in multiple vessel features and (2) the goodstatistical properties of Hidden Markov Model (HMM) [25]First we extract vessel axis from a gray-scale 3-D CT scanby using our previous method [9] Then along this extractedvessel axis voxel series are generated on the cross-sectionsfor training and testing purposes Subsequently multiplevessel features are calculated for each voxel in the voxelseries Finally a MHMM is trained based on these vesselfeatures The trained MHMM can detect vessel boundarywith the presence of pathologies by expressing the similaritymarching degree (posterior probability)

21 Training Samples and Testing Samples We randomlyselected 50 CT datasets of abdominal artery from 120 CTdatasets which were collected by our collaborators (the clini-cal workers from the 2119899119889 affiliated Hospital of HarbinMedicalUniversity) These 120 CT datasets were collected from 120patients 73 males and 47 females with mean age 65 years(min 58 max 91) who entered our study nonconsecutivelyfrom October 2014 to October 2017 These 50 selected CTdatasets are known with aortoiliac stenosis calcification andocclusion

Two expert raters were asked to segment the datasetsWe understand that the ground truth segmentations of thoseclinical datasets do not exist even segmented by multipleexperts Thus we developed a graphical user interface (GUI)in our lab [9] to help the experts mark different tissuesin 3-D CT images including pathologies With this GUIthe user can do the marking job in two stages propagatingstage and checking stage In the propagating stage the GUIcan propagate to mark the target tissue in 3-D CT imageautomatically with seed points given by experts In thechecking stage the GUI helps the user to cine-page throughthe CT slices scroll in and out of individual tissue adjustwindow setting and zoom to improve visualization As aresult the user can check the propagating result and setnew seed points By using this GUI two expert raters wereasked to mark vessels and pathologies (calcification and iliacstent)

BioMed Research International 3

Vessel axis

Cross-section

(a) (b)

Rays

(c)

i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i13 i14 i15 i16 i17 i18

Vi

Figure 1 Collecting training samples and testing samples (a) Vessel cross-section plane orthogonal to the extracted vessel axis (b) Collectingvoxel series along the rays as training samples and testing samples The black points indicate the voxels on the ray The rays space every 5∘from the axis point (c) One voxel series along the ray Along each ray we collect 18 voxels

We collect voxel series as training samples and testingsamples based on the segmentations provided by the expertraters Firstly vessel axis is extracted by using our previousmethod [9] see Figure 1(a) for a snapshot Then rays arespaced every 5∘ from the axis point on the cross-sectionshown in Figure 1(b) Finally voxel series are collected alongthe rays (Figure 1(c)) Along the vessel axes the voxel seriesare gathered cross-section by cross-section to form thetraining samples and the testing samples Let us denote allthe voxel series as 119881 = 1198811 119881119894 119881119873 where 119881119894 =V1198941 V119894119895 V119894119899 is a voxel series for one ray V119894119895 is a voxelin the voxel series 119881119894 and 119873 is the number of voxel seriesPlease notice that one voxel series is considered as a whole bythe proposed MHMM to describe the tissue transition fromthe inner vessel to the outside of vessel

We target at accurate vessel segmentation with the pres-ence of pathologies However the pathology obscures thevessel boundary and makes it difficult to identify vessel frompathology Thus we divide the voxels into 4 classes lumen(vessel) intima (vessel boundary) pathology (pathologicaltissue) and adventitia (outer tissue) By doing so we can train

theMHMMto focus on obscure vessel boundary To form thevessel boundary class we strip the outermost layer away fromvessel along the ray Since the vessel wall thickness changeswith vessel scale we change the size of the outermost layerfrom 2 voxels to 4 voxels to cover the vessel scale changesaccording to the CT scan resolution in this work

22 Feature Set for Multiple Hidden Markov Model Due tothe presence of pathologies it is challenging to segmentvessels accurately And the variance of vessel intensity makesthis even worse In our previous work [26] we found thatno vessel feature is optimal in this challenging case Thuswe employ multiple vessel-specific features here and try toexplore the redundant information included in these featureswhich can cover the widest possible spectrum of situationsSince the diameter (scale) changes in vessels all the vessel-specific features we chose aremultiscale vessel featuresThesefeatures are extracted by using Hessian matrix which usesGaussian convolution to capture the gradient based shapeinformation And the scale of vessel 119904 is represented by thestandard deviation of Gaussian convolution In the following

4 BioMed Research International

we introduce the multiscale vessel-specific features employedin this paper

(1) Sato feature (1198911) [5] this feature is designed for healthyvessel with bright tubular structure in a dark environmentFor one scale 119904 the Sato vessel feature 1198911 can be described asfollows

1198911 (1205821 1205822 119904)

=

1205822 sdot exp(minus 120582212 (12057211205822)2) 1205821 le 0 1205822 = 01205822 sdot exp(minus 120582212 (12057221205822)2) 1205821 gt 0 1205822 = 00 1205822 = 0

(1)

where 1205821 1205822 and 1205823 are the eigenvalues of Hessian matrixsubject to 1205821 gt 1205822 gt 1205823 [5] These eigenvalues are calculatedby using Gaussian convolution and the scale 119904 is the standarddeviation for Gaussian convolution 1205721 and 1205722 are two presetparameters 1205721 lt 1205722 In this work 1205721 and 1205722 were fixed to 05and 2 respectively

(2) Frangi feature 1198912 [14] this feature promotes theenhancement of tubular structure and smoothes other struc-tures out In the original work this feature gives promis-ing performance to the vessels with low contrast For asingle scale 119904 the Frangi vessel feature is given as fol-lows

1198912 (1205821 1205822 1205823 119904) =

0 1205822 gt 0 119900119903 1205823 gt 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] 119900119905ℎ119890119903119908119894119904119890 (2)

where 1205821 1205822 and 1205823 are defined in (1) The scale 119904 isalso the standard deviation for Gaussian convolution 119877119860 =|1205822||1205823| (subject to 120572) identifies plate-like structures fromtubular structures while 119877119861 = |1205821|radic|12058221205823| (subject to 120573)identifies blob-like structures from tubular structures 119878 =radic12058221 + 12058222 + 12058223 (subject to 120574) smoothes background noise outBy following the original research we set the parameters asfollows 120572 = 05 and 120573 = 05 Here 120574 is equal to half of themaximum Frobenius norm of the Hessian over all Frobeniusnorms computed on the whole image

(3) Shikata feature 1198913 [27] based on Frangi featureShikata feature assumes the cross-section of tubular structurehas 2-D Gaussian intensity distribution This assumptiongives Shikata feature the capability of detecting small vesselsThe feature 1198913 is given as follows

1198913 (997888rarr119909 1205822 119904) = 1199042 sdot 1205822119868 (997888rarr119909) (3)

where1205822 is the second eigenvalues of Hessian matrix definedin (1) and 119868(997888rarr119909) is the intensity at voxel 997888rarr119909

(4) Li feature 1198914 [28] this feature enhances the tubularstructures by using curvature analysis which gives Li featurethe potentiality to distinguish tubular structures from otherstructures This Li feature 1198914 can be described as follows

1198914 (1205821 1205822 1205823 119904)=

100381610038161003816100381612058221003816100381610038161003816 (100381610038161003816100381612058221003816100381610038161003816 minus 100381610038161003816100381612058231003816100381610038161003816)100381610038161003816100381612058211003816100381610038161003816 1205821 lt 0 1205822 lt 00 119900119905ℎ119890119903119908119894119904119890

(4)

(5) Manniesing feature 1198915 [29] focusing on backgroundnoise and small vessels this feature improves the Frangifeature by using a nonlinear anisotropic diffusion approachThis feature 1198915 can be given as follows

1198915 (1205821 1205822 1205823 119904) =

0 1205822 ge 0 119900119903 1205823 ge 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] exp(minus 21198882100381610038161003816100381612058221003816100381610038161003816 12058223) 119900119905ℎ119890119903119908119894119904119890 (5)

where 119877119860 = |1205822||1205823| is designed to identify plate-likestructures from line-like structures 119877119861 = |1205821|radic|12058221205823|has the capability to discriminate blob-like structures fromline-like structures and 119878 = radic12058221 + 12058222 + 12058223 eliminatesbackground noise By following the original research wepreset 120572 = 05 120573 = 05 in this study And 120574 is defined in(2)

By following our previous work [26] we set the vesselscale as 119904 = 06 times 2(119908minus1)2 119908 = 1 2 6 for each of the fivefeatures to cover both large and small vessels (the diameterof vessel changes from 07 mm to 60 mm) The responseof one vessel feature reaches its maximum when the scaleof the feature matches the size of local tubular structuresThe maximum response can be collected as the local vesselfeature

BioMed Research International 5

Lumen Intima Pathology Adventitia

T1 T2 T3 T4

Vi

Figure 2 One single HMM 120601 describes the state transition from inner vessel to the outside of vessel along the ray

For each voxel in the voxel series we calculate featurevalues to form feature series Let us take Sato feature forexample For the voxel series 119881119894 = V1198941 V119894119895 V119894119899we calculate the Sato feature for each voxel in 119881119894 and thenobtain a Sato feature series 1198651119894 = 11989111198941 1198911119894119895 11989111198941198991198911119894119895 is the Sato feature value corresponding to voxel V119894119895After calculating the Sato feature for all the voxel series1198811 119881119873 a subset of Sato feature series can be obtained1198651 = 11986511 1198651119894 1198651119873 By using the five proposed vesselfeatures we finally obtain five subsets of the trainingtestingsamples 119865 = 1198651 119865119896 1198655 where 119865119896 is the 119896th subsetcorresponding to the 119896th feature 119896 = 1 5 These fivesubsets are the inputs of MHMM

23 HMM-Based Recognition Model The proposed MHMMis the combination of multidimensional HMMs Beforepresenting the MHMM we would like to introduce oneindividual HMM first This HMM is trained by using one ofthe five features

HMM is considered to be the best for modeling varia-tions in observations of similar data series and for findingdissimilarities across different series One HMM (120601) can beexpressed as a five item array as 120601 = (119872119873 120587 119860 119861) where119872is the number of invisible tissue states In this paper we set thenumber of invisible tissue states as 4 to represent four tissuestates lumen (vessel) intima (vessel boundary) pathology(pathological tissue) and adventitia (outer tissue) 119873 is thenumber of observation values which are decided by the vesselfeatures We will describe this observation value later 120587119896 isthe initial state distribution 120587 = 120587119898119898 = 1 119872 Since westart detecting lumen and intima from the axis point on thecross-section the initial state distribution is 1205871 = 1 120587119895 = 0119895 = 2 119872119860 is the state transition matrix with size119872times119872And 119861 is the emission matrix with size 119873 times 119872 These twomatrixes are the key parameters of HMM whichwe are goingto estimate in the training process

