Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 715325 7 pageshttpdxdoiorg1011552013715325

Research ArticleDevelopment of Image Segmentation Methods forIntracranial Aneurysms

Yuka Sen Yi Qian Alberto Avolio and Michael Morgan

The Australian School of Advanced Medicine Macquarie University Sydney NSW 2109 Australia

Correspondence should be addressed to Yi Qian yiqianmqeduau

Received 17 January 2013 Accepted 8 March 2013

Academic Editor Peng Feng

Copyright copy 2013 Yuka Sen et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Though providing vital means for the visualization diagnosis and quantification of decision-making processes for the treatment ofvascular pathologies vascular segmentation remains a process that continues to be marred by numerous challenges In this studywe validate eight aneurysms via the use of two existing segmentation methods the Region Growing Threshold and Chan-Vesemodel These methods were evaluated by comparison of the results obtained with a manual segmentation performed Based uponthis validation study we propose a newThreshold-Based Level Set (TLS) method in order to overcome the existing problemsWithdivergentmethods of segmentation we discovered that the volumes of the aneurysmmodels reached amaximumdifference of 24The local artery anatomical shapes of the aneurysms were likewise found to significantly influence the results of these simulationsIn contrast however the volume differences calculated via use of the TLSmethod remained at a relatively low figure at only around5 thereby revealing the existence of inherent limitations in the application of cerebrovascular segmentation The proposed TLSmethod holds the potential for utilisation in automatic aneurysm segmentation without the setting of a seed point or intensitythreshold This technique will further enable the segmentation of anatomically complex cerebrovascular shapes thereby allowingfor more accurate and efficient simulations of medical imagery

1 Introduction

Specification of intracranial aneurysm morphology andhemodynamic analysis requires segmentation of vasculargeometries from three-dimensional (3D) medical imagesproduced via CTA orMRA Methods for such manipulationsof medical images are directly linked to the accuracy ofaneurysm model construction particularly regarding thegeometry of complex shapes and volumes In most casesthis process involves extraction of the 2D image from CTAor MRA followed by reconstruction of the 3D aneurysmsurface model As such several approaches exist and arecurrently utilized in cerebrovascular segmentation On onehand the fuzzy-based approach has been adapted for detect-ing malformed and small vessels in MRA images [1] whileregion growing approaches are popular in medical imagesegmentation due to their simplicity and computationalefficiency [2] Major problems however include leakagewhen the boundary is blurred and sensitivity to seed positionUtilization of implicit active contourmethodswithin the levelset framework seems to be widespread in medical image

segmentation [3ndash5] as the method does not suffer fromparameterization surface problems [6] and has the capabilityto handle complex geometries and topological changes [7 8]More recently active contour methods have also appeared inthe modeling of intracranial aneurysms and cerebrovascularsegmentation [9 10] Law and Chung proposed a methodbased upon multirange filters and local variances to performthe segmentation of intracranial aneurysms on Phase Con-trast Magnetic Resonance Angiography data [11] Hernandezand Frangi have developed a segmentation method forintracranial aneurysms based on Geometric Active Regions(GAR) using CTA and 3D Rotational Angiography data[12] whilst several Geodesic Active Contours (GAC) basedmethods have since been adapted for segmentation of brainaneurysms from CTA data [13 14] These methods eitherrequire sufficient training sets or they are reliant on boundaryinformation obtained from medical imaging Furthermoreboundary-based active contour level set methods may easilyleak when the target boundary is not clearly definedThoughFirouzian et al proposed a Geodesic Active Contours basedlevel set method which employs region information and

2 Computational and Mathematical Methods in Medicine

intensity it requires a user-defined seed point in order tocalculate intensity threshold [15]

Despite the availabity of many image segmentationmeth-ods with varying approaches and algorithms there is nodominant method in terms of effectiveness across all areas[16ndash18] Our previous study indicated that the volume ofthe aneurysm models depends strongly on the differentsegmentation methods The segmentation method likewiseinfluences the local geometric shapes of the aneurysms [19]Validation will thus become necessary comparing segmenta-tion methods and adjusting the parameters of these segmen-tation techniques in order to assure the quality of patient-specific cerebral-vascular hemodynamic analysis Althougha number of commercial software packages for segmentationare available in the market there is a conspicuous lackof discussion of methodology and information regardingvalidation processes

In this paper the authors propose a new Threshold-Based Level Set method for cerebral aneurysmsThis methodis based on the Geodesic Active Contours model [20]and Chan-Vese model (CV) [21] integrating both regionand boundary information to segment cerebral aneurysmsthrough the use of a global threshold and gradientmagnitudeto form the speed functionThe initial threshold is calculatedfrom the Chan-Vese model and is then iteratively updatedthroughout the process of segmentation Upon reaching theaneurysm boundary the change in the threshold value willdecrease because of the contrast between aneurysm andnonaneurysm intensities and the iteration will stop Thealgorithm may then be implemented in an automatic orsemiautomatic manner depending on the complexity of theaneurysm shape

The results of 3D automatic aneurysm segmentationsfrom the Region Growing Threshold (RGT) the Chan-Vese model (CV) and the Threshold-Based Level Set (TLS)are compared to results obtained via manual segmentationperformed by an expert radiologist over eight data sets ofCTA imagery Evaluationwas based on six validationmetricsvolume difference (VD) Jaccardrsquos measure (volume overlapmetric JM) false positive ratio (rfp) false negative ratio(rfn) Hausdorff distance (maximum surface distance HD)and mean absolute surface distance (MASD) This studywill also discuss the impact of parameter adjustments onsegmentation results

2 Methods

21 RegionGrowingThreshold Connecting (RGT) TheRegionGrowing Threshold method starts with a seed(s) selectedwithin the area of the object to be segmented It requires twointensity values for the pixel of the object a low threshold1198791 and high threshold 119879

2values Neighboring pixels whose

intensity values fall within this range are accepted andincluded in the region When no more neighbor pixelsare found that satisfy the criterion the segmentation isconsidered to have been completed The selection criterionis described by the following equation

119868 (119883) isin [119883 minus 1198791 119883 + 119879

2] (1)

where 1198791and 119879

2represent the low and high thresholds of

the region intensities 119868(119883) represent the image and 119883 theposition of the particular neighboring pixel being consideredfor inclusion in the region Problems surrounding RGTinclude threshold selection and sensitivity to seed position[22]

22 Chan-Vese Model (CV) [21] The Chan-Vese model isbased upon the Mumford-Shah functional [23] The associ-ated evolution PDE in the level set framework is

120597120593

120597119905=

1003816100381610038161003816nabla1205931003816100381610038161003816 [1205822 (119868 minus 120583out)

2

minus 1205821(119868 minus 120583in)

2

minus 120572

+ 120573div(nabla120593

1003816100381610038161003816nabla1205931003816100381610038161003816

)]

(2)

where 120583in is the mean of the target object of intensity 120583outrepresents the mean of the background of intensity and1205821 1205822120572 and 120573 are positive constants The Chan-Vese model

does not require a term related to the image gradient Insteadregion intensity information is utilized for the target objectsof segmentation This model has exhibited significant effec-tiveness in segmentation of images with blurred boundaries

23 Threshold-Based Level Set (TLS) The Threshold-BasedLevel Set combines both the Geodesic Active Contour andthe Chan-Vese model within the level set framework

Under the level set scheme the contour is seen to deformby the function 120597Γ(119905)120597119905 + 119865|nabla120593| = 0 with an embeddedsurface Γ(119905) represented as the zero level set of 120593 by Γ(119905) =

119909 119910 isin 119877 | 120593(119909 119910 119905) = 0119865 represents a function for speed which drives the Γ(119905)

surface evolution in the normal direction It is clear that 119865exerts a direct impact upon the quality of medical imagesegmentation The associated evolution PDE in the level setframework is represented as follows

120597120593

120597119905=1003816100381610038161003816nabla120593

1003816100381610038161003816 (120572 ( 119868 minus 119879) + 120573div(119892nabla120593