The HMM 120601 describes the state transition from theinner vessel to the outside of vessel as shown in Figure 2This state transition is a visible random process which givesthe similarities between states and voxels Let us denote thefour tissue states (lumen intima pathology and adventitia)as 119879 = 1198791 1198794 As shown in Figure 2 we model thepathologies only existing outside the intima The pathologieswe target at are calcification stenosis occlusion and lowcontrast vessel Within these pathologies calcification isa main pathophysiological process in vasculature and theother pathological tissues come with it More specificallycalcification determines the location of the other pathologicaltissues [30] The location of calcification can be dividedinto superficial or deep In the calcification process deepcalcification is followed by plaque shrinkage and arterialremodeling in which a kind of internal elastic lamina coversthe calcification plaque [30] Based on this finding manyclinical trials consider deep or multiple calcifications assuperficial calcification for blood supply prediction [31]Thus we model the pathologies to be outside of the intima

Different from other algorithms (such as SVM andAdaBoost classifier) the vessel feature values cannot be theinput of HMM directly due to the computational time issueand the convergence issue in the training process [25] Forone vessel feature the feature values vary in a large area dueto different tissues Associating each feature value with a statewill cause a heavy burden for the HMM which may lead toslow convergence or nonconvergence Thus the HMM asksfor quantization of feature space into a smaller number ofdiscrete space called observation space This quantization ismore like a binning process Firstly we divide the featurespace into several bins Let us denote the bin set as 120579 =1205791 cup 1205792 cup 120579119870 Then we associate feature values with bins Ifa feature value 119886 falls into a bin 120579119896 119886 isin 120579119896 this feature 119886 canbe associated with 120579119896 By associating feature values with binswe can turn the feature series into a bin series which is theobservation series for HMM

6 BioMed Research International

Lumen Pathology Adventitia

Intima

Alumen

Aintima

Apathology

Voxel(a) (b)

f170

60

50

40

30

20

10

0

minus100 2 4 6 8 10 12 14 16 18

Figure 3The distribution of Sato feature values in one feature series (a)The feature series collected along one rayThe black points indicatethe voxels we collect along the ray (b) The distribution of Sato feature values It can be observed that area 119860119901119886119905ℎ119900119897119900119892119910 overlaps 119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886

Table 1 Segment method

Interval [0 1198861) [1198861 1198862) [1198862 1198863) [1198863 +infin)Dividing method One bin Average Average One binNumber of bins 1 1198701 1198702 1

Table 2 Overlapping areas for different features

[1198861 1198862) [1198862 1198863)Sato feature 1198911 [25 35) [35 50)Frangi feature 1198912 [15 20) [20 30)Shikata feature 1198913 [85 95) [95 120)Li feature 1198914 [40 45) [45 55)Manniesing feature 1198915 [15 25) [25 45)

The method of dividing bins is the key for HMM In ourexperiment we found that the capability of HMM correlateswith the number of binsMore specifically the number of binsdetermines the capability of HMM in identifying differenttissues in one given area of the feature space The largerthe number of bins is the more powerful the HMM isHere we take the Sato feature for example to demonstratethe method we use in dividing bins Firstly we look intothe distribution of feature values along the ray (Figure 3(a))Let us denote the distributions of lumen intima pathologyand adventitia as 119860 119897119906119898119890119899 119860 119894119899119905119894119898119886 119860119901119886119905ℎ119900119897119900119892119910 and 119860119886119889V119890119899119905119894119905119894119886respectively And the distributions of different tissues alongthe ray are shown in Figure 3(b) It can be easily observedthat the distribution of pathology (119860119901119886119905ℎ119900119897119900119892119910) overlaps thedistributions of lumen (119860 119897119906119898119890119899) and intima (119860 119894119899119905119894119898119886) Sincewe target delineating the vessel boundary (intima) accuratelywith the presence of pathologies we want the HMM to bepowerful in these two areas (119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886) Assume that119860119901119886119905ℎ119900119897119900119892119910 overlaps119860 119894119899119905119894119898119886 and119860 119897119906119898119890119899 in intervals [1198861 1198862) and

[1198862 1198863) respectively We give more bins to the overlappingintervals to make the HMM more powerful in these areasThe dividing method we use here is shown in Table 1 In thiswork we set 1198701 and 1198702 as1198701 = 51198702 = 3 for all the featuresThe five features we use in this work have different ranges ofoverlapping areas which are shown in Table 2 Please noticethat the number of bins should not be large due to theconvergence issue The computation time will be discussedin Section 4

After turning the feature series into observation seriesthe HMM 120601 = (119872119873 120587 119860 119861) can be trained by usingBaum-Welch algorithm [32] The initialization conditionused for HMM training can be summarized as follows

(1) the number of invisible states119872 = 4(2) the number of observation values119873 = 10(3) the initial state distribution 1205871 = 1 and 120587119895 = 0 119895 =2 4

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 3

Vessel axis

Cross-section

(a) (b)

Rays

(c)

i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i13 i14 i15 i16 i17 i18

Vi

Figure 1 Collecting training samples and testing samples (a) Vessel cross-section plane orthogonal to the extracted vessel axis (b) Collectingvoxel series along the rays as training samples and testing samples The black points indicate the voxels on the ray The rays space every 5∘from the axis point (c) One voxel series along the ray Along each ray we collect 18 voxels

We collect voxel series as training samples and testingsamples based on the segmentations provided by the expertraters Firstly vessel axis is extracted by using our previousmethod [9] see Figure 1(a) for a snapshot Then rays arespaced every 5∘ from the axis point on the cross-sectionshown in Figure 1(b) Finally voxel series are collected alongthe rays (Figure 1(c)) Along the vessel axes the voxel seriesare gathered cross-section by cross-section to form thetraining samples and the testing samples Let us denote allthe voxel series as 119881 = 1198811 119881119894 119881119873 where 119881119894 =V1198941 V119894119895 V119894119899 is a voxel series for one ray V119894119895 is a voxelin the voxel series 119881119894 and 119873 is the number of voxel seriesPlease notice that one voxel series is considered as a whole bythe proposed MHMM to describe the tissue transition fromthe inner vessel to the outside of vessel

We target at accurate vessel segmentation with the pres-ence of pathologies However the pathology obscures thevessel boundary and makes it difficult to identify vessel frompathology Thus we divide the voxels into 4 classes lumen(vessel) intima (vessel boundary) pathology (pathologicaltissue) and adventitia (outer tissue) By doing so we can train

theMHMMto focus on obscure vessel boundary To form thevessel boundary class we strip the outermost layer away fromvessel along the ray Since the vessel wall thickness changeswith vessel scale we change the size of the outermost layerfrom 2 voxels to 4 voxels to cover the vessel scale changesaccording to the CT scan resolution in this work

22 Feature Set for Multiple Hidden Markov Model Due tothe presence of pathologies it is challenging to segmentvessels accurately And the variance of vessel intensity makesthis even worse In our previous work [26] we found thatno vessel feature is optimal in this challenging case Thuswe employ multiple vessel-specific features here and try toexplore the redundant information included in these featureswhich can cover the widest possible spectrum of situationsSince the diameter (scale) changes in vessels all the vessel-specific features we chose aremultiscale vessel featuresThesefeatures are extracted by using Hessian matrix which usesGaussian convolution to capture the gradient based shapeinformation And the scale of vessel 119904 is represented by thestandard deviation of Gaussian convolution In the following

4 BioMed Research International

we introduce the multiscale vessel-specific features employedin this paper

(1) Sato feature (1198911) [5] this feature is designed for healthyvessel with bright tubular structure in a dark environmentFor one scale 119904 the Sato vessel feature 1198911 can be described asfollows

1198911 (1205821 1205822 119904)

=

1205822 sdot exp(minus 120582212 (12057211205822)2) 1205821 le 0 1205822 = 01205822 sdot exp(minus 120582212 (12057221205822)2) 1205821 gt 0 1205822 = 00 1205822 = 0

(1)

where 1205821 1205822 and 1205823 are the eigenvalues of Hessian matrixsubject to 1205821 gt 1205822 gt 1205823 [5] These eigenvalues are calculatedby using Gaussian convolution and the scale 119904 is the standarddeviation for Gaussian convolution 1205721 and 1205722 are two presetparameters 1205721 lt 1205722 In this work 1205721 and 1205722 were fixed to 05and 2 respectively

(2) Frangi feature 1198912 [14] this feature promotes theenhancement of tubular structure and smoothes other struc-tures out In the original work this feature gives promis-ing performance to the vessels with low contrast For asingle scale 119904 the Frangi vessel feature is given as fol-lows

1198912 (1205821 1205822 1205823 119904) =

0 1205822 gt 0 119900119903 1205823 gt 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] 119900119905ℎ119890119903119908119894119904119890 (2)

where 1205821 1205822 and 1205823 are defined in (1) The scale 119904 isalso the standard deviation for Gaussian convolution 119877119860 =|1205822||1205823| (subject to 120572) identifies plate-like structures fromtubular structures while 119877119861 = |1205821|radic|12058221205823| (subject to 120573)identifies blob-like structures from tubular structures 119878 =radic12058221 + 12058222 + 12058223 (subject to 120574) smoothes background noise outBy following the original research we set the parameters asfollows 120572 = 05 and 120573 = 05 Here 120574 is equal to half of themaximum Frobenius norm of the Hessian over all Frobeniusnorms computed on the whole image

(3) Shikata feature 1198913 [27] based on Frangi featureShikata feature assumes the cross-section of tubular structurehas 2-D Gaussian intensity distribution This assumptiongives Shikata feature the capability of detecting small vesselsThe feature 1198913 is given as follows

1198913 (997888rarr119909 1205822 119904) = 1199042 sdot 1205822119868 (997888rarr119909) (3)

where1205822 is the second eigenvalues of Hessian matrix definedin (1) and 119868(997888rarr119909) is the intensity at voxel 997888rarr119909

(4) Li feature 1198914 [28] this feature enhances the tubularstructures by using curvature analysis which gives Li featurethe potentiality to distinguish tubular structures from otherstructures This Li feature 1198914 can be described as follows

1198914 (1205821 1205822 1205823 119904)=

100381610038161003816100381612058221003816100381610038161003816 (100381610038161003816100381612058221003816100381610038161003816 minus 100381610038161003816100381612058231003816100381610038161003816)100381610038161003816100381612058211003816100381610038161003816 1205821 lt 0 1205822 lt 00 119900119905ℎ119890119903119908119894119904119890

(4)

(5) Manniesing feature 1198915 [29] focusing on backgroundnoise and small vessels this feature improves the Frangifeature by using a nonlinear anisotropic diffusion approachThis feature 1198915 can be given as follows

1198915 (1205821 1205822 1205823 119904) =

0 1205822 ge 0 119900119903 1205823 ge 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] exp(minus 21198882100381610038161003816100381612058221003816100381610038161003816 12058223) 119900119905ℎ119890119903119908119894119904119890 (5)

where 119877119860 = |1205822||1205823| is designed to identify plate-likestructures from line-like structures 119877119861 = |1205821|radic|12058221205823|has the capability to discriminate blob-like structures fromline-like structures and 119878 = radic12058221 + 12058222 + 12058223 eliminatesbackground noise By following the original research wepreset 120572 = 05 120573 = 05 in this study And 120574 is defined in(2)

By following our previous work [26] we set the vesselscale as 119904 = 06 times 2(119908minus1)2 119908 = 1 2 6 for each of the fivefeatures to cover both large and small vessels (the diameterof vessel changes from 07 mm to 60 mm) The responseof one vessel feature reaches its maximum when the scaleof the feature matches the size of local tubular structuresThe maximum response can be collected as the local vesselfeature

BioMed Research International 5

Lumen Intima Pathology Adventitia

T1 T2 T3 T4

Vi

Figure 2 One single HMM 120601 describes the state transition from inner vessel to the outside of vessel along the ray

For each voxel in the voxel series we calculate featurevalues to form feature series Let us take Sato feature forexample For the voxel series 119881119894 = V1198941 V119894119895 V119894119899we calculate the Sato feature for each voxel in 119881119894 and thenobtain a Sato feature series 1198651119894 = 11989111198941 1198911119894119895 11989111198941198991198911119894119895 is the Sato feature value corresponding to voxel V119894119895After calculating the Sato feature for all the voxel series1198811 119881119873 a subset of Sato feature series can be obtained1198651 = 11986511 1198651119894 1198651119873 By using the five proposed vesselfeatures we finally obtain five subsets of the trainingtestingsamples 119865 = 1198651 119865119896 1198655 where 119865119896 is the 119896th subsetcorresponding to the 119896th feature 119896 = 1 5 These fivesubsets are the inputs of MHMM

23 HMM-Based Recognition Model The proposed MHMMis the combination of multidimensional HMMs Beforepresenting the MHMM we would like to introduce oneindividual HMM first This HMM is trained by using one ofthe five features

HMM is considered to be the best for modeling varia-tions in observations of similar data series and for findingdissimilarities across different series One HMM (120601) can beexpressed as a five item array as 120601 = (119872119873 120587 119860 119861) where119872is the number of invisible tissue states In this paper we set thenumber of invisible tissue states as 4 to represent four tissuestates lumen (vessel) intima (vessel boundary) pathology(pathological tissue) and adventitia (outer tissue) 119873 is thenumber of observation values which are decided by the vesselfeatures We will describe this observation value later 120587119896 isthe initial state distribution 120587 = 120587119898119898 = 1 119872 Since westart detecting lumen and intima from the axis point on thecross-section the initial state distribution is 1205871 = 1 120587119895 = 0119895 = 2 119872119860 is the state transition matrix with size119872times119872And 119861 is the emission matrix with size 119873 times 119872 These twomatrixes are the key parameters of HMM whichwe are goingto estimate in the training process

The HMM 120601 describes the state transition from theinner vessel to the outside of vessel as shown in Figure 2This state transition is a visible random process which givesthe similarities between states and voxels Let us denote thefour tissue states (lumen intima pathology and adventitia)as 119879 = 1198791 1198794 As shown in Figure 2 we model thepathologies only existing outside the intima The pathologieswe target at are calcification stenosis occlusion and lowcontrast vessel Within these pathologies calcification isa main pathophysiological process in vasculature and theother pathological tissues come with it More specificallycalcification determines the location of the other pathologicaltissues [30] The location of calcification can be dividedinto superficial or deep In the calcification process deepcalcification is followed by plaque shrinkage and arterialremodeling in which a kind of internal elastic lamina coversthe calcification plaque [30] Based on this finding manyclinical trials consider deep or multiple calcifications assuperficial calcification for blood supply prediction [31]Thus we model the pathologies to be outside of the intima

Different from other algorithms (such as SVM andAdaBoost classifier) the vessel feature values cannot be theinput of HMM directly due to the computational time issueand the convergence issue in the training process [25] Forone vessel feature the feature values vary in a large area dueto different tissues Associating each feature value with a statewill cause a heavy burden for the HMM which may lead toslow convergence or nonconvergence Thus the HMM asksfor quantization of feature space into a smaller number ofdiscrete space called observation space This quantization ismore like a binning process Firstly we divide the featurespace into several bins Let us denote the bin set as 120579 =1205791 cup 1205792 cup 120579119870 Then we associate feature values with bins Ifa feature value 119886 falls into a bin 120579119896 119886 isin 120579119896 this feature 119886 canbe associated with 120579119896 By associating feature values with binswe can turn the feature series into a bin series which is theobservation series for HMM

6 BioMed Research International

Lumen Pathology Adventitia

Intima

Alumen

Aintima

Apathology

Voxel(a) (b)

f170

60

50

40

30

20

10

0

minus100 2 4 6 8 10 12 14 16 18

Figure 3The distribution of Sato feature values in one feature series (a)The feature series collected along one rayThe black points indicatethe voxels we collect along the ray (b) The distribution of Sato feature values It can be observed that area 119860119901119886119905ℎ119900119897119900119892119910 overlaps 119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886

Table 1 Segment method

Interval [0 1198861) [1198861 1198862) [1198862 1198863) [1198863 +infin)Dividing method One bin Average Average One binNumber of bins 1 1198701 1198702 1

Table 2 Overlapping areas for different features

[1198861 1198862) [1198862 1198863)Sato feature 1198911 [25 35) [35 50)Frangi feature 1198912 [15 20) [20 30)Shikata feature 1198913 [85 95) [95 120)Li feature 1198914 [40 45) [45 55)Manniesing feature 1198915 [15 25) [25 45)

The method of dividing bins is the key for HMM In ourexperiment we found that the capability of HMM correlateswith the number of binsMore specifically the number of binsdetermines the capability of HMM in identifying differenttissues in one given area of the feature space The largerthe number of bins is the more powerful the HMM isHere we take the Sato feature for example to demonstratethe method we use in dividing bins Firstly we look intothe distribution of feature values along the ray (Figure 3(a))Let us denote the distributions of lumen intima pathologyand adventitia as 119860 119897119906119898119890119899 119860 119894119899119905119894119898119886 119860119901119886119905ℎ119900119897119900119892119910 and 119860119886119889V119890119899119905119894119905119894119886respectively And the distributions of different tissues alongthe ray are shown in Figure 3(b) It can be easily observedthat the distribution of pathology (119860119901119886119905ℎ119900119897119900119892119910) overlaps thedistributions of lumen (119860 119897119906119898119890119899) and intima (119860 119894119899119905119894119898119886) Sincewe target delineating the vessel boundary (intima) accuratelywith the presence of pathologies we want the HMM to bepowerful in these two areas (119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886) Assume that119860119901119886119905ℎ119900119897119900119892119910 overlaps119860 119894119899119905119894119898119886 and119860 119897119906119898119890119899 in intervals [1198861 1198862) and

[1198862 1198863) respectively We give more bins to the overlappingintervals to make the HMM more powerful in these areasThe dividing method we use here is shown in Table 1 In thiswork we set 1198701 and 1198702 as1198701 = 51198702 = 3 for all the featuresThe five features we use in this work have different ranges ofoverlapping areas which are shown in Table 2 Please noticethat the number of bins should not be large due to theconvergence issue The computation time will be discussedin Section 4

After turning the feature series into observation seriesthe HMM 120601 = (119872119873 120587 119860 119861) can be trained by usingBaum-Welch algorithm [32] The initialization conditionused for HMM training can be summarized as follows

(1) the number of invisible states119872 = 4(2) the number of observation values119873 = 10(3) the initial state distribution 1205871 = 1 and 120587119895 = 0 119895 =2 4

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

4 BioMed Research International

we introduce the multiscale vessel-specific features employedin this paper

(1) Sato feature (1198911) [5] this feature is designed for healthyvessel with bright tubular structure in a dark environmentFor one scale 119904 the Sato vessel feature 1198911 can be described asfollows

1198911 (1205821 1205822 119904)

=

1205822 sdot exp(minus 120582212 (12057211205822)2) 1205821 le 0 1205822 = 01205822 sdot exp(minus 120582212 (12057221205822)2) 1205821 gt 0 1205822 = 00 1205822 = 0

(1)

where 1205821 1205822 and 1205823 are the eigenvalues of Hessian matrixsubject to 1205821 gt 1205822 gt 1205823 [5] These eigenvalues are calculatedby using Gaussian convolution and the scale 119904 is the standarddeviation for Gaussian convolution 1205721 and 1205722 are two presetparameters 1205721 lt 1205722 In this work 1205721 and 1205722 were fixed to 05and 2 respectively

(2) Frangi feature 1198912 [14] this feature promotes theenhancement of tubular structure and smoothes other struc-tures out In the original work this feature gives promis-ing performance to the vessels with low contrast For asingle scale 119904 the Frangi vessel feature is given as fol-lows

1198912 (1205821 1205822 1205823 119904) =

0 1205822 gt 0 119900119903 1205823 gt 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] 119900119905ℎ119890119903119908119894119904119890 (2)

where 1205821 1205822 and 1205823 are defined in (1) The scale 119904 isalso the standard deviation for Gaussian convolution 119877119860 =|1205822||1205823| (subject to 120572) identifies plate-like structures fromtubular structures while 119877119861 = |1205821|radic|12058221205823| (subject to 120573)identifies blob-like structures from tubular structures 119878 =radic12058221 + 12058222 + 12058223 (subject to 120574) smoothes background noise outBy following the original research we set the parameters asfollows 120572 = 05 and 120573 = 05 Here 120574 is equal to half of themaximum Frobenius norm of the Hessian over all Frobeniusnorms computed on the whole image