1003816100381610038161003816nabla1205931003816100381610038161003816

)) (3)

where 119868 represents the image to be segmented119879 the intensitythreshold 119892 is the image gradient 120581 = div(nabla120593|nabla120593|)the curvature 120572 the image propagation constant and 120573

represents the spatial modifier constant for the curvature 120581120572 and 120573 serve to weight the relative influence of each of theseterms on the movement of the surface contour

The first term of the RHS of the formula 120572(119868minus119879) definesthe region where 119879 is an automatically defined parameterindicating the lower boundary of the intensity level for thetarget object In this work the target aneurysm is alwaysassumed to possess a relatively higher intensity level than itsbackground It can thus be seen that this first term forces thecontours to enclose regions with intensity levels greater than119879 When the contour lies within the aneurysm region (119868 minus119879) ge 0 it expands in the normal direction When (119868 minus

119879) lt 0 the contour lies beyond the aneurysm region andthus shrinks with a negative speed This process stops whenthe contours converge to the aneurysm boundary with the

Computational and Mathematical Methods in Medicine 3

Table 1 Validation results of segmentation methodsCase 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Average

VD ()GT 0 0 0 0 0 0 0 0TLS 155 469 448 046 292 012 355 227 251RGT 765 447 886 137 552 609 321 1090 601CV 1163 1823 560 404 247 251 2418 1402 1034

JM ()GT 100 100 100 100 100 100 100 100TLS 9187 8966 8857 9325 9164 9235 9155 9379 9159RGT 9012 8824 8702 9300 9139 9090 9427 8958 9057CV 8824 8402 8673 8953 9185 9182 7696 8959 8734

rfp ()GT 0 0 0 0 0 0 0 0TLS 497 291 320 165 360 399 406 211 331RGT 064 380 1472 092 922 164 595 013 463CV 1184 1802 1326 538 460 554 2875 1162 1238

rfn ()GT 0 0 0 0 0 0 0 0TLS 357 325 151 521 140 397 473 423 348RGT 926 840 017 615 018 761 012 1030 527CV 132 084 178 566 393 309 092 000 219

HD (pixel)GT 0 0 0 0 0 0 0 0TLS 051 065 068 117 079 189 065 079 089RGT 077 064 089 141 055 186 049 076 092CV 075 117 104 209 119 051 100 095 109

MASD (pixel)GT 0 0 0 0 0 0 0 0TLS 008 008 007 009 007 005 007 010 008RGT 010 010 012 010 010 007 007 010 010CV 006 006 007 011 008 005 007 010 008

image 119868 reaching a threshold of 119879 If we isolate this first termof the RHS of (3) it becomes the selection criteria for thelower threshold in the Region Growing Threshold methodThe second term in the formula would likewise become theGeodesic Active Contour term

231 Method for Automatic Threshold Selection TheThresh-old-Based Level Set requires an appropriate estimate of thethreshold value from proper segmentation of the aneurysmobtained using Chan-Vese model and the statistical dataspecifically confidence interval (CI) and confidence level(CL)

232 Confidence Interval (CI) and Confidence Level (CL)The confidence level (CL) represents how often the truepercentage of a population lies within the confidence interval(CI) Based on Chebyshevrsquos inequality [24] a general rela-tionship for symmetric distribution between CI and CL canbe established The inequality for symmetric distribution isgiven as

119875 (1003816100381610038161003816119883 minus 120583

1003816100381610038161003816 ge 119896120590) le1

1198962119896 gt 0 (4)

where 119883 is the random variable population 120583 is the popula-tion mean and confidence interval is represented by 119896 times120590 standard deviation Equation (4) indicates that more than(1 minus (1119896

2) times 100) percent of the population lies between 119896

standard deviations from the population meanFor nonsymmetric distribution the one-tailed version of

the inequality is used This is given by

119875 (119883 minus 120583 ge 119896120590) le1

1 + 1198962

119896 gt 0 (5)

For this inequality it follows that when 119896 = 1 more than 50of the population is located one standard deviation away fromthe mean

233 Initial Threshold Selection According to the theoryof confidence interval the lower bound threshold of theaneurysm can be defined by

119879119894= 120583119886minus 119896119894120590119886

119894 ge 0 (6)

The threshold 119879 represents the difference between the meanof the intensity of the aneurysm (120583

119886) and 119896 times its standard

4 Computational and Mathematical Methods in Medicine

deviation (120590119886) The intensities of the aneurysm and its

background regions are different with the lowest intensitythreshold of the aneurysm being the same as the highestintensity threshold of the background Thus the relationship120583119887+ 119896119887120590119887= 120583119886minus 119896119886120590119886would apply The confidence levels for

both the aneurysm and its background are considered to bethe same 119896

119887= 119896119886= 119896 thereby allowing 119896 to be expressed as

119896 =120583119886minus 120583119887

120590119886minus 120590119887

(7)

We have utilized the Chan-Vesemodel method to perform aninitial segmentation From the results obtained the initial 119896

0

was seen to be calculated via (7) The initial 1198790can likewise

be found using (6)

24 Data Acquisition Clinical studies were performed withthe consent of the patient in relation to acquisition ofaneurysm imagesThese protocols were approved by the localinstitutional review board and the regional research ethicscommittee with eight data sets of patients harboring internalcarotid artery aneurysms acquired by 3D CTA scans (GEHealthcare)

Cross-sectional images were acquired by a CT angiogra-phy scanner with multidetector-row capability a table speedof 9mms and zero-degree table (and gantry tilt) Scanningwas initiated from the common carotid artery and continuedparallel to the orbitomeatal line to the level of the Circle ofWillis during this intravenous injection of contrast materialwas administered at a rate of 35mlss Aneurysm image was512 times 512 pixel field while slices of continuous thickness wereused to segment and reconstruct 3D vascular geometry Pixelsare expressed in Hounsfield Units (HU)

25 Experiment Setting For quantitative evaluation manualsegmentation of eight aneurysms using open source software3D Slicer was conducted by an expert radiologistThe resultswere utilized as a ground truth (GT) for the comparison ofother methods A region of interest (ROI) a good represen-tation of the targeted region for segmentation was selecteddepending on the aneurysm size All the experiments wereperformed on cropped data sets to reduce calculation timeand memory usage with preparatory work being completedprior to the conduction of the experiments

251 Parameter Setting

The Threshold-Based Level Set The initial zero level set is arectangular prism surface constructed by the subtraction oftwo pixels on either side of the ROI Thus three parametersneeded to be set 120572 120573 from (3) and 119888 from (8) All eightexperiments utilized a fixed setting of 120572 = 10 120573 = 3 and119888 in the range between 01 and 001 The role of this will beanalyzed in Section 4

The Chan-Vese Model The initial zero level set is a cuboidsurface constructed in the same manner as the TLS with theparameters in (2) fixed for all cases 120582

1= 1205822= 0001 120572 = 0

and 120573 = 03

GTTLS

RGTCV

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8Case number

Ane

urys

m v

olum

e (m

m3)

Figure 1 Aneurysm volume against segmentation methods

The Region Growing Threshold According to each case aninitial seed point is required to determine the starting lociwithin the specific aneurysm For low and high intensitythresholds 119879

1and 119879

2in (1) 119879

1was selected to utilize the

threshold of the TLS result for each case with1198792representing

the highest intensity of the aneurysm

26 Evaluation

(i) Aneurysm volume was calculated through the useof the boundary geometry segmented using variousmethods The volume difference (VD) was calculatedusing the equationVD = |(119881

2minus1198811)1198811|times100 where

1198811represents the volume of GT and119881

2represents the

volume of the TLS RGT or CV methods

(ii) Jaccardrsquos measure (JM) is a volume overlap metricused to count the percentage of voxel intersections forthe paired segmentations