(3) Shikata feature 1198913 [27] based on Frangi featureShikata feature assumes the cross-section of tubular structurehas 2-D Gaussian intensity distribution This assumptiongives Shikata feature the capability of detecting small vesselsThe feature 1198913 is given as follows

1198913 (997888rarr119909 1205822 119904) = 1199042 sdot 1205822119868 (997888rarr119909) (3)

where1205822 is the second eigenvalues of Hessian matrix definedin (1) and 119868(997888rarr119909) is the intensity at voxel 997888rarr119909

(4) Li feature 1198914 [28] this feature enhances the tubularstructures by using curvature analysis which gives Li featurethe potentiality to distinguish tubular structures from otherstructures This Li feature 1198914 can be described as follows

1198914 (1205821 1205822 1205823 119904)=

100381610038161003816100381612058221003816100381610038161003816 (100381610038161003816100381612058221003816100381610038161003816 minus 100381610038161003816100381612058231003816100381610038161003816)100381610038161003816100381612058211003816100381610038161003816 1205821 lt 0 1205822 lt 00 119900119905ℎ119890119903119908119894119904119890

(4)

(5) Manniesing feature 1198915 [29] focusing on backgroundnoise and small vessels this feature improves the Frangifeature by using a nonlinear anisotropic diffusion approachThis feature 1198915 can be given as follows

1198915 (1205821 1205822 1205823 119904) =

0 1205822 ge 0 119900119903 1205823 ge 0[1 minus exp(minus 119877211986021205722)] sdot exp(minus

119877211986121205732) sdot [1 minus exp(minus 119878221205742)] exp(minus 21198882100381610038161003816100381612058221003816100381610038161003816 12058223) 119900119905ℎ119890119903119908119894119904119890 (5)

where 119877119860 = |1205822||1205823| is designed to identify plate-likestructures from line-like structures 119877119861 = |1205821|radic|12058221205823|has the capability to discriminate blob-like structures fromline-like structures and 119878 = radic12058221 + 12058222 + 12058223 eliminatesbackground noise By following the original research wepreset 120572 = 05 120573 = 05 in this study And 120574 is defined in(2)

By following our previous work [26] we set the vesselscale as 119904 = 06 times 2(119908minus1)2 119908 = 1 2 6 for each of the fivefeatures to cover both large and small vessels (the diameterof vessel changes from 07 mm to 60 mm) The responseof one vessel feature reaches its maximum when the scaleof the feature matches the size of local tubular structuresThe maximum response can be collected as the local vesselfeature

BioMed Research International 5

Lumen Intima Pathology Adventitia

T1 T2 T3 T4

Vi

Figure 2 One single HMM 120601 describes the state transition from inner vessel to the outside of vessel along the ray

For each voxel in the voxel series we calculate featurevalues to form feature series Let us take Sato feature forexample For the voxel series 119881119894 = V1198941 V119894119895 V119894119899we calculate the Sato feature for each voxel in 119881119894 and thenobtain a Sato feature series 1198651119894 = 11989111198941 1198911119894119895 11989111198941198991198911119894119895 is the Sato feature value corresponding to voxel V119894119895After calculating the Sato feature for all the voxel series1198811 119881119873 a subset of Sato feature series can be obtained1198651 = 11986511 1198651119894 1198651119873 By using the five proposed vesselfeatures we finally obtain five subsets of the trainingtestingsamples 119865 = 1198651 119865119896 1198655 where 119865119896 is the 119896th subsetcorresponding to the 119896th feature 119896 = 1 5 These fivesubsets are the inputs of MHMM

23 HMM-Based Recognition Model The proposed MHMMis the combination of multidimensional HMMs Beforepresenting the MHMM we would like to introduce oneindividual HMM first This HMM is trained by using one ofthe five features

HMM is considered to be the best for modeling varia-tions in observations of similar data series and for findingdissimilarities across different series One HMM (120601) can beexpressed as a five item array as 120601 = (119872119873 120587 119860 119861) where119872is the number of invisible tissue states In this paper we set thenumber of invisible tissue states as 4 to represent four tissuestates lumen (vessel) intima (vessel boundary) pathology(pathological tissue) and adventitia (outer tissue) 119873 is thenumber of observation values which are decided by the vesselfeatures We will describe this observation value later 120587119896 isthe initial state distribution 120587 = 120587119898119898 = 1 119872 Since westart detecting lumen and intima from the axis point on thecross-section the initial state distribution is 1205871 = 1 120587119895 = 0119895 = 2 119872119860 is the state transition matrix with size119872times119872And 119861 is the emission matrix with size 119873 times 119872 These twomatrixes are the key parameters of HMM whichwe are goingto estimate in the training process

The HMM 120601 describes the state transition from theinner vessel to the outside of vessel as shown in Figure 2This state transition is a visible random process which givesthe similarities between states and voxels Let us denote thefour tissue states (lumen intima pathology and adventitia)as 119879 = 1198791 1198794 As shown in Figure 2 we model thepathologies only existing outside the intima The pathologieswe target at are calcification stenosis occlusion and lowcontrast vessel Within these pathologies calcification isa main pathophysiological process in vasculature and theother pathological tissues come with it More specificallycalcification determines the location of the other pathologicaltissues [30] The location of calcification can be dividedinto superficial or deep In the calcification process deepcalcification is followed by plaque shrinkage and arterialremodeling in which a kind of internal elastic lamina coversthe calcification plaque [30] Based on this finding manyclinical trials consider deep or multiple calcifications assuperficial calcification for blood supply prediction [31]Thus we model the pathologies to be outside of the intima

Different from other algorithms (such as SVM andAdaBoost classifier) the vessel feature values cannot be theinput of HMM directly due to the computational time issueand the convergence issue in the training process [25] Forone vessel feature the feature values vary in a large area dueto different tissues Associating each feature value with a statewill cause a heavy burden for the HMM which may lead toslow convergence or nonconvergence Thus the HMM asksfor quantization of feature space into a smaller number ofdiscrete space called observation space This quantization ismore like a binning process Firstly we divide the featurespace into several bins Let us denote the bin set as 120579 =1205791 cup 1205792 cup 120579119870 Then we associate feature values with bins Ifa feature value 119886 falls into a bin 120579119896 119886 isin 120579119896 this feature 119886 canbe associated with 120579119896 By associating feature values with binswe can turn the feature series into a bin series which is theobservation series for HMM

6 BioMed Research International

Lumen Pathology Adventitia

Intima

Alumen

Aintima

Apathology

Voxel(a) (b)

f170

60

50

40

30

20

10

0

minus100 2 4 6 8 10 12 14 16 18

Figure 3The distribution of Sato feature values in one feature series (a)The feature series collected along one rayThe black points indicatethe voxels we collect along the ray (b) The distribution of Sato feature values It can be observed that area 119860119901119886119905ℎ119900119897119900119892119910 overlaps 119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886

Table 1 Segment method

Interval [0 1198861) [1198861 1198862) [1198862 1198863) [1198863 +infin)Dividing method One bin Average Average One binNumber of bins 1 1198701 1198702 1

Table 2 Overlapping areas for different features

[1198861 1198862) [1198862 1198863)Sato feature 1198911 [25 35) [35 50)Frangi feature 1198912 [15 20) [20 30)Shikata feature 1198913 [85 95) [95 120)Li feature 1198914 [40 45) [45 55)Manniesing feature 1198915 [15 25) [25 45)

The method of dividing bins is the key for HMM In ourexperiment we found that the capability of HMM correlateswith the number of binsMore specifically the number of binsdetermines the capability of HMM in identifying differenttissues in one given area of the feature space The largerthe number of bins is the more powerful the HMM isHere we take the Sato feature for example to demonstratethe method we use in dividing bins Firstly we look intothe distribution of feature values along the ray (Figure 3(a))Let us denote the distributions of lumen intima pathologyand adventitia as 119860 119897119906119898119890119899 119860 119894119899119905119894119898119886 119860119901119886119905ℎ119900119897119900119892119910 and 119860119886119889V119890119899119905119894119905119894119886respectively And the distributions of different tissues alongthe ray are shown in Figure 3(b) It can be easily observedthat the distribution of pathology (119860119901119886119905ℎ119900119897119900119892119910) overlaps thedistributions of lumen (119860 119897119906119898119890119899) and intima (119860 119894119899119905119894119898119886) Sincewe target delineating the vessel boundary (intima) accuratelywith the presence of pathologies we want the HMM to bepowerful in these two areas (119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886) Assume that119860119901119886119905ℎ119900119897119900119892119910 overlaps119860 119894119899119905119894119898119886 and119860 119897119906119898119890119899 in intervals [1198861 1198862) and

[1198862 1198863) respectively We give more bins to the overlappingintervals to make the HMM more powerful in these areasThe dividing method we use here is shown in Table 1 In thiswork we set 1198701 and 1198702 as1198701 = 51198702 = 3 for all the featuresThe five features we use in this work have different ranges ofoverlapping areas which are shown in Table 2 Please noticethat the number of bins should not be large due to theconvergence issue The computation time will be discussedin Section 4

After turning the feature series into observation seriesthe HMM 120601 = (119872119873 120587 119860 119861) can be trained by usingBaum-Welch algorithm [32] The initialization conditionused for HMM training can be summarized as follows

(1) the number of invisible states119872 = 4(2) the number of observation values119873 = 10(3) the initial state distribution 1205871 = 1 and 120587119895 = 0 119895 =2 4

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 5

Lumen Intima Pathology Adventitia

T1 T2 T3 T4

Vi

Figure 2 One single HMM 120601 describes the state transition from inner vessel to the outside of vessel along the ray

For each voxel in the voxel series we calculate featurevalues to form feature series Let us take Sato feature forexample For the voxel series 119881119894 = V1198941 V119894119895 V119894119899we calculate the Sato feature for each voxel in 119881119894 and thenobtain a Sato feature series 1198651119894 = 11989111198941 1198911119894119895 11989111198941198991198911119894119895 is the Sato feature value corresponding to voxel V119894119895After calculating the Sato feature for all the voxel series1198811 119881119873 a subset of Sato feature series can be obtained1198651 = 11986511 1198651119894 1198651119873 By using the five proposed vesselfeatures we finally obtain five subsets of the trainingtestingsamples 119865 = 1198651 119865119896 1198655 where 119865119896 is the 119896th subsetcorresponding to the 119896th feature 119896 = 1 5 These fivesubsets are the inputs of MHMM

23 HMM-Based Recognition Model The proposed MHMMis the combination of multidimensional HMMs Beforepresenting the MHMM we would like to introduce oneindividual HMM first This HMM is trained by using one ofthe five features

HMM is considered to be the best for modeling varia-tions in observations of similar data series and for findingdissimilarities across different series One HMM (120601) can beexpressed as a five item array as 120601 = (119872119873 120587 119860 119861) where119872is the number of invisible tissue states In this paper we set thenumber of invisible tissue states as 4 to represent four tissuestates lumen (vessel) intima (vessel boundary) pathology(pathological tissue) and adventitia (outer tissue) 119873 is thenumber of observation values which are decided by the vesselfeatures We will describe this observation value later 120587119896 isthe initial state distribution 120587 = 120587119898119898 = 1 119872 Since westart detecting lumen and intima from the axis point on thecross-section the initial state distribution is 1205871 = 1 120587119895 = 0119895 = 2 119872119860 is the state transition matrix with size119872times119872And 119861 is the emission matrix with size 119873 times 119872 These twomatrixes are the key parameters of HMM whichwe are goingto estimate in the training process

The HMM 120601 describes the state transition from theinner vessel to the outside of vessel as shown in Figure 2This state transition is a visible random process which givesthe similarities between states and voxels Let us denote thefour tissue states (lumen intima pathology and adventitia)as 119879 = 1198791 1198794 As shown in Figure 2 we model thepathologies only existing outside the intima The pathologieswe target at are calcification stenosis occlusion and lowcontrast vessel Within these pathologies calcification isa main pathophysiological process in vasculature and theother pathological tissues come with it More specificallycalcification determines the location of the other pathologicaltissues [30] The location of calcification can be dividedinto superficial or deep In the calcification process deepcalcification is followed by plaque shrinkage and arterialremodeling in which a kind of internal elastic lamina coversthe calcification plaque [30] Based on this finding manyclinical trials consider deep or multiple calcifications assuperficial calcification for blood supply prediction [31]Thus we model the pathologies to be outside of the intima

Different from other algorithms (such as SVM andAdaBoost classifier) the vessel feature values cannot be theinput of HMM directly due to the computational time issueand the convergence issue in the training process [25] Forone vessel feature the feature values vary in a large area dueto different tissues Associating each feature value with a statewill cause a heavy burden for the HMM which may lead toslow convergence or nonconvergence Thus the HMM asksfor quantization of feature space into a smaller number ofdiscrete space called observation space This quantization ismore like a binning process Firstly we divide the featurespace into several bins Let us denote the bin set as 120579 =1205791 cup 1205792 cup 120579119870 Then we associate feature values with bins Ifa feature value 119886 falls into a bin 120579119896 119886 isin 120579119896 this feature 119886 canbe associated with 120579119896 By associating feature values with binswe can turn the feature series into a bin series which is theobservation series for HMM

6 BioMed Research International

Lumen Pathology Adventitia

Intima

Alumen

Aintima

Apathology

Voxel(a) (b)

f170

60

50

40

30

20

10

0

minus100 2 4 6 8 10 12 14 16 18

Figure 3The distribution of Sato feature values in one feature series (a)The feature series collected along one rayThe black points indicatethe voxels we collect along the ray (b) The distribution of Sato feature values It can be observed that area 119860119901119886119905ℎ119900119897119900119892119910 overlaps 119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886

Table 1 Segment method

Interval [0 1198861) [1198861 1198862) [1198862 1198863) [1198863 +infin)Dividing method One bin Average Average One binNumber of bins 1 1198701 1198702 1

Table 2 Overlapping areas for different features

[1198861 1198862) [1198862 1198863)Sato feature 1198911 [25 35) [35 50)Frangi feature 1198912 [15 20) [20 30)Shikata feature 1198913 [85 95) [95 120)Li feature 1198914 [40 45) [45 55)Manniesing feature 1198915 [15 25) [25 45)

The method of dividing bins is the key for HMM In ourexperiment we found that the capability of HMM correlateswith the number of binsMore specifically the number of binsdetermines the capability of HMM in identifying differenttissues in one given area of the feature space The largerthe number of bins is the more powerful the HMM isHere we take the Sato feature for example to demonstratethe method we use in dividing bins Firstly we look intothe distribution of feature values along the ray (Figure 3(a))Let us denote the distributions of lumen intima pathologyand adventitia as 119860 119897119906119898119890119899 119860 119894119899119905119894119898119886 119860119901119886119905ℎ119900119897119900119892119910 and 119860119886119889V119890119899119905119894119905119894119886respectively And the distributions of different tissues alongthe ray are shown in Figure 3(b) It can be easily observedthat the distribution of pathology (119860119901119886119905ℎ119900119897119900119892119910) overlaps thedistributions of lumen (119860 119897119906119898119890119899) and intima (119860 119894119899119905119894119898119886) Sincewe target delineating the vessel boundary (intima) accuratelywith the presence of pathologies we want the HMM to bepowerful in these two areas (119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886) Assume that119860119901119886119905ℎ119900119897119900119892119910 overlaps119860 119894119899119905119894119898119886 and119860 119897119906119898119890119899 in intervals [1198861 1198862) and

[1198862 1198863) respectively We give more bins to the overlappingintervals to make the HMM more powerful in these areasThe dividing method we use here is shown in Table 1 In thiswork we set 1198701 and 1198702 as1198701 = 51198702 = 3 for all the featuresThe five features we use in this work have different ranges ofoverlapping areas which are shown in Table 2 Please noticethat the number of bins should not be large due to theconvergence issue The computation time will be discussedin Section 4

After turning the feature series into observation seriesthe HMM 120601 = (119872119873 120587 119860 119861) can be trained by usingBaum-Welch algorithm [32] The initialization conditionused for HMM training can be summarized as follows

(1) the number of invisible states119872 = 4(2) the number of observation values119873 = 10(3) the initial state distribution 1205871 = 1 and 120587119895 = 0 119895 =2 4

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

6 BioMed Research International

Lumen Pathology Adventitia

Intima

Alumen

Aintima

Apathology

Voxel(a) (b)

f170

60

50

40

30

20

10

0

minus100 2 4 6 8 10 12 14 16 18

Figure 3The distribution of Sato feature values in one feature series (a)The feature series collected along one rayThe black points indicatethe voxels we collect along the ray (b) The distribution of Sato feature values It can be observed that area 119860119901119886119905ℎ119900119897119900119892119910 overlaps 119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886

Table 1 Segment method

Interval [0 1198861) [1198861 1198862) [1198862 1198863) [1198863 +infin)Dividing method One bin Average Average One binNumber of bins 1 1198701 1198702 1

Table 2 Overlapping areas for different features

[1198861 1198862) [1198862 1198863)Sato feature 1198911 [25 35) [35 50)Frangi feature 1198912 [15 20) [20 30)Shikata feature 1198913 [85 95) [95 120)Li feature 1198914 [40 45) [45 55)Manniesing feature 1198915 [15 25) [25 45)

The method of dividing bins is the key for HMM In ourexperiment we found that the capability of HMM correlateswith the number of binsMore specifically the number of binsdetermines the capability of HMM in identifying differenttissues in one given area of the feature space The largerthe number of bins is the more powerful the HMM isHere we take the Sato feature for example to demonstratethe method we use in dividing bins Firstly we look intothe distribution of feature values along the ray (Figure 3(a))Let us denote the distributions of lumen intima pathologyand adventitia as 119860 119897119906119898119890119899 119860 119894119899119905119894119898119886 119860119901119886119905ℎ119900119897119900119892119910 and 119860119886119889V119890119899119905119894119905119894119886respectively And the distributions of different tissues alongthe ray are shown in Figure 3(b) It can be easily observedthat the distribution of pathology (119860119901119886119905ℎ119900119897119900119892119910) overlaps thedistributions of lumen (119860 119897119906119898119890119899) and intima (119860 119894119899119905119894119898119886) Sincewe target delineating the vessel boundary (intima) accuratelywith the presence of pathologies we want the HMM to bepowerful in these two areas (119860 119897119906119898119890119899 and119860 119894119899119905119894119898119886) Assume that119860119901119886119905ℎ119900119897119900119892119910 overlaps119860 119894119899119905119894119898119886 and119860 119897119906119898119890119899 in intervals [1198861 1198862) and

[1198862 1198863) respectively We give more bins to the overlappingintervals to make the HMM more powerful in these areasThe dividing method we use here is shown in Table 1 In thiswork we set 1198701 and 1198702 as1198701 = 51198702 = 3 for all the featuresThe five features we use in this work have different ranges ofoverlapping areas which are shown in Table 2 Please noticethat the number of bins should not be large due to theconvergence issue The computation time will be discussedin Section 4

After turning the feature series into observation seriesthe HMM 120601 = (119872119873 120587 119860 119861) can be trained by usingBaum-Welch algorithm [32] The initialization conditionused for HMM training can be summarized as follows

(1) the number of invisible states119872 = 4(2) the number of observation values119873 = 10(3) the initial state distribution 1205871 = 1 and 120587119895 = 0 119895 =2 4

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 7

Table 3 A similarity map for one voxel series The maximums of the similarities are shown in bold

1198791 1198792 1198793 1198794 StateV1198941 0943 0055 0002 0 1198791V1198942 0901 0098 0001 0 1198791V1198943 0842 0153 0004 0001 1198791V1198944 0801 0195 0002 0002 1198791V1198945 0744 0254 0001 0001 1198791V1198946 0706 0290 0002 0002 1198791V1198947 0301 0593 0101 0005 1198792V1198948 0001 0643 0151 0205 1198792V1198949 0007 0301 0572 0120 1198793V11989410 0001 0165 0732 0102 1198793V11989411 0002 0044 0812 0142 1198793V11989412 0001 0020 0509 0470 1198793V11989413 0001 0006 0401 0592 1198794V11989414 0002 0002 0303 0693 1198794V11989415 0001 0001 0265 0733 1198794V11989416 0001 0002 0115 0882 1198794V11989417 0 0001 0109 0890 1198794V11989418 0 0 0043 0957 1198794