This can be seen as JM = 2 lowast |1198781cap 1198782|1198781cup 1198782 where

1198781represents the voxels created by the GT and 119878

2the

voxels generated through the use of the TLS RGT orCV methods

(iii) False positive ratio (rfp) represents the percentage ofthe extra voxels of 119878

2 located outside of 119878

1 When the

rfp equates to zero no voxels in 1198782will be located

outside of 1198781 Accordingly rfp = (|119904

2| minus |1199041cap 1199042|)|1199041|

where 1198781represents the voxels created by the GT and

1198782represents the voxels generated by the TLS RGT

or CV methods

(iv) False negative ratio (rfn) represents the percentage ofthe lost voxels of 119878

2 which cover the internal surface

of the 1198781

This may be seen as rfn = (|1199041| minus |1199041cap 1199042|)|1199041| where

1198781represents the voxels created by the GT and 119878

2

Computational and Mathematical Methods in Medicine 5

Figure 2 3D geometries of segmentation results comparison from left to right CV RGT and TLS

Bleb

Figure 3 Segmentation results comparison (Case 1 aneurysm with bleb) from left to right GT CV RGT TLS and photo from open headsurgery

represents the voxels generated by the TLS RGT orCV methods

(v) Hausdorff distance (HD) measures the maximumsurface distance This measure is extremely sensitiveto outliers and may not reflect the overall degree ofcorrelation

(vi) Themean absolute surface distance (MASD) indicatesthe average degree of difference between two surfacesand does not depend on aneurysm size [15]

3 Results

The calculated values of VD JM rfp rfn HD and MASDfor the eight cases considered are tabulated in Table 1 Theaverage values are also shown Figure 1 depicts the volumeof the aneurysm The minimum VD can be seen in the TLSmethod The average value of VD is seen to be 251 Themaximum VD however is seen for Case 7 using the CVmethod The values of JM indicate that the TLS methodhas the highest overlap rate in comparison to the other twomethods with an average of 9159 A study of rfp and rfnindicates a 331 overflow and 348 absence on average forthe TLS method The largest rfp and the smallest rfn werefound to occur via the use of the CV method These resultslikewise indicate that the largest volume was generated by theCV method when compared to all other methods

Results obtained for the surface distancemetrics (HD andMASD) indicate the reliability of all segmentation methodswith the HD values for the TLS method being between 051to 189 pixels and the maximumMASD being 008

Figure 2 shows the 3D geometry of Case 4 restructuredvia three segmentation methods Only TLS was effective in

fully reconstructing the parent artery and aneurysm whilethe other two methods were not able to construct a portionof the artery One reason for this is that the aneurysm size inCase 4 is larger in comparison to other cases Another pointis that the distal parent artery itself is curved to lie proximallyto the aneurysm These results likewise indicate that the TLSmethod may be utilized in the segmentation of aneurysmswith blurred boundaries

Figure 3 represents the segmented aneurysm surfaces ofCase 1 where only TLS is able to restructure the bleb locatedat the top of the aneurysm The resulting image is similar tothe picture taken during open-skull surgery

4 Discussion

41 TLS Boundary Detect Function In this study the TLSmethod utilizes a boundary feature map

119892 (|nabla119868|) =1

1 + 119888|nabla119868|2 (8)

where 119892 is for the detection of vascular boundaries |nabla119868|represents a gradient magnitude and 119888 is a constant thatcontrols the slope of the boundary detect function119892(|nabla119868|) Atthe region of the artery and aneurysm the boundary intensitygradient was seen to increase significantly Thus a relativelylow 119888 value was sufficient for the adjustment of the decreasingspeed of 119892 in order to ensure that the search for the boundarysurface was stopped at the arterial boundary Figure 4 showsthe process of selection for the value of 119888 in Case 1 the resultsindicating that both VD and JM converged to a constant andMASD ceased all fluctuation when 119888 was taken to equate to05

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

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2 Computational and Mathematical Methods in Medicine

intensity it requires a user-defined seed point in order tocalculate intensity threshold [15]

Despite the availabity of many image segmentationmeth-ods with varying approaches and algorithms there is nodominant method in terms of effectiveness across all areas[16ndash18] Our previous study indicated that the volume ofthe aneurysm models depends strongly on the differentsegmentation methods The segmentation method likewiseinfluences the local geometric shapes of the aneurysms [19]Validation will thus become necessary comparing segmenta-tion methods and adjusting the parameters of these segmen-tation techniques in order to assure the quality of patient-specific cerebral-vascular hemodynamic analysis Althougha number of commercial software packages for segmentationare available in the market there is a conspicuous lackof discussion of methodology and information regardingvalidation processes

In this paper the authors propose a new Threshold-Based Level Set method for cerebral aneurysmsThis methodis based on the Geodesic Active Contours model [20]and Chan-Vese model (CV) [21] integrating both regionand boundary information to segment cerebral aneurysmsthrough the use of a global threshold and gradientmagnitudeto form the speed functionThe initial threshold is calculatedfrom the Chan-Vese model and is then iteratively updatedthroughout the process of segmentation Upon reaching theaneurysm boundary the change in the threshold value willdecrease because of the contrast between aneurysm andnonaneurysm intensities and the iteration will stop Thealgorithm may then be implemented in an automatic orsemiautomatic manner depending on the complexity of theaneurysm shape

The results of 3D automatic aneurysm segmentationsfrom the Region Growing Threshold (RGT) the Chan-Vese model (CV) and the Threshold-Based Level Set (TLS)are compared to results obtained via manual segmentationperformed by an expert radiologist over eight data sets ofCTA imagery Evaluationwas based on six validationmetricsvolume difference (VD) Jaccardrsquos measure (volume overlapmetric JM) false positive ratio (rfp) false negative ratio(rfn) Hausdorff distance (maximum surface distance HD)and mean absolute surface distance (MASD) This studywill also discuss the impact of parameter adjustments onsegmentation results

2 Methods

21 RegionGrowingThreshold Connecting (RGT) TheRegionGrowing Threshold method starts with a seed(s) selectedwithin the area of the object to be segmented It requires twointensity values for the pixel of the object a low threshold1198791 and high threshold 119879

2values Neighboring pixels whose

intensity values fall within this range are accepted andincluded in the region When no more neighbor pixelsare found that satisfy the criterion the segmentation isconsidered to have been completed The selection criterionis described by the following equation

119868 (119883) isin [119883 minus 1198791 119883 + 119879

2] (1)

where 1198791and 119879

2represent the low and high thresholds of

the region intensities 119868(119883) represent the image and 119883 theposition of the particular neighboring pixel being consideredfor inclusion in the region Problems surrounding RGTinclude threshold selection and sensitivity to seed position[22]

22 Chan-Vese Model (CV) [21] The Chan-Vese model isbased upon the Mumford-Shah functional [23] The associ-ated evolution PDE in the level set framework is

120597120593

120597119905=

1003816100381610038161003816nabla1205931003816100381610038161003816 [1205822 (119868 minus 120583out)

2

minus 1205821(119868 minus 120583in)

2

minus 120572

+ 120573div(nabla120593

1003816100381610038161003816nabla1205931003816100381610038161003816

)]

(2)

where 120583in is the mean of the target object of intensity 120583outrepresents the mean of the background of intensity and1205821 1205822120572 and 120573 are positive constants The Chan-Vese model

does not require a term related to the image gradient Insteadregion intensity information is utilized for the target objectsof segmentation This model has exhibited significant effec-tiveness in segmentation of images with blurred boundaries

23 Threshold-Based Level Set (TLS) The Threshold-BasedLevel Set combines both the Geodesic Active Contour andthe Chan-Vese model within the level set framework

Under the level set scheme the contour is seen to deformby the function 120597Γ(119905)120597119905 + 119865|nabla120593| = 0 with an embeddedsurface Γ(119905) represented as the zero level set of 120593 by Γ(119905) =

119909 119910 isin 119877 | 120593(119909 119910 119905) = 0119865 represents a function for speed which drives the Γ(119905)

surface evolution in the normal direction It is clear that 119865exerts a direct impact upon the quality of medical imagesegmentation The associated evolution PDE in the level setframework is represented as follows

120597120593

120597119905=1003816100381610038161003816nabla120593

1003816100381610038161003816 (120572 ( 119868 minus 119879) + 120573div(119892nabla120593

1003816100381610038161003816nabla1205931003816100381610038161003816

)) (3)

where 119868 represents the image to be segmented119879 the intensitythreshold 119892 is the image gradient 120581 = div(nabla120593|nabla120593|)the curvature 120572 the image propagation constant and 120573

represents the spatial modifier constant for the curvature 120581120572 and 120573 serve to weight the relative influence of each of theseterms on the movement of the surface contour

The first term of the RHS of the formula 120572(119868minus119879) definesthe region where 119879 is an automatically defined parameterindicating the lower boundary of the intensity level for thetarget object In this work the target aneurysm is alwaysassumed to possess a relatively higher intensity level than itsbackground It can thus be seen that this first term forces thecontours to enclose regions with intensity levels greater than119879 When the contour lies within the aneurysm region (119868 minus119879) ge 0 it expands in the normal direction When (119868 minus

119879) lt 0 the contour lies beyond the aneurysm region andthus shrinks with a negative speed This process stops whenthe contours converge to the aneurysm boundary with the

Computational and Mathematical Methods in Medicine 3

Table 1 Validation results of segmentation methodsCase 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Average

VD ()GT 0 0 0 0 0 0 0 0TLS 155 469 448 046 292 012 355 227 251RGT 765 447 886 137 552 609 321 1090 601CV 1163 1823 560 404 247 251 2418 1402 1034

JM ()GT 100 100 100 100 100 100 100 100TLS 9187 8966 8857 9325 9164 9235 9155 9379 9159RGT 9012 8824 8702 9300 9139 9090 9427 8958 9057CV 8824 8402 8673 8953 9185 9182 7696 8959 8734

rfp ()GT 0 0 0 0 0 0 0 0TLS 497 291 320 165 360 399 406 211 331RGT 064 380 1472 092 922 164 595 013 463CV 1184 1802 1326 538 460 554 2875 1162 1238

rfn ()GT 0 0 0 0 0 0 0 0TLS 357 325 151 521 140 397 473 423 348RGT 926 840 017 615 018 761 012 1030 527CV 132 084 178 566 393 309 092 000 219

HD (pixel)GT 0 0 0 0 0 0 0 0TLS 051 065 068 117 079 189 065 079 089RGT 077 064 089 141 055 186 049 076 092CV 075 117 104 209 119 051 100 095 109

MASD (pixel)GT 0 0 0 0 0 0 0 0TLS 008 008 007 009 007 005 007 010 008RGT 010 010 012 010 010 007 007 010 010CV 006 006 007 011 008 005 007 010 008

image 119868 reaching a threshold of 119879 If we isolate this first termof the RHS of (3) it becomes the selection criteria for thelower threshold in the Region Growing Threshold methodThe second term in the formula would likewise become theGeodesic Active Contour term

231 Method for Automatic Threshold Selection TheThresh-old-Based Level Set requires an appropriate estimate of thethreshold value from proper segmentation of the aneurysmobtained using Chan-Vese model and the statistical dataspecifically confidence interval (CI) and confidence level(CL)

232 Confidence Interval (CI) and Confidence Level (CL)The confidence level (CL) represents how often the truepercentage of a population lies within the confidence interval(CI) Based on Chebyshevrsquos inequality [24] a general rela-tionship for symmetric distribution between CI and CL canbe established The inequality for symmetric distribution isgiven as

119875 (1003816100381610038161003816119883 minus 120583

1003816100381610038161003816 ge 119896120590) le1

1198962119896 gt 0 (4)

where 119883 is the random variable population 120583 is the popula-tion mean and confidence interval is represented by 119896 times120590 standard deviation Equation (4) indicates that more than(1 minus (1119896

2) times 100) percent of the population lies between 119896

standard deviations from the population meanFor nonsymmetric distribution the one-tailed version of

the inequality is used This is given by

119875 (119883 minus 120583 ge 119896120590) le1

1 + 1198962

119896 gt 0 (5)

For this inequality it follows that when 119896 = 1 more than 50of the population is located one standard deviation away fromthe mean

233 Initial Threshold Selection According to the theoryof confidence interval the lower bound threshold of theaneurysm can be defined by

119879119894= 120583119886minus 119896119894120590119886

119894 ge 0 (6)

The threshold 119879 represents the difference between the meanof the intensity of the aneurysm (120583

119886) and 119896 times its standard

4 Computational and Mathematical Methods in Medicine

deviation (120590119886) The intensities of the aneurysm and its

background regions are different with the lowest intensitythreshold of the aneurysm being the same as the highestintensity threshold of the background Thus the relationship120583119887+ 119896119887120590119887= 120583119886minus 119896119886120590119886would apply The confidence levels for

both the aneurysm and its background are considered to bethe same 119896

119887= 119896119886= 119896 thereby allowing 119896 to be expressed as

119896 =120583119886minus 120583119887

120590119886minus 120590119887

(7)

We have utilized the Chan-Vesemodel method to perform aninitial segmentation From the results obtained the initial 119896

0

was seen to be calculated via (7) The initial 1198790can likewise

be found using (6)

24 Data Acquisition Clinical studies were performed withthe consent of the patient in relation to acquisition ofaneurysm imagesThese protocols were approved by the localinstitutional review board and the regional research ethicscommittee with eight data sets of patients harboring internalcarotid artery aneurysms acquired by 3D CTA scans (GEHealthcare)

Cross-sectional images were acquired by a CT angiogra-phy scanner with multidetector-row capability a table speedof 9mms and zero-degree table (and gantry tilt) Scanningwas initiated from the common carotid artery and continuedparallel to the orbitomeatal line to the level of the Circle ofWillis during this intravenous injection of contrast materialwas administered at a rate of 35mlss Aneurysm image was512 times 512 pixel field while slices of continuous thickness wereused to segment and reconstruct 3D vascular geometry Pixelsare expressed in Hounsfield Units (HU)

25 Experiment Setting For quantitative evaluation manualsegmentation of eight aneurysms using open source software3D Slicer was conducted by an expert radiologistThe resultswere utilized as a ground truth (GT) for the comparison ofother methods A region of interest (ROI) a good represen-tation of the targeted region for segmentation was selecteddepending on the aneurysm size All the experiments wereperformed on cropped data sets to reduce calculation timeand memory usage with preparatory work being completedprior to the conduction of the experiments

251 Parameter Setting

The Threshold-Based Level Set The initial zero level set is arectangular prism surface constructed by the subtraction oftwo pixels on either side of the ROI Thus three parametersneeded to be set 120572 120573 from (3) and 119888 from (8) All eightexperiments utilized a fixed setting of 120572 = 10 120573 = 3 and119888 in the range between 01 and 001 The role of this will beanalyzed in Section 4

The Chan-Vese Model The initial zero level set is a cuboidsurface constructed in the same manner as the TLS with theparameters in (2) fixed for all cases 120582

1= 1205822= 0001 120572 = 0

and 120573 = 03

GTTLS

RGTCV

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8Case number

Ane

urys

m v

olum

e (m

m3)

Figure 1 Aneurysm volume against segmentation methods

The Region Growing Threshold According to each case aninitial seed point is required to determine the starting lociwithin the specific aneurysm For low and high intensitythresholds 119879

1and 119879

2in (1) 119879

1was selected to utilize the

threshold of the TLS result for each case with1198792representing

the highest intensity of the aneurysm

26 Evaluation

(i) Aneurysm volume was calculated through the useof the boundary geometry segmented using variousmethods The volume difference (VD) was calculatedusing the equationVD = |(119881