MHMM

HMM 1 HMM 5

F1F5

Figure 4 The Multiple Hidden Markov Model (MHMM) Φ istrained by five subsets 1198651 1198655 These subsets 1198651 1198655correspond to the five proposed vessel features 1198911 1198915 Eachsubset trains a Hidden Markov Model (HMM) And the MHMM isthe combination of the five trained HMMs

(4) the state transition matrix 119860 uniform distribution byusing general principle [25]

(5) the emission matrix 119861 uniform distribution by usinggeneral principle [25]

24 Multiple Hidden Markov Model Inspired by redundantinformation (multiple vessel features) [26] and good statis-tical properties (HMM random process) we formulate theproblem of vessel segmentation as the joint segmentationof multidimensional HMMs Since we target accurate vesselsegmentation with the presence of pathologies coveringthe widest possible spectrum of challenging situations isthe key We try to combine multidimensional HMMs byusing multiple vessel features as shown in Figure 4 Thecombination of multidimensional HMMs is the Multiple

Hidden Markov Model (MHMM) Φ which can be given asfollows

Φ = 5sum119896=1

120572119896120601119896 (6)

where120601119896 is oneHMMtrained by using the training subset119865119896119896 = 1 5 120572119896 119896 = 1 5 are nonnegative terms whichgive the relative strengths of the respective HMMs Thesenonnegative terms are calculated in the training processwhich we will describe later

In the detecting (testing) process after the testing voxelseries1198811015840 = 11988110158401 119881101584072 (the rays space every 5∘) are collectedon the cross-section feature series 1198651015840 = 11986511015840 11986551015840 canbe calculated for the voxel series by using the five proposedvessel featuresWith the feature series1198651015840 the trainedMHMMΦ can detect vessel boundary (intima) on this cross-sectionby calculating the posterior probability 119875(119879 | Φ 1198651015840) where119879 = 1198791 1198794 are the four tissue states 119875(119879 | Φ 1198651015840) is asimilarity map between the four tissue states and the voxelsin the testing voxel series which is defined as follows

119875 (119879 | Φ 1198651015840) = 5sum119896=1

120572119896119875(119879 | 120601119896 1198651198961015840) (7)

where119875(119879 | 120601119896 1198651198961015840) is the similaritymap estimated by the 119896thHMM These similarity maps are calculated by the forward-backward procedures [32] in the same way as for traininga HMM A similarity map for one voxel series calculatedby 119875(119879 | 1206011 11986511015840 ) is shown in Table 3 for example As themaximums of the similarities are shown in bold the statetransition from the axis point to the outside of vessel can beeasily obtained

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

8 BioMed Research International

For each testing voxel series we can obtain a state series1198791015840 by using maximum likelihood estimation as follows

1198791015840 = argmax119879=1198791 1198794

119875 (119879 | Φ 1198651015840) (8)

Based on the state series 1198791015840 (label series) the lumen(vessel) and intima (vessel boundary) can be segmented onthe cross-section along the rays Then along the vessel axeswe can obtain the whole vessel segmentation Since we collectvoxel series along the rays every 5∘ for training and testinga given voxel can appear in multiple series and then getsdifferent labels fromdifferent series potentially Tohandle thismultiple labels issue mean similarity values of the four statesare calculated for one given voxel and the state (label) withmaximum value will be signed to this voxel In our work weobserve a few voxels have equal values in the lumen state andthe intima state Since we consider voxels in these two statesas vessel finally it does not affect the final segmentation result

As we described in Section 23 multidimensional HMMsare trained separately For feature 119891119896 (training subset 119865119896) theHMM (120601119896) can be trained by adjusting the parameters of 120601119896to get the local maximum of the posterior probability 119875(119879 |120601119896 119865119896) by using the Baum-Welch algorithm [32] Then thetrained HMM (120601119896) can describe the state transition from theinner vessel to the outside of vessel with the similarity mapAnd the training precision of this HMM can be estimatedby calculating 119875119903119890119888119894119904119894119900119899119896 = 119879119875(119879119875 + 119865119875) where 119879119875is the true positive representing the number of positivesamples detected as positive samples 119865119875 is the false positiverepresenting the number of negative samples detected aspositive samples After all the five HMMs have been trainedthe nonnegative term 120572119896 for HMM 120601119896 can be defined as 120572119896 =119875119903119890119888119894119904119894119900119899119896sum5119908=1 119875119903119890119888119894119904119894119900119899119908 Finally their combination (Eq(6)) the proposed MHMM can be obtained

3 Results

In order to evaluate the performance of the proposedMHMMwe test it in two challenging cases (1) synthetic vas-cular experiment with different levels of Gaussian noise (2)abdominal artery segmentation with the presence of patholo-gies Moreover we compare ourmethod with twomethods toillustrate the capability of our method in delineating accuratevessel boundary with the presence of pathologies

31 Two Methods for Comparison The two chosen methodsare state-of-the-art methods a vessel tractography methodproposed by Cetin [33] and a learning-based regressionmethod introduced by Schaap [12] The vessel tractographymethod (Cetinrsquos method) is a vessel axis-based methodwhich combines a vessel tensor with a vessel axis tracingmethod This vessel tensor is the key for Cetinrsquos methodwhichmodels the vessel as a cylinder And the learning-basedregression method (Schaaprsquos method) can learn the geometryand the appearance of the vessels from annotated dataNotably these two methods target at geometrical featuresof vessel Since the pathologies do not have an explicitlygeometrical feature we believe that these two methods have

the capability to identify vessels from pathologies That isthe reason we choose these two state-of-the-art methodsfor comparison We implemented these two algorithms our-selves with changes needed to utilize our clinical datasets byfollowing the original researches

Cetinrsquos method and Schaaprsquos method ask a single seedpoint and an approximate centerline for initializationsrespectively With the vessel axis extracted by using ourprevious method we set the start point of the vessel axis asthe seed point for Cetinrsquos method and set the vessel axis asthe approximate centerline for Schaaprsquos method

Although Cetinrsquos method is an unsupervised clusteringmethod some key parameters are estimated by using thetraining samples as follows the calcium threshold 119905119888119886119897119888 =1500 the height of the cylinder ℎ = 4119903 the number ofdirections for tensor fitting 119898 = 24 the number of directionsfor branch detection 119873 = 256 the initial radius range[07 6] the termination ratios 1205730 = 02 and 1205731 = 09 andthe angle parameters 1198601 = 51205873 and 1198602 = 1205879

For the implementation of Schaaprsquos method severalparameters are optimized by following the original optimiza-tion sequence [12] the calcium removal parameters 120575119911 = 20120575119894 = 300 and 119888 = 250 the radius of the region of interest 25voxels the expected error of the119870-nearest neighbors (KNN)estimate 120575119896119899119899 = 025 the number of shape parameters119872 =12 the number of principal components 119875 = 32 and thenumber of neighbors119870 = 16 The remaining parameters theregression matrix 119877119877 and the shape parameters 120573lowast119909 can betrained by using our training samples

32 Evaluation Metrics and Statistical Tests In order topresent the comparison results between the proposedMHMM and the two state-of-the-art methods quantitativeanalysis is employed to quantify the performance of thesethree methods by calculating the value of overlap and accu-racy Here the manual reference segmentations (Section 21)are used as ground truth Two volume and surface basedmetrics are borrowed from literatures Dice Overlap Coeffi-cient (DOC) [34] and Average symmetric Surface Distance(ASD) [35] The values of DOC and ASD are calculated bycomparing the segmented vessels with the manual referencesegmentations (ground truth) For DOC (ASD) the larger(smaller) the value is the better the segmentation result isAnd the DOC (ASD) is given in percent (millimeters)

In order to acquire obvious results in comparison weemploy the paired 119879-test which can assess the differences insegmentation accuracy between the MHMM and the othertwo methods The significant differences in comparison aremarked with symbol lowast And the differences with a level set at119901 lt 005 will be considered to be statistically significant

33 Synthetic Vascular Datasets The synthetic vascular data-sets we use here are released by Hamarneh and Jassi [36]in March 2013 which contain 120 datasets Since the vas-cular trees in the synthetic vascular datasets are simulatedthey can be used as ground truth segmentations As wediscussed previously the ground truth segmentations of realclinical datasets do not exist which makes the comparisonon synthetic vascular datasets valuable Furthermore we

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 9

Figure 5 Synthetic vessel tree example before (left) and after (right)adding Gaussian noise

simulate the challenging case the vessel boundary obscuredby pathologies by adding different levels of Gaussian noiseFigure 5 shows the synthetic vessel tree example before andafter adding Gaussian noise

All the 120 datasets available online are used in our syn-thetic validation experiments Gaussian noise with differentlevels 1205902119899119900119894119904119890 = 20 1205902119899119900119894119904119890 = 40 1205902119899119900119894119904119890 = 60 and 1205902119899119900119894119904119890 = 80is added to the datasets to form the training datasets (240datasets) and the testing datasets (240 datasets) 1205902119899119900119894119904119890 = 20and 1205902119899119900119894119904119890 = 40 are used to simulate the normal noise levelsin CT scans [37] And 1205902119899119900119894119904119890 = 60 is for the low dose scans[37] To our knowledge noise level changes with body sizeand higher noise level can be found in larger body size [38]Based on this finding 1205902119899119900119894119904119890 = 80 is added to the syntheticdatasets to simulate the real challenging case (low dose scanswith large body size) The three methods are tested on thetesting datasets The comparison results are summarized inFigure 6

Let us focus on the DOC results first As we can easilyobserve the three methods yield similar results with thepresence of low levels of noise (1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 40)They all produce a high average DOC as high as 9291 plusmn798 When the level of noise comes to 1205902119899119900119894119904119890 = 60 theaverage DOC of Cetinrsquos method and Schaaprsquos method goesdown dramatically to 8528 plusmn 649 and 8401 plusmn 744respectively With the highest level of noise the situationsfor these two methods become even worse However theperformance of our method maintains relatively stable withthe four levels of noise Our method yields a high averageDOC of 9237 plusmn 694 9222 plusmn 435 9006 plusmn 607 and8508 plusmn 766

Then we present the comparison results by using ASDAn average ASD of 046 plusmn 051mm 122 plusmn 033mm 185 plusmn086mm and 253 plusmn 141mm is obtained by the Cetinrsquosmethod These values are changed to 049 plusmn 042mm 094 plusmn053mm 174 plusmn 079mm and 252 plusmn 157mm by the Schaaprsquosmethod and the values are improved to 044 plusmn 036mm091 plusmn 043mm 136 plusmn 052mm and 159 plusmn 087mm by ourmethod