2minus1198811)1198811|times100 where

1198811represents the volume of GT and119881

2represents the

volume of the TLS RGT or CV methods

(ii) Jaccardrsquos measure (JM) is a volume overlap metricused to count the percentage of voxel intersections forthe paired segmentations

This can be seen as JM = 2 lowast |1198781cap 1198782|1198781cup 1198782 where

1198781represents the voxels created by the GT and 119878

2the

voxels generated through the use of the TLS RGT orCV methods

(iii) False positive ratio (rfp) represents the percentage ofthe extra voxels of 119878

2 located outside of 119878

1 When the

rfp equates to zero no voxels in 1198782will be located

outside of 1198781 Accordingly rfp = (|119904

2| minus |1199041cap 1199042|)|1199041|

where 1198781represents the voxels created by the GT and

1198782represents the voxels generated by the TLS RGT

or CV methods

(iv) False negative ratio (rfn) represents the percentage ofthe lost voxels of 119878

2 which cover the internal surface

of the 1198781

This may be seen as rfn = (|1199041| minus |1199041cap 1199042|)|1199041| where

1198781represents the voxels created by the GT and 119878

2

Computational and Mathematical Methods in Medicine 5

Figure 2 3D geometries of segmentation results comparison from left to right CV RGT and TLS

Bleb

Figure 3 Segmentation results comparison (Case 1 aneurysm with bleb) from left to right GT CV RGT TLS and photo from open headsurgery

represents the voxels generated by the TLS RGT orCV methods

(v) Hausdorff distance (HD) measures the maximumsurface distance This measure is extremely sensitiveto outliers and may not reflect the overall degree ofcorrelation

(vi) Themean absolute surface distance (MASD) indicatesthe average degree of difference between two surfacesand does not depend on aneurysm size [15]

3 Results

The calculated values of VD JM rfp rfn HD and MASDfor the eight cases considered are tabulated in Table 1 Theaverage values are also shown Figure 1 depicts the volumeof the aneurysm The minimum VD can be seen in the TLSmethod The average value of VD is seen to be 251 Themaximum VD however is seen for Case 7 using the CVmethod The values of JM indicate that the TLS methodhas the highest overlap rate in comparison to the other twomethods with an average of 9159 A study of rfp and rfnindicates a 331 overflow and 348 absence on average forthe TLS method The largest rfp and the smallest rfn werefound to occur via the use of the CV method These resultslikewise indicate that the largest volume was generated by theCV method when compared to all other methods

Results obtained for the surface distancemetrics (HD andMASD) indicate the reliability of all segmentation methodswith the HD values for the TLS method being between 051to 189 pixels and the maximumMASD being 008

Figure 2 shows the 3D geometry of Case 4 restructuredvia three segmentation methods Only TLS was effective in

fully reconstructing the parent artery and aneurysm whilethe other two methods were not able to construct a portionof the artery One reason for this is that the aneurysm size inCase 4 is larger in comparison to other cases Another pointis that the distal parent artery itself is curved to lie proximallyto the aneurysm These results likewise indicate that the TLSmethod may be utilized in the segmentation of aneurysmswith blurred boundaries

Figure 3 represents the segmented aneurysm surfaces ofCase 1 where only TLS is able to restructure the bleb locatedat the top of the aneurysm The resulting image is similar tothe picture taken during open-skull surgery

4 Discussion

41 TLS Boundary Detect Function In this study the TLSmethod utilizes a boundary feature map

119892 (|nabla119868|) =1

1 + 119888|nabla119868|2 (8)

where 119892 is for the detection of vascular boundaries |nabla119868|represents a gradient magnitude and 119888 is a constant thatcontrols the slope of the boundary detect function119892(|nabla119868|) Atthe region of the artery and aneurysm the boundary intensitygradient was seen to increase significantly Thus a relativelylow 119888 value was sufficient for the adjustment of the decreasingspeed of 119892 in order to ensure that the search for the boundarysurface was stopped at the arterial boundary Figure 4 showsthe process of selection for the value of 119888 in Case 1 the resultsindicating that both VD and JM converged to a constant andMASD ceased all fluctuation when 119888 was taken to equate to05

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

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Disease Markers

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Oxidative Medicine and Cellular Longevity

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PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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ObesityJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

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Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 3

Table 1 Validation results of segmentation methodsCase 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Average

VD ()GT 0 0 0 0 0 0 0 0TLS 155 469 448 046 292 012 355 227 251RGT 765 447 886 137 552 609 321 1090 601CV 1163 1823 560 404 247 251 2418 1402 1034

JM ()GT 100 100 100 100 100 100 100 100TLS 9187 8966 8857 9325 9164 9235 9155 9379 9159RGT 9012 8824 8702 9300 9139 9090 9427 8958 9057CV 8824 8402 8673 8953 9185 9182 7696 8959 8734

rfp ()GT 0 0 0 0 0 0 0 0TLS 497 291 320 165 360 399 406 211 331RGT 064 380 1472 092 922 164 595 013 463CV 1184 1802 1326 538 460 554 2875 1162 1238

rfn ()GT 0 0 0 0 0 0 0 0TLS 357 325 151 521 140 397 473 423 348RGT 926 840 017 615 018 761 012 1030 527CV 132 084 178 566 393 309 092 000 219

HD (pixel)GT 0 0 0 0 0 0 0 0TLS 051 065 068 117 079 189 065 079 089RGT 077 064 089 141 055 186 049 076 092CV 075 117 104 209 119 051 100 095 109

MASD (pixel)GT 0 0 0 0 0 0 0 0TLS 008 008 007 009 007 005 007 010 008RGT 010 010 012 010 010 007 007 010 010CV 006 006 007 011 008 005 007 010 008

image 119868 reaching a threshold of 119879 If we isolate this first termof the RHS of (3) it becomes the selection criteria for thelower threshold in the Region Growing Threshold methodThe second term in the formula would likewise become theGeodesic Active Contour term

231 Method for Automatic Threshold Selection TheThresh-old-Based Level Set requires an appropriate estimate of thethreshold value from proper segmentation of the aneurysmobtained using Chan-Vese model and the statistical dataspecifically confidence interval (CI) and confidence level(CL)

232 Confidence Interval (CI) and Confidence Level (CL)The confidence level (CL) represents how often the truepercentage of a population lies within the confidence interval(CI) Based on Chebyshevrsquos inequality [24] a general rela-tionship for symmetric distribution between CI and CL canbe established The inequality for symmetric distribution isgiven as

119875 (1003816100381610038161003816119883 minus 120583

1003816100381610038161003816 ge 119896120590) le1

1198962119896 gt 0 (4)

where 119883 is the random variable population 120583 is the popula-tion mean and confidence interval is represented by 119896 times120590 standard deviation Equation (4) indicates that more than(1 minus (1119896

2) times 100) percent of the population lies between 119896

standard deviations from the population meanFor nonsymmetric distribution the one-tailed version of

the inequality is used This is given by

119875 (119883 minus 120583 ge 119896120590) le1

1 + 1198962

119896 gt 0 (5)

For this inequality it follows that when 119896 = 1 more than 50of the population is located one standard deviation away fromthe mean

233 Initial Threshold Selection According to the theoryof confidence interval the lower bound threshold of theaneurysm can be defined by

119879119894= 120583119886minus 119896119894120590119886

119894 ge 0 (6)

The threshold 119879 represents the difference between the meanof the intensity of the aneurysm (120583

119886) and 119896 times its standard

4 Computational and Mathematical Methods in Medicine

deviation (120590119886) The intensities of the aneurysm and its

background regions are different with the lowest intensitythreshold of the aneurysm being the same as the highestintensity threshold of the background Thus the relationship120583119887+ 119896119887120590119887= 120583119886minus 119896119886120590119886would apply The confidence levels for

both the aneurysm and its background are considered to bethe same 119896

119887= 119896119886= 119896 thereby allowing 119896 to be expressed as

119896 =120583119886minus 120583119887

120590119886minus 120590119887

(7)

We have utilized the Chan-Vesemodel method to perform aninitial segmentation From the results obtained the initial 119896

0

was seen to be calculated via (7) The initial 1198790can likewise

be found using (6)

24 Data Acquisition Clinical studies were performed withthe consent of the patient in relation to acquisition ofaneurysm imagesThese protocols were approved by the localinstitutional review board and the regional research ethicscommittee with eight data sets of patients harboring internalcarotid artery aneurysms acquired by 3D CTA scans (GEHealthcare)

Cross-sectional images were acquired by a CT angiogra-phy scanner with multidetector-row capability a table speedof 9mms and zero-degree table (and gantry tilt) Scanningwas initiated from the common carotid artery and continuedparallel to the orbitomeatal line to the level of the Circle ofWillis during this intravenous injection of contrast materialwas administered at a rate of 35mlss Aneurysm image was512 times 512 pixel field while slices of continuous thickness wereused to segment and reconstruct 3D vascular geometry Pixelsare expressed in Hounsfield Units (HU)

25 Experiment Setting For quantitative evaluation manualsegmentation of eight aneurysms using open source software3D Slicer was conducted by an expert radiologistThe resultswere utilized as a ground truth (GT) for the comparison ofother methods A region of interest (ROI) a good represen-tation of the targeted region for segmentation was selecteddepending on the aneurysm size All the experiments wereperformed on cropped data sets to reduce calculation timeand memory usage with preparatory work being completedprior to the conduction of the experiments

251 Parameter Setting

The Threshold-Based Level Set The initial zero level set is arectangular prism surface constructed by the subtraction oftwo pixels on either side of the ROI Thus three parametersneeded to be set 120572 120573 from (3) and 119888 from (8) All eightexperiments utilized a fixed setting of 120572 = 10 120573 = 3 and119888 in the range between 01 and 001 The role of this will beanalyzed in Section 4

The Chan-Vese Model The initial zero level set is a cuboidsurface constructed in the same manner as the TLS with theparameters in (2) fixed for all cases 120582

1= 1205822= 0001 120572 = 0

and 120573 = 03

GTTLS

RGTCV

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8Case number

Ane

urys

m v

olum

e (m

m3)

Figure 1 Aneurysm volume against segmentation methods

The Region Growing Threshold According to each case aninitial seed point is required to determine the starting lociwithin the specific aneurysm For low and high intensitythresholds 119879

1and 119879

2in (1) 119879

1was selected to utilize the

threshold of the TLS result for each case with1198792representing

the highest intensity of the aneurysm

26 Evaluation

(i) Aneurysm volume was calculated through the useof the boundary geometry segmented using variousmethods The volume difference (VD) was calculatedusing the equationVD = |(119881

2minus1198811)1198811|times100 where

1198811represents the volume of GT and119881

2represents the

volume of the TLS RGT or CV methods

(ii) Jaccardrsquos measure (JM) is a volume overlap metricused to count the percentage of voxel intersections forthe paired segmentations

This can be seen as JM = 2 lowast |1198781cap 1198782|1198781cup 1198782 where

1198781represents the voxels created by the GT and 119878

2the

voxels generated through the use of the TLS RGT orCV methods

(iii) False positive ratio (rfp) represents the percentage ofthe extra voxels of 119878

2 located outside of 119878

1 When the

rfp equates to zero no voxels in 1198782will be located

outside of 1198781 Accordingly rfp = (|119904

2| minus |1199041cap 1199042|)|1199041|

where 1198781represents the voxels created by the GT and

1198782represents the voxels generated by the TLS RGT

or CV methods

(iv) False negative ratio (rfn) represents the percentage ofthe lost voxels of 119878

2 which cover the internal surface

of the 1198781

This may be seen as rfn = (|1199041| minus |1199041cap 1199042|)|1199041| where

1198781represents the voxels created by the GT and 119878

2

Computational and Mathematical Methods in Medicine 5

Figure 2 3D geometries of segmentation results comparison from left to right CV RGT and TLS

Bleb

Figure 3 Segmentation results comparison (Case 1 aneurysm with bleb) from left to right GT CV RGT TLS and photo from open headsurgery

represents the voxels generated by the TLS RGT orCV methods

(v) Hausdorff distance (HD) measures the maximumsurface distance This measure is extremely sensitiveto outliers and may not reflect the overall degree ofcorrelation

(vi) Themean absolute surface distance (MASD) indicatesthe average degree of difference between two surfacesand does not depend on aneurysm size [15]

3 Results

The calculated values of VD JM rfp rfn HD and MASDfor the eight cases considered are tabulated in Table 1 Theaverage values are also shown Figure 1 depicts the volumeof the aneurysm The minimum VD can be seen in the TLSmethod The average value of VD is seen to be 251 Themaximum VD however is seen for Case 7 using the CVmethod The values of JM indicate that the TLS methodhas the highest overlap rate in comparison to the other twomethods with an average of 9159 A study of rfp and rfnindicates a 331 overflow and 348 absence on average forthe TLS method The largest rfp and the smallest rfn werefound to occur via the use of the CV method These resultslikewise indicate that the largest volume was generated by theCV method when compared to all other methods

Results obtained for the surface distancemetrics (HD andMASD) indicate the reliability of all segmentation methodswith the HD values for the TLS method being between 051to 189 pixels and the maximumMASD being 008

Figure 2 shows the 3D geometry of Case 4 restructuredvia three segmentation methods Only TLS was effective in

fully reconstructing the parent artery and aneurysm whilethe other two methods were not able to construct a portionof the artery One reason for this is that the aneurysm size inCase 4 is larger in comparison to other cases Another pointis that the distal parent artery itself is curved to lie proximallyto the aneurysm These results likewise indicate that the TLSmethod may be utilized in the segmentation of aneurysmswith blurred boundaries

Figure 3 represents the segmented aneurysm surfaces ofCase 1 where only TLS is able to restructure the bleb locatedat the top of the aneurysm The resulting image is similar tothe picture taken during open-skull surgery

4 Discussion

41 TLS Boundary Detect Function In this study the TLSmethod utilizes a boundary feature map

119892 (|nabla119868|) =1

1 + 119888|nabla119868|2 (8)

where 119892 is for the detection of vascular boundaries |nabla119868|represents a gradient magnitude and 119888 is a constant thatcontrols the slope of the boundary detect function119892(|nabla119868|) Atthe region of the artery and aneurysm the boundary intensitygradient was seen to increase significantly Thus a relativelylow 119888 value was sufficient for the adjustment of the decreasingspeed of 119892 in order to ensure that the search for the boundarysurface was stopped at the arterial boundary Figure 4 showsthe process of selection for the value of 119888 in Case 1 the resultsindicating that both VD and JM converged to a constant andMASD ceased all fluctuation when 119888 was taken to equate to05

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

4 Computational and Mathematical Methods in Medicine

deviation (120590119886) The intensities of the aneurysm and its

background regions are different with the lowest intensitythreshold of the aneurysm being the same as the highestintensity threshold of the background Thus the relationship120583119887+ 119896119887120590119887= 120583119886minus 119896119886120590119886would apply The confidence levels for

both the aneurysm and its background are considered to bethe same 119896

119887= 119896119886= 119896 thereby allowing 119896 to be expressed as

119896 =120583119886minus 120583119887

120590119886minus 120590119887

(7)

We have utilized the Chan-Vesemodel method to perform aninitial segmentation From the results obtained the initial 119896

0

was seen to be calculated via (7) The initial 1198790can likewise

be found using (6)

24 Data Acquisition Clinical studies were performed withthe consent of the patient in relation to acquisition ofaneurysm imagesThese protocols were approved by the localinstitutional review board and the regional research ethicscommittee with eight data sets of patients harboring internalcarotid artery aneurysms acquired by 3D CTA scans (GEHealthcare)