The results summarized in Figure 6 demonstrate thatthe MHMM can delineate vessel boundary accurately whenthe boundary is blurred by high level of noise Moreoverthe MHMM is more resistant to Gaussian noise compared

MHMM

MHMM

Cetinrsquos

Schaaprsquos

Schaaprsquos

Cetinrsquos

9237plusmn694 9222plusmn435 9006plusmn607 8508plusmn766

044plusmn036 091plusmn043 136plusmn052 159plusmn087

9291plusmn798 9147plusmn543

9237plusmn721 9110plusmn447

049plusmn042 094plusmn053

046plusmn051 122plusmn033

DOC()

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

60 8020 40

ASD(mm)

8528plusmn649lowast

8401plusmn744lowast

185plusmn086lowast

174plusmn079lowast

6982plusmn849lowast

7326plusmn835lowast

253plusmn141lowast

252plusmn157lowast

100

90

80

70

60

50

40

Dic

e Ove

rlap

Coe

ffici

ent (

)

2noise

Figure 6 Summary of comparison evaluation on the testingdatasets (240 synthetic vascular volumes) Dice overlap coefficients(DOC) using the three methods are plotted The averages of DOCand average ASD as well as the statistical significance are shownin the following table where the best results are presented in boldand lowast indicates the statistically significant differences between ourmethod (MHMM) and the other twomethods at a significance levelof 005

to Cetinrsquos method and Schaaprsquos method The differences ofDOC and ASD between our method and the other two arestatistically significant (119901 lt 005) with high levels of noisewhich are denoted by the symbol lowast

Figure 7 shows the 3-D views of segmentation resultson two randomly selected synthetic vascular trees with theGaussian noise of 1205902119899119900119894119904119890 = 20 and 1205902119899119900119894119904119890 = 80 It can be easilyobserved that the segmentations obtained by our method aremore accurate than those of Cetinrsquos and Schaaprsquos methods

34 Abdominal Artery Datasets Recently there has been atrend towards minimally invasive surgery in the treatment ofabdominal artery disease which means less pain a shorterhospital stay and fewer complications This minimally inva-sive surgery asks for accurate segmentation of abdominalartery which can help the surgeon operate with precisionflexibility and control However the extensive vessel cal-cification in abdominal artery disease obscures the vesselboundary (see Figure 8 for a snapshot) and makes it reallychallenging to segment vessel accurately Thus we collectedour abdominal artery datasets from patients with knownabdominal artery diseases We obtained 50 abdominal CTimages (120 kV 40 mAs) by using a Philips Brilliance 64

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

10 BioMed Research International

Figure 7 The comparison results on two randomly selected synthetic vascular trees with the presence of two levels of Gaussian noises1205902119899119900119894119904119890 = 20 (top) and1205902119899119900119894119904119890 = 80 (bottom) respectivelyThefirst column the second column and the third column showCetinrsquos segmentationsSchaaprsquos segmentations and the segmentations of our method respectively The overlapping voxels between one of the three computationalmethods and the corresponding ground truth are shown in gray while the voxels detected by the computational methods but do not belongto the ground truth are shown in red

Figure 8 Several challenging cases in abdominal vessel segmentation caused by extensive vessel calcification Arrows indicate the vesselcalcification which can result in stenosis occlusion low contrast vessel boundary low contrast vessel and vessel-like calcification belt

CT scanner For all the images the in-plane resolution variesfrom 065 to 100 mm and the slice thickness varies from 05to 10 mm For training and testing purpose we randomlydivide the 50 abdominal CT images into two datasets Each ofthem contains 25 abdominal CT images Please note that allthe 50 abdominal CT images were segmented by two expertraters

The comparison results of the three methods on theabdominal artery datasets are summarized in Figure 9 Withthe symbol lowast we can easily observe that the differencesbetween our method and the other two are statisticallysignificant in both DOC and ASD The DOCs are 8482 plusmn391 8510 plusmn 514 and 9015 plusmn 319 for the CetinrsquosSchaaprsquos and ourmethods respectively whileASDs are 233plusmn151mm 197plusmn187mm and 088plusmn071mmThese significantdifferences indicate ourmethod achieves better segmentationaccuracy than the other two state-of-the-art methods

As far as we know the abdominal artery with thepresence of pathologies should be segmented accuratelyfor the surgery plan since the blood supply prediction iscritical for the minimally invasive surgery Here in order to

give an intuitive impression of our method we present thecomparison results in 3-D Figure 10 Two abdominal arteriesshown in Figure 10 are with the challenges in Figure 8We use the white rectangles to show the comparison areaswith significant differences between different segmentationsIn comparison area (a) (Figure 10(a)) the vessel kisses avessel-like calcification belt Cetinrsquos method and Schaaprsquosmethod suffer obvious oversegmentation In the stenosisarea (Figure 10(b)) Cetinrsquos method and Schaaprsquos methodunderestimate or overestimate the radius of vessel In thelow contrast areas (Figures 10(c) and 10(d)) these twomethods fail to identify vessel boundary from pathologiesHowever our method segments vessel accurately in thesechallenging cases These comparison results show that ourmethod has the capability in dealing with the challengingcases caused by pathologies while the other two methodsdo not Moreover we show several examples of 2-D cross-sections with pathologies in Figure 11 In the calcificationareas the first and second rows in Figure 11 Cetinrsquos andSchaaprsquos methods have more oversegmentations than ourmethod And in the stenosis area the third row in Figure 11

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 11

MHMM

Schaaprsquos Method

Cetinrsquos Method Average

Median

9015 plusmn 319

088 plusmn 071

DOC()

ASD(mm)

MHMM

MHMM

Schaaprsquos

Cetinrsquos

Schaaprsquos

Cetinrsquos 233 plusmn 151lowast

8510 plusmn 514lowast

8482 plusmn 391lowast

197 plusmn 187lowast

100

90

80

70

Dic

e Ove

rlap

Coe

ffici

ent (

)

Figure 9 Summary of accuracy evaluation on 30 carotid artery datasets for the threemethodsDOCsusingCetinrsquos Schaaprsquos and ourmethodsare plotted Average DOC and ASD values and statistical significance are also shown just below the box plot in a table In the table the bestresults are presented in bold and symbol lowast indicates the statistically significant differences between our method and the other two

Cetinrsquos and Schaaprsquos methods suffer from undersegmentationand oversegmentation respectively It can be observed thatour method produces the most similar results with themanual reference segmentations which are considered asground truth in this paper

4 Discussion

At the very beginning we tried to model a single HMMwithmultiple vessel features by concatenating features to form alarge feature vector However one single HMMwith multiplefeatures suffers from poor performance due to large numberof parameters to learn even nonconvergence [39] As a resultwe failed to train a singleHMMwith five features by using ourdatasets Then inspired by joint segmentation we turned toMHMM which combines multidimensional HMMs

The proposed MHMM was implemented in MatlabR2016b with Core i7-8700 (6 cores at 32 GHz) and 16 GBRAM as well as the other two methods The computationtime of the three proposed methods is shown in Table 4 forcomparison

It can be observed that the computation time of ourmethod is much larger than that of the other two methodsAlthough the proposed MHMM produces accurate segmen-tations with the presence of pathologies it suffers fromslow convergence That is the reason we did not apply it

to large-scale scans with complex branches such as lungdatasets and brain datasets In the future we plan to designa cascade-AdaBoost-MHMM classifier which organizes theAdaBoost classifiers andMHMM classifiers in a cascade wayThis cascade-AdaBoost-MHMM classifier can wipe healthyvessels away just leaving the problem areas to MHMM

Although vessel segmentation plays a fundamental rolein many clinical fields the low segmentation accuracy issuecaused by pathologies prevents it from widespread use Sev-eral methods [10 12] have been proposed to deal with someparticular challenges such as low contrast vessel by usingminimal radius based method or area based method How-ever these methods fail to identify vessels from pathologieswhen facing stenosis and complicated vessel cross-sectionsThus we propose the MHMM combining the redundantinformation (multiple vessel features) and the statisticalproperties (HMM) to cover the widest possible spectrum ofchallenging situations

The absence of a systematic evaluation workflow [40]makes the quantitative validation challenging in this work Itis challenging to compare ourmethod with others because ofdifferent databases different target populations and differentquality metrics In order to deal with this challenge andpresent our method in a more intuitive way we compareour method with two state-of-the-art algorithms on the samedatabase with the same metrics We show the comparison

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

12 BioMed Research International

(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

(d) (d) (d)

Figure 10 Comparison results of two challenging abdominal artery cases for the three methods The two rows illustrate the twoabdominal arteries The first column the second column and the third column show Cetinrsquos segmentations Schaaprsquos segmentations andthe segmentations of our method respectively The white rectangles indicate the significant differences of the three methods

Table 4 Computation time of the three methods

Cetinrsquos Schaaprsquos Ours

Synthetic Training 22 min 212 min 386 minTesting 68 min 241 min 322 min

Abdominal Training 14 min 114 min 251 minTesting 45 min 125 min 228 min

results by combining box plots and tables which gives acomprehensive view of our method And the comparisonresults indicate that our method (MHMM) has the capabilityin segmenting vessels accuratelywith the presence of patholo-gies

5 Conclusion

Targeting at vessels with the presence of pathologies wepropose a posterior probability classifier by combining mul-tiple HMMs for accurate vessel segmentation This classifieris an axis-based method which works with a vessel axis+ cross-section model This model gives our method two

advantages (1) constraining the classifier around the vesselaxes and (2) making the classifier focus on identifying vesselsfrom vessel-like structures The redundant information thatcomes with the multiple vessel features helps our methodto delineate the obscure vessel boundary accurately Inthe synthetic experiment we use 240 complex-structureddatasets (after adding noise) to evaluate the performanceof our method Our method achieves both good DOC andASD scores even with the highest level of noise And thecomparison experiment on real clinical datasets makes ourmethod more promising since the scores achieved by ourmethod are much higher than two state-of-the-art meth-ods

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

BioMed Research International 13

Figure 11 Three examples of 2-D cross-sections with pathologiesThe five columns from left to right show the 2-D cross-sectionsof original images usersegmented overlays Cetinrsquos output overlaysSchaaprsquos output overlays and our output overlays