Cross-sectional images were acquired by a CT angiogra-phy scanner with multidetector-row capability a table speedof 9mms and zero-degree table (and gantry tilt) Scanningwas initiated from the common carotid artery and continuedparallel to the orbitomeatal line to the level of the Circle ofWillis during this intravenous injection of contrast materialwas administered at a rate of 35mlss Aneurysm image was512 times 512 pixel field while slices of continuous thickness wereused to segment and reconstruct 3D vascular geometry Pixelsare expressed in Hounsfield Units (HU)

25 Experiment Setting For quantitative evaluation manualsegmentation of eight aneurysms using open source software3D Slicer was conducted by an expert radiologistThe resultswere utilized as a ground truth (GT) for the comparison ofother methods A region of interest (ROI) a good represen-tation of the targeted region for segmentation was selecteddepending on the aneurysm size All the experiments wereperformed on cropped data sets to reduce calculation timeand memory usage with preparatory work being completedprior to the conduction of the experiments

251 Parameter Setting

The Threshold-Based Level Set The initial zero level set is arectangular prism surface constructed by the subtraction oftwo pixels on either side of the ROI Thus three parametersneeded to be set 120572 120573 from (3) and 119888 from (8) All eightexperiments utilized a fixed setting of 120572 = 10 120573 = 3 and119888 in the range between 01 and 001 The role of this will beanalyzed in Section 4

The Chan-Vese Model The initial zero level set is a cuboidsurface constructed in the same manner as the TLS with theparameters in (2) fixed for all cases 120582

1= 1205822= 0001 120572 = 0

and 120573 = 03

GTTLS

RGTCV

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8Case number

Ane

urys

m v

olum

e (m

m3)

Figure 1 Aneurysm volume against segmentation methods

The Region Growing Threshold According to each case aninitial seed point is required to determine the starting lociwithin the specific aneurysm For low and high intensitythresholds 119879

1and 119879

2in (1) 119879

1was selected to utilize the

threshold of the TLS result for each case with1198792representing

the highest intensity of the aneurysm

26 Evaluation

(i) Aneurysm volume was calculated through the useof the boundary geometry segmented using variousmethods The volume difference (VD) was calculatedusing the equationVD = |(119881

2minus1198811)1198811|times100 where

1198811represents the volume of GT and119881

2represents the

volume of the TLS RGT or CV methods

(ii) Jaccardrsquos measure (JM) is a volume overlap metricused to count the percentage of voxel intersections forthe paired segmentations

This can be seen as JM = 2 lowast |1198781cap 1198782|1198781cup 1198782 where

1198781represents the voxels created by the GT and 119878

2the

voxels generated through the use of the TLS RGT orCV methods

(iii) False positive ratio (rfp) represents the percentage ofthe extra voxels of 119878

2 located outside of 119878

1 When the

rfp equates to zero no voxels in 1198782will be located

outside of 1198781 Accordingly rfp = (|119904

2| minus |1199041cap 1199042|)|1199041|

where 1198781represents the voxels created by the GT and

1198782represents the voxels generated by the TLS RGT

or CV methods

(iv) False negative ratio (rfn) represents the percentage ofthe lost voxels of 119878

2 which cover the internal surface

of the 1198781

This may be seen as rfn = (|1199041| minus |1199041cap 1199042|)|1199041| where

1198781represents the voxels created by the GT and 119878

2

Computational and Mathematical Methods in Medicine 5

Figure 2 3D geometries of segmentation results comparison from left to right CV RGT and TLS

Bleb

Figure 3 Segmentation results comparison (Case 1 aneurysm with bleb) from left to right GT CV RGT TLS and photo from open headsurgery

represents the voxels generated by the TLS RGT orCV methods

(v) Hausdorff distance (HD) measures the maximumsurface distance This measure is extremely sensitiveto outliers and may not reflect the overall degree ofcorrelation

(vi) Themean absolute surface distance (MASD) indicatesthe average degree of difference between two surfacesand does not depend on aneurysm size [15]

3 Results

The calculated values of VD JM rfp rfn HD and MASDfor the eight cases considered are tabulated in Table 1 Theaverage values are also shown Figure 1 depicts the volumeof the aneurysm The minimum VD can be seen in the TLSmethod The average value of VD is seen to be 251 Themaximum VD however is seen for Case 7 using the CVmethod The values of JM indicate that the TLS methodhas the highest overlap rate in comparison to the other twomethods with an average of 9159 A study of rfp and rfnindicates a 331 overflow and 348 absence on average forthe TLS method The largest rfp and the smallest rfn werefound to occur via the use of the CV method These resultslikewise indicate that the largest volume was generated by theCV method when compared to all other methods

Results obtained for the surface distancemetrics (HD andMASD) indicate the reliability of all segmentation methodswith the HD values for the TLS method being between 051to 189 pixels and the maximumMASD being 008

Figure 2 shows the 3D geometry of Case 4 restructuredvia three segmentation methods Only TLS was effective in

fully reconstructing the parent artery and aneurysm whilethe other two methods were not able to construct a portionof the artery One reason for this is that the aneurysm size inCase 4 is larger in comparison to other cases Another pointis that the distal parent artery itself is curved to lie proximallyto the aneurysm These results likewise indicate that the TLSmethod may be utilized in the segmentation of aneurysmswith blurred boundaries

Figure 3 represents the segmented aneurysm surfaces ofCase 1 where only TLS is able to restructure the bleb locatedat the top of the aneurysm The resulting image is similar tothe picture taken during open-skull surgery

4 Discussion

41 TLS Boundary Detect Function In this study the TLSmethod utilizes a boundary feature map

119892 (|nabla119868|) =1

1 + 119888|nabla119868|2 (8)

where 119892 is for the detection of vascular boundaries |nabla119868|represents a gradient magnitude and 119888 is a constant thatcontrols the slope of the boundary detect function119892(|nabla119868|) Atthe region of the artery and aneurysm the boundary intensitygradient was seen to increase significantly Thus a relativelylow 119888 value was sufficient for the adjustment of the decreasingspeed of 119892 in order to ensure that the search for the boundarysurface was stopped at the arterial boundary Figure 4 showsthe process of selection for the value of 119888 in Case 1 the resultsindicating that both VD and JM converged to a constant andMASD ceased all fluctuation when 119888 was taken to equate to05

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 5

Figure 2 3D geometries of segmentation results comparison from left to right CV RGT and TLS

Bleb

Figure 3 Segmentation results comparison (Case 1 aneurysm with bleb) from left to right GT CV RGT TLS and photo from open headsurgery

represents the voxels generated by the TLS RGT orCV methods

(v) Hausdorff distance (HD) measures the maximumsurface distance This measure is extremely sensitiveto outliers and may not reflect the overall degree ofcorrelation

(vi) Themean absolute surface distance (MASD) indicatesthe average degree of difference between two surfacesand does not depend on aneurysm size [15]

3 Results

The calculated values of VD JM rfp rfn HD and MASDfor the eight cases considered are tabulated in Table 1 Theaverage values are also shown Figure 1 depicts the volumeof the aneurysm The minimum VD can be seen in the TLSmethod The average value of VD is seen to be 251 Themaximum VD however is seen for Case 7 using the CVmethod The values of JM indicate that the TLS methodhas the highest overlap rate in comparison to the other twomethods with an average of 9159 A study of rfp and rfnindicates a 331 overflow and 348 absence on average forthe TLS method The largest rfp and the smallest rfn werefound to occur via the use of the CV method These resultslikewise indicate that the largest volume was generated by theCV method when compared to all other methods

Results obtained for the surface distancemetrics (HD andMASD) indicate the reliability of all segmentation methodswith the HD values for the TLS method being between 051to 189 pixels and the maximumMASD being 008

Figure 2 shows the 3D geometry of Case 4 restructuredvia three segmentation methods Only TLS was effective in

fully reconstructing the parent artery and aneurysm whilethe other two methods were not able to construct a portionof the artery One reason for this is that the aneurysm size inCase 4 is larger in comparison to other cases Another pointis that the distal parent artery itself is curved to lie proximallyto the aneurysm These results likewise indicate that the TLSmethod may be utilized in the segmentation of aneurysmswith blurred boundaries