Data Availability

(1)The synthetic vascular data used to support the findings ofthis study are openly available from the Vascusynth Team athttpvascusynthcssfucaDatahtml (2) The crotch arterydata used to support the findings of this study have not beenmade available because the data are owned by a third party(the 2nd Affiliated Hospital of Harbin Medical University)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (grants 61772159 and 61571158) theNature Science Foundation of Heilongjiang Province ofChina (No F2015005 and No QC2016090) and ChinaScholarship Council

References

[1] C Kirbas and F Quek ldquoA review of vessel extraction techniquesand algorithmsrdquo ACMComputing Surveys vol 36 no 2 pp 81ndash121 2004

[2] F Bukenya A Kiweewa and L Bai ldquoA review of vessel segmen-tation techniquesrdquo Research Gate 2017

[3] D Lesage E D Angelini I Bloch and G Funka-Lea ldquoA reviewof 3D vessel lumen segmentation techniques models featuresand extraction schemesrdquoMedical Image Analysis vol 13 no 6pp 819ndash845 2009

[4] U T V Nguyen A Bhuiyan L A F Park and K Ramamoha-narao ldquoAn effective retinal blood vessel segmentation methodusing multi-scale line detectionrdquo Pattern Recognition vol 46no 3 pp 703ndash715 2013

[5] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[6] P Makowski T S Sorensen S V Therkildsen A Materka HStodkilde-Jorgensen and E M Pedersen ldquoTwo-phase activecontour method for semiautomatic segmentation of the heartand blood vessels from MRI images for 3D visualizationrdquoComputerized Medical Imaging and Graphics vol 26 no 1 pp9ndash17 2002

[7] R Manniesing M A Viergever and W J Niessen ldquoVessel axistracking using topology constrained surface evolutionrdquo IEEETransactions on Medical Imaging vol 26 no 3 pp 309ndash3162007

[8] Hua Li and A Yezzi ldquoVessels as 4D Curves Global Minimal4D Paths to Extract 3D Tubular Surfacesrdquo in Proceedings of the2006 Conference on Computer Vision and Pattern RecognitionWorkshop (CVPRWrsquo06) pp 82-82 New York NY USA 2006

[9] Y Cheng X Hu J Wang Y Wang and S Tamura ldquoAccuratevessel segmentation with constrained B-snakerdquo IEEE Transac-tions on Image Processing vol 24 no 8 pp 2440ndash2455 2015

[10] S Cetin andG Unal ldquoA higher-order tensor vessel tractographyfor segmentation of vascular structuresrdquo IEEE Transactions onMedical Imaging vol 34 no 10 pp 2172ndash2185 2015

[11] M Holtzman-Gazit R Kimmel N Peled and D GoldsherldquoSegmentation of thin structures in volumetricmedical imagesrdquoIEEE Transactions on Image Processing vol 15 no 2 pp 354ndash363 2006

[12] M Schaap T Van Walsum L Neefjes et al ldquoRobust shaperegression for supervised vessel segmentation and its applica-tion to coronary segmentation in ctardquo IEEE Transactions onMedical Imaging vol 30 no 11 pp 1974ndash1986 2011

[13] Y Masutani H MacMahon and K Doi ldquoComputerized detec-tion of pulmonary embolism in spiral CT angiography basedon volumetric image analysisrdquo IEEE Transactions on MedicalImaging vol 21 no 12 pp 1517ndash1523 2002

[14] A F Frangi W J Nissen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998

[15] K Krissian G Malandain N Ayache R Vaillant and YTrousset ldquoModel-based detection of tubular structures in 3DimagesrdquoComputer Vision and Image Understanding vol 80 no2 pp 130ndash171 2000

[16] G Agam S G Armato III and C Wu ldquoVessel tree reconstruc-tion in thoracic CT scans with application to nodule detectionrdquoIEEE Transactions on Medical Imaging vol 24 no 4 pp 486ndash499 2005

[17] O Wink W J Niessen and M A Viergever ldquoMultiscale vesseltrackingrdquo IEEE Transactions on Medical Imaging vol 23 no 1pp 130ndash133 2004

[18] J Chen and A A Amini ldquoQuantifying 3-D vascular structuresin MRA images using hybrid PDE and geometric deformablemodelsrdquo IEEE Transactions on Medical Imaging vol 23 no 10pp 1251ndash1262 2004

[19] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[20] Y Fridman S Pizer S Aylward and E Bullitt ldquoSegmenting 3-Dbranching tubular structures using coresrdquo in Proceedings of theMedical Image Computing and Computer-Assisted Intervention(MICCAI) vol 2879 pp 570ndash577 Springer Montreal QCCanada 2003

14 BioMed Research International

[21] J A Tyrrell E Di Tomaso D Fuja et al ldquoRobust 3-Dmodeling of vasculature imagery using superellipsoidsrdquo IEEETransactions on Medical Imaging vol 26 no 2 pp 223ndash2372007

[22] W C K Wong and A C S Chung ldquoBayesian image seg-mentation using local iso-intensity structural orientationrdquo IEEETransactions on Image Processing vol 14 no 10 pp 1512ndash15232005

[23] D L Wilson and J A Noble ldquoAn adaptive segmentationalgorithm for time-of-flight MRA datardquo IEEE Transactions onMedical Imaging vol 18 no 10 pp 938ndash945 1999

[24] A C S Chung J A Noble and P Summers ldquoVascular segmen-tation of phase contrast magnetic resonance angiograms basedon statistical mixture modeling and local phase coherencerdquoIEEE Transactions on Medical Imaging vol 23 no 12 pp 1490ndash1507 2004

[25] L Tong Q Song Y Ge and M Liu ldquoHMM-based human falldetection and predictionmethod using tri-axial accelerometerrdquoIEEE Sensors Journal vol 13 no 5 pp 1849ndash1856 2013

[26] X Hu Y Cheng D Ding and D Chu ldquoAxis-guided vessel seg-mentation using a self-constructing cascade-AdaBoost-SVMclassifierrdquo BioMed Research International vol 2018 Article ID3636180 12 pages 2018

[27] H Shikata E A Huffman and M Sonka ldquoAutomated seg-mentation of pulmonary vascular tree From 3D CT imagesrdquo inProceedings of the Medical Imaging 2004 Physiology Functionand Structure from Medical Images pp 107ndash116 USA February2004

[28] Q Li S Sone and K Doi ldquoSelective enhancement filtersfor nodules vessels and airway walls in two- and three-dimensional CT scansrdquoMedical Physics vol 30 no 8 pp 2040ndash2051 2003

[29] R Manniesing M A Viergever and W J Niessen ldquoVesselenhancing diffusion A scale space representation of vesselstructuresrdquoMedical Image Analysis vol 10 no 6 pp 815ndash8252006

[30] Y Zeng R Cavalcante C Collet et al ldquoCoronary calcificationas a mechanism of plaquemedia shrinkage in vessels treatedwith bioresorbable vascular scaffold A multimodality intra-coronary imaging studyrdquoAtherosclerosis vol 269 pp 6ndash13 2018

[31] L C Adams S M Boker Y Y Bender et al ldquoDetection ofvessel wall calcifications in vertebral arteries using susceptibilityweighted imagingrdquo Neuroradiology vol 59 no 9 pp 861ndash8722017

[32] G J McLachlan and T Krishnan The EM Algorithm andExtensions John Wiley amp Sons New York NY USA 1997

[33] S Cetin ADemir A YezziMDegertekin andGUnal ldquoVesseltractography using an intensity based tensormodel with branchdetectionrdquo IEEE Transactions on Medical Imaging vol 32 no 2pp 348ndash363 2013

[34] L R Dice ldquoMeasures of the amount of ecologic associationbetween speciesrdquo Ecology vol 26 pp 297ndash302 1945

[35] M Schaap C T Metz T van Walsum et al ldquoStandardizedevaluation methodology and reference database for evaluat-ing coronary artery centerline extraction algorithmsrdquo MedicalImage Analysis vol 13 no 5 pp 701ndash714 2009 Includes SpecialSection on the 12th International Conference on MedicalImaging and Computer Assisted Intervention

[36] G Hamarneh and P Jassi ldquoVascuSynth Simulating vasculartrees for generating volumetric image data with ground-truthsegmentation and tree analysisrdquo Computerized Medical Imagingand Graphics vol 34 no 8 pp 605ndash616 2010

[37] Z Li L Yu J D Trzasko et al ldquoAdaptive nonlocal meansfiltering based on local noise level for CT denoisingrdquo MedicalPhysics vol 41 no 1 Article ID 011908 2014

[38] B Karmazyn Y Liang P Klahr and S G Jennings ldquoEffectof tube voltage on ct noise levels in different phantom sizesrdquoAmerican Journal of Roentgenology vol 200 no 5 pp 1001ndash1005 2013

[39] P KumarH Gauba P P Roy andD PDogra ldquoCoupledHMM-based multi-sensor data fusion for sign language recognitionrdquoPattern Recognition Letters vol 86 pp 1ndash8 2017

[40] S Moccia E De Momi S El Hadji and L S Mattos ldquoBloodvessel segmentation algorithms mdash Review of methods datasetsand evaluation metricsrdquo Computer Methods and Programs inBiomedicine vol 158 pp 71ndash91 2018

Hindawiwwwhindawicom

International Journal of

Volume 2018

Zoology

Hindawiwwwhindawicom Volume 2018

Anatomy Research International

PeptidesInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of Parasitology Research

GenomicsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Neuroscience Journal

Hindawiwwwhindawicom Volume 2018

BioMed Research International

Cell BiologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

ArchaeaHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Genetics Research International

Hindawiwwwhindawicom Volume 2018

Advances in

Virolog y Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

International Journal of

MicrobiologyHindawiwwwhindawicom

Nucleic AcidsJournal of

Volume 2018

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom

International Journal of

Volume 2018

Zoology

Hindawiwwwhindawicom Volume 2018

Anatomy Research International

PeptidesInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of Parasitology Research

GenomicsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Neuroscience Journal

Hindawiwwwhindawicom Volume 2018

BioMed Research International

Cell BiologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

ArchaeaHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Genetics Research International

Hindawiwwwhindawicom Volume 2018

Advances in

Virolog y Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

International Journal of

MicrobiologyHindawiwwwhindawicom

Nucleic AcidsJournal of

Volume 2018

Submit your manuscripts atwwwhindawicom