Figure 3 represents the segmented aneurysm surfaces ofCase 1 where only TLS is able to restructure the bleb locatedat the top of the aneurysm The resulting image is similar tothe picture taken during open-skull surgery

4 Discussion

41 TLS Boundary Detect Function In this study the TLSmethod utilizes a boundary feature map

119892 (|nabla119868|) =1

1 + 119888|nabla119868|2 (8)

where 119892 is for the detection of vascular boundaries |nabla119868|represents a gradient magnitude and 119888 is a constant thatcontrols the slope of the boundary detect function119892(|nabla119868|) Atthe region of the artery and aneurysm the boundary intensitygradient was seen to increase significantly Thus a relativelylow 119888 value was sufficient for the adjustment of the decreasingspeed of 119892 in order to ensure that the search for the boundarysurface was stopped at the arterial boundary Figure 4 showsthe process of selection for the value of 119888 in Case 1 the resultsindicating that both VD and JM converged to a constant andMASD ceased all fluctuation when 119888 was taken to equate to05

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

6 Computational and Mathematical Methods in Medicine

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12 14 16 18 20Iteration number

Case 1Case 2Case 3Case 4

Case 5Case 6Case 7Case 8

119879

Figure 4 The convergence history of threshold 119879

0

2

4

6

8

10

80

85

90

95

100

105

0 01 02 03 04 05 06 07 08

MA

SD (

)

VD

and

JM (

)

Boundary of intensity of the background and the aneurysm

VDJMMASD

C

Figure 5 Validation of TLS boundary detect function C (Case 1)

42 TLSThreshold Theconvergence history of threshold119879 isshown in Figure 5 with the 119879 volumes exhibiting a tendencyto converge after 15 iterations The stability of the 119879 volumeagainst a range of value of 119888 was likewise tested The volumewas found to be very stable for the range of 119888 between 05and 07 We thus suggest that the value of 119888 is set at a volumebetween 05 and 07 for accurate boundary detection As it isonly TLS that does not require selection of any seeds duringsegmentation it is suitable for the performance of automaticsegmentations

5 Conclusion

Various methods of segmentation generate a range of geo-metric models with changes in shape and volume withthe occurrence of uncertain results having the reductive

potential to negatively affect clinical treatment decisionsThrough analysis of eight cerebral aneurysm models thisstudy indicated that limitations continue to surround currentsegmentation methods The validation of the methods andanalysis of errors seem vital In this study the TLS methodwas proposed to improve cerebrovascular aneurysm segmen-tation application It is a technique with the ability to segmentaneurysms anatomically without the setting of a seed pointor intensity threshold The method is also suitable for thesegmentation of complex cerebrovascular anatomical shapes

Acknowledgments

The authors would like to thank members of MacquarieMedical Imaging Macquarie University Hospital for theirkind support and contributions to these cases

References

[1] N D Forkert A Schmidt-Richberg J Fiehler et al ldquoFuzzy-based vascular structure enhancement in Time-of-Flight MRAimages for improved segmentationrdquoMethods of Information inMedicine vol 50 no 1 pp 74ndash83 2011

[2] B E Chapman J O Stapelton and D L Parker ldquoIntracra-nial vessel segmentation from time-of-flight MRA using pre-processing of theMIP Z-buffer accuracy of the ZBS algorithmrdquoMedical Image Analysis vol 8 no 2 pp 113ndash126 2004

[3] M Droskey B Meyerz M Rumpfy and K Schaller ldquoAnadaptive level set method for medical image segmentationrdquo inProceedings of the Annual Symposium on Information Processingin Medical Imaging London UK 2001

[4] M E Leventon W E L Grimson and O Faugeras ldquoStatisticalshape influence in geodesic active contoursrdquo in Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo00) pp 316ndash323 June 2000

[5] P A Yushkevich J Piven H C Hazlett et al ldquoUser-guided 3Dactive contour segmentation of anatomical structures signifi-cantly improved efficiency and reliabilityrdquo NeuroImage vol 31no 3 pp 1116ndash1128 2006

[6] J A Sethian Level Set Methods and Fast Marching MethodsEvolving Interfaces in Geometry Fluid Mechanics ComputerVision and Materials Science Cambridge University 2nd edi-tion 1999

[7] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[8] S Osher and J A Sethian ldquoFronts propagating with curvature-dependent speed algorithms based onHamilton-Jacobi formu-lationsrdquo Journal of Computational Physics vol 79 no 1 pp 12ndash49 1988

[9] S Demirci G Lejeune and N Navab ldquoHybrid deformablemodel for aneurysm segmentationrdquo in Proceedings of IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo09) pp 33ndash36 July 2009

[10] N Wilson K Wang R W Dutton and C Taylor ldquoA softwareframework for creating patient specific geometric models frommedical imaging data for simulation based medical planningof vascular surgeryrdquo in Proceedings of the 4th InternationalConference onMedical Image Computing andComputer-AssistedIntervention (MICCAI rsquo01) pp 449ndash456 2001

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 7

[11] M W K Law and A C S Chung ldquoVessel and intracranialaneurysm segmentation using multi-range filters and localvariancesrdquo in Proceedings of the International Conference onMedical Image Computing and Computer-Assisted Intervention(MICCAI rsquo07) vol 10 part 1 pp 866ndash874 2007

[12] M Hernandez and A F Frangi ldquoNon-parametric geodesicactive regions method and evaluation for cerebral aneurysmssegmentation in 3DRA and CTArdquoMedical Image Analysis vol11 no 3 pp 224ndash241 2007

[13] T Deschamps P Schwartz D Trebotich P Colella D SalonerandRMalladi ldquoVessel segmentation and blood flow simulationusing level-sets and embedded boundary methodsrdquo Interna-tional Congress Series vol 1268 pp 75ndash80 2004

[14] R Manniesing B K Velthuis M S van Leeuwen I C vander Schaaf P J van Laar and W J Niessen ldquoLevel set basedcerebral vasculature segmentation and diameter quantificationin CT angiographyrdquo Medical Image Analysis vol 10 no 2 pp200ndash214 2006

[15] A Firouzian R Manniesing Z H Flach et al ldquoIntracranialaneurysm segmentation in 3D CT angiography method andquantitative validation with and without prior noise filteringrdquoEuropean Journal of Radiology vol 79 no 2 pp 299ndash304 2011

[16] T Zuva O O Olugbara S O Ojo and S M Ngwira ldquoImagesegmentation available techniques developments and openissuesrdquo Canadian Journal on Image Processing and ComputerVision vol 2 no 3 pp 20ndash29 2011

[17] H Zhang J E Fritts and S A Goldman ldquoImage segmentationevaluation a survey of unsupervised methodsrdquo ComputerVision and Image Understanding vol 110 no 2 pp 260ndash2802008

[18] 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

[19] Y Sen Y Qian Y Zhang and M Morgan ldquoA comparison ofmedical image segmentation methods for cerebral aneurysmcomputational hemodynamicsrdquo in Proceedings of the 4th Inter-national Conference on Biomedical Engineering and Informatics(BMEI rsquo11) vol 2 pp 901ndash904 2011

[20] V Caselles R Kimmel and G Sapiro ldquoGeodesic active con-toursrdquo International Journal of Computer Vision vol 22 no 1pp 61ndash79 1997

[21] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772001

[22] HuGrossberg andMageras ldquoSurvey of recent volumetricmed-ical image segmentation techniquesrdquo inBiomedical EngineeringC A B de Mello Ed InTech 2009

[23] D B Mumford and J Shah ldquoOptimal approximations by piece-wise smooth functions and associated variational problemsrdquoCommunications on Pure and Applied Mathematics vol 42 no5 pp 577ndash685 1989

[24] J Russell and R Cohn Chebyshevrsquos Inequality Book onDemand 2012

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom