-
CGI.2007 :: Computer Graphics International 2007 :: Petrópolis -
RJ - Brazil Página 1 de 6
H 10 t I Call for I Call for I Video I Conferenceome a es Papers
Tutorials Festival Organization
ConferenceProqr am
Accepted Papers
ConferenceRegistration I
Final ISubmission i
Conference Papers
# TitleYongBin Kang (Institute for CInterfaces)25748
XMegaWall: A Scalable, Super High-Resolution TiledDisplay using
a PC Cluster
25963 A sketch-based interactive framework for real-time
meshsegmentation
Authors
Huai-Yu Wu (Institute of Aut:Chineses Academy of Scienc:Chunhong
Pan (Institute of P.Chinese Academy of Science:Jia Pan (institute
of automatiacademy of sciences),Qing Yang (Institute of
AutorAcademy of Sciences),Songde Ma (Institute of AutoChinese
Academy of Science:
25988 A Novel Scheme for Efficient Cross-Parametehzation
Jia Pan (institute of automatiacademy of sciences),Huai-Yu Wu
(Institute of Aut.Chineses Academy of scienoChunhong Pan (Institute
of PChinese Academy of Science:Qing Yang (Institute of AutorAcademy
of Sciences)
26017 Attributes Processing for High Dynamic Range Images
Ming-Long Huang (National CUniversity),Chung-Ming Wang
(NationalUniversity)
26034A New Interest Point Detection and DescriptionAlgorithm
based on Bidimensional Empirical ModeDecomposition
----_.
Dongfeng Han (Jilin UniversitWenhui Li (Jilin University)
26037 Mass-based Comparison Metrics for Motion Graphs Mikiko
Matsunaga (UC RíversVictor Zordan (UC Riverside)
26038 Improved error estimate for extraordinary
Catmull-Clarksubdivision surface patches
Zhangjin Huang (Peking UnivGuoping Wang (Peking Unive
http.z/www.inf.ufrgs.br/cgizüü? /accepted.htm 1 23/4/2007
-
CGI.2007 :: Computer Graphics International 2007 :: Petrópolis -
RJ - Brazil Página 2 de 6
26050
26096
3D Reconstruction, Visualization and Volume Calculationof
Fruits
Lucio Jorge (Embrapa)
Shuhua Lai (Virginia State UrFuhua (Frank) Cheng
(UniverKentucky)
26219 Takahiro Harada (The Univer
26244
Shadow Generation for Scenes Represented by Catmull-Clark
Subdivision Surfaces
Smoothed Particle Hydrodynamics on GPUs
Visualization of Chaotic Dynamical Systems Based onMandelbrot
Set Methodology
Jin Cheng (Zhejiang Universi
26259 Min Tang (Zhejiang UniversitGeometry Image-based Shadow
Volume Algorithm forSubdivision Surfaces
26293 Automatically Construct Skeletons and ParametricStructures
for Polygonal Human Bodies Jituo Li (Academy of Chinese
26342-- -- ---- ------- ---
A unidimensional track motion method for acousticelastography
images under dynamic compression
Lucío.Pereira Neves (UniversPaulo),Ana Perini (University of
SãoAntonio A. O. Carneiro (Univ:Paulo)
26364 Manolis Lourakis (Foundationand Technology -
Hellas)Accurate Constraint-Based Modeling From A SinglePerspective
View
26385 30 As-Rlqld-As-Posslble Deformations Using MLS, ,
Alvaro Cuno (Universidade FIde Janeiro),Claudio Esperança
(UFRJ),Antonio Alberto Fernandes dE(Universidade Federal do
RioPaulo Cavalcanti (Universida:Rio de Janeiro)
26403
26416
26524
Slt~tistical Spherical Wavelet Moments for Content-based Hamid
Laga (Tokyo Institute3D Model Retrieval
Technology)---------------------------Dynamic Visualization of
Geographic Networks UsingDeformations
Gps, Gis and Video fusion for urban rnodelinq
Basak Alper (University of CcSanta Barbara),Selcuk Sumengen
(Sabanci LSelim Balcisoy (Sabanci Univ
Gaél Sourimant (Irisa / InriaLuce Morin (Irisa / UniversitÉKadi
Bouatouch (Irisa / Univr1)
26948
26966
A Framework for Real-Time Animation of Liquid-RigidBody
Interaction
A tool for teaching musical metrics based on computervision
Melih Kandemir (Bilkent UnivTolga Capin (Bilkent UniversiBulent
Ozguc (Bilkent Univer
Rodrigo Schramm (UNISmO~Claudio Jung (Universidade ddos Sinos
(UNISINOS))
26974 Stratified helix information of Medial-axis-pointsMatching
for 3D Model Retrieval
Ji Jia (Xi'an Jiaotong UniversiZheng Qin (Tsinghua UniversJiang
Lu (Xi'an Jiaotong Univ
27003 Generating Steering Behaviors for Virtual Humanoidsusing
BVP Control
Fábio Dapper (UFRGS),Edson Prestes e Silva Jr (UFFLuciana Nedel
(UFRGS)
http://www.inf.ufrgs.br/cgi2007/accepted.html
Carlos Cony (Universidade d<dos Sinos),
2314/2007
http://www.inf.ufrgs.br/cgi2007/accepted.html
-
As a consequence of the effort, we managed to put togethera
methodology, uncommon to find in the literature, which
_--'-'----'-~ __ ~'--~__"__~ çom-I~IÜ;es_.!he_whole_process of
creation of volumetricmodels, from acquisition to visualization and
propertycalculation, going through each step. Works published
inrelated subjects present techniques for each individual step,or a
combination of two of the steps (such as segmentationand
reconstruction, or reconstruction and visualization), butdo not
give a whole sequence of procedures, from thecollection of data on
the phenomenon under observation (inthis case fruits) to a
computational object that representstheir structure. Even in those
cases (as in medical images)where these techniques have been widely
employed, thereis little effort applied to the validation of the
final model.To complete the methodology, we also provide
itsvalidation by calculating the approximation error ofvolume
measurements.
L.A.C. Jorge, R. Minghim, L.G. Nonato, C.1.Biscegli, E.C.
Pedrino, V. O. Roda, M.S.V.Paiva
3D RECONSTRUCTION,VISUALIZATIONANDVOLUME CALCULATION OFFRUITS ,
'
,,I
, ,
Abstract This work presents a methodology.for the
threedimensional (3D) models frorn 2D magnetic- resonanceimage
frames, aimed for some studies on fruits. The 3Dmodels can be
employed for precise volumetric descriptionof objects of interest.
Becausc the volumetric model isprecise, the methcdology lends
itself to reliable volumecalculation. As anillustration of its use
in agriculture, a testcase of a mango tissue collapse is.used, The
.various partsof interest in the mango are reconstructed and their
volumedetermined. Validation of the developed methodology
wasperformed applying it for the reconstruction of two objectswith
known geometry and volumetric properties(phantorns). This gives an
estimare of the error imposed bythe procedure (0.15% .to 2.30/d),
thus legitimating themethodology fór' 3D model reconstruction.
Thecoritributions of this work include the full description of
thereconstruction process, from acquisition to visualizationand
manipulation, and the validation of the model formed.Additionally,
its novelty in thé field of agriculture opensncw possibilities for
researchers in that field ofactivity.
Kcywor ds 3D Reconstruction,Visualization, Fruit Analysis, MRI,
VTK
Segmentation,
I lntroduction
In scientific visualization, many three-dimensional
(3D)techniques for 20 image data analysis have been putforward and
applied to various fields, opening enormouspossibilitics in many
research areas, as well as manyquestions. New applications appear
oftcn, and in some ofthcm invasivc procedures may destroy parts of
the veryphcnornenon one wishes 10 observe and also may disturbthe
mcasuremcnts accuracy, such as volume. In agriculture,grcat effort
has been put imo quantifying fruit quality,including non-invasive
techniques based on data collectionfrom MRI and CT scans, those
are, however, mainly 2Dstrategies. The potential benefit from 3D
techniques in thiscontext highlights some questions, for instance:
howreliable are the modcls? \Vhat are lhe techniques suitable
10cvaluate fruit quality in visualization? \Vhat types ofpropcrties
can bc analyzed? This lias been the motivation
for lhe union of efforts between researchcrs in visualizationand
in agriculturc to develop the methodology for analysisof volumetric
fruit properties. Because thosc propertics canhelp interpret
physical and physiological structures, wecarried out an effort to
define what precision could beobtained from the data collection
available. Thefundamental problem solved by the
developedmethodology can be stated as: given images collected by
aMRI equipment with 0.2 em spacing intra-slice with nospacing
between si ices and resolution of 256x256 pixels,what kind of error
could be expected in the volumecalculation if a whole process of
reconstruction were to beapplied without any particular processing
to controlapproximation errors?
The main contributions of this work are: the developmentof an
effective methodology for 3D model reconstructionfrom MRl images
devised to produce a robusi and precisevolumetric mesh of the
reconstructed objects; thevalidation of such model for reliability
of volumecalculation; and the use of these results in the analysis
offruit problems, taking as test case the disease thatmotivated the
e ffo rt in the first place: mango tissuecollapse. An additional
real life application of thedeveloped methodology is presented, the
volurneuicreconstruction of a cashew nut.
ln the I next scction we give an overview of themethodology and
related work and justify for the particularchoices of tcchniques.
These techniques are described inthe subsequent sections and a
description of lhe resultsfollows.
2 Relatcd Work
There have been a nurnber of methods developed togenerate; 3D
models from 2D data. Research on thesemethods' can be found in the
field of the scientificvisualization, which has been widely applied
in medicine.We refer to the books edited by Fitzpatrick and Sonka
[10],Kirn and Horii [19) and Van Metter et aI. [22) as sources
ofmethods and references on the subject. There are examplesof
visualization in combination with other techniques inartificial
ncuron visualization and fluid dynarnics, as wellas dentistry [31).
Nowadays, the particular scqucnce ofmethods and pararncters
employed must be individually
-
I' . I
L.Á.c. Jorge, R. Minghim, L. G. Nonato, Ci l , l3isccgli, E.C.
Pedrino, V.O. Roda, M.S.V. Paiva
adaptcd to each problem, in thc case of this application
onagriculture.
Three steps are required to generate 3D models, namely:data
acquisition [I], image segmentation [29], [16], and
3Dreconstruction [26].
The first step, data acquisition, obtains two-dimensionalimages
frorn three-dirnensional objects. lt can be performedbya number of
devices, such as CT, MR1, and microscopicphotography. MRl has been
used in a number of fruitstudies with good results [7]. This fact
and the quality andresolution of lhe images produced motivated its
use in thepresent work. Several non-destructive methods to
analyzeand measure internal fruit defects have been presented inlhe
literature [38]; [7]; [6]; [14]. ln general, theselechniques apply
irnage processing methods that extractimportam features to estimate
area, shape, and evolution of
~fl'llit~degradation.-"fhese~pproaches are
linrited=almostexclusively to two-dimensional (20) images,
irnpairing theanalysis of three-dimensional (3D) structures, which
mightprove useful in certain applications. Making use ofcornputer
tornography (CT) [36] or magnetic resonanceimaging (MR1) [7]
devices to obtain 3D models from 2'0data has been a comrnon
practice mainly in medica]applications. By extending their use to
the fruits analysisand other agricultural products, it may be
possible toadvance our understanding about some diseases andthereby
aid the control of their manifestations. This isespecially true
where invasive procedures, such as actually. slicing 01-dicing, are
no! desirable [37]. ' .
The second step of the methodology, segmentation,.processes the.
images to identify and select elernents ofinterest.. There are many
techniques in '.the literaturedevoted ,to. image segmentation and
they can be groupedII1to several categories: edge-based [5], [24],
region-based[2], Markov random field-based [18], [4],
deformablemodels [39], and hybrid techniques [16]. Some of
thesemethods search for regions of interest, while some degreeof
similarity inside a region is used to detect its area. Othermethods
separate objects of interest by detecting edges thatseparate them.
Many of them use hybrid approaches. Thegoal in lhe class of
problems addressed here is to findboundaries bctwecn regions of
interest as well as 10describe lhe interior of these arcas. The
sezmentarionlecl.lnique proposed in [27] and used here ;as a
typeregion-bascd tcchnique, One of its advantages lies in thefact
that contour dcscriprion is intrinsic of the process,whilc othcr
region-based methods need a second pass at thedeicctcd regions 10
define thcm. Segmentation step requireslhe most proccssing time of
the whole procedure, includinuvarious levels of intcraction with
the user 10 achieve goodresults.
The Iast stcp of lhe process, three-dirnensionalrcconstruction,
builds gcometric models from thescgrnented images so thal they can
be used in simulationvisualization, intcraction, and data analysis.
In lhe type of3D reconstruction known as mesh generation (MG),
a1110del IS defincd by a number of cells, which could beplanar
cells (such as triangles) or volurnetric cells (such
astetrahedrons). Classes of techniques to obtain such modelsincJude
optimal [32], [23], deformable [34], and heuristicmodels [9], [3],
thc lauer being lhe rnost popular. These
techniques make use of graph theory, geornctry, anelproximity
metrics 10 achievc a satisfactory modcl frorncoruours thal define
the boundary of regions of interest inthe image seI. lt is also
possible to build meshes frorn lheoriginal data by 'detecting '
isosurfaces in thc data set (i.e.,without contour exlraction). In
this typc of approach, lheseries of original images are piled up 10
forrn a volume, andeach volume unit is checked for surface
intersection [20],[35]. The resulting models obtained from
isosurfacedetection have additional problems than those built
usingcontours. Meshes are toa large, details have
poorrepresentation, and defining if a particular face of the
rneshis 'inside' or ,'outside'. regarding a particular surface is
ae1ifficult task [28]. The reconstruction technique ernployedin
this work falls into the heuristic category, and lhe metricused for
mesh refinement has a topological nature, morerobust for
computational implementation. The choice ofthis-method was
determined by-the-characreristics of-lhemesh formed, which is
volumetric with comparatively lownumber of cells, and the aspect of
the model makes itadequate for simulation and visualization, as
shown inprevious works [28], [26].
One novel result on the applicability of lhe 3D modclsgenerated
by this methodology is related to lhe lhevalidation of lhe mesh
formation based on lhe calculationof the volume of the
reconstructed parts. An estimation ofthe error for the
reconstruction process supports lhe use ofthe methodology in a
number of applications in agricultureand elsewhere.· To validate
volume calculation, twophantom objects were used, for which precise
volumemeasurements were known. One was shaped as a sphereand the
other was constructed with a more complex, cube-shaped geometry. By
submitting these objects to the three-step procedure lhe
reconstruction error was obtained.
In order to demonstrate the potential of the tools putforward in
this work for agricultural applications,measurements of a mango
disease, the interna I collapse(Mangifera indica L.) were cornputed
and analyzed. Thisdisease is characterized by disintegration and
de-colorationof the pulp, with loss of its natural consistency. 11
rnakesthe fruit partially or totally inadequate for
consumption.Syrnptorns are the disinlcgration of the vascular
system inlhe regiot of ~ond bctween pcdunele and endocarp, whilelhe
fruit IS still 111 the tree. This causes the seed to bephysically
and physiologically insulated from tissues thatkeep thcm together
and gives rise to voids between theregions of the peduncle and
endocarp, so that tissucsaround this empty space start to lose
color. The sameoccurs to the pulp, which also begins to lose color,
mainlynear the cndocarp [8]. These features were not mcasurcdwith
precision before, and it is our expectation ihat beinzab!e to do so
\ViII open new frontiers in the study of thi~problern as well as
others in agriculture.
An additíonal example of applicability of the technique isthe
volumetric reconstruction of the cashew nut, The goalwith the
rcconstruction of this fruit is to build a zeometricalmodel that
will be useful to simulate forces applied durinzextraction of lhe
almond. In this case the precision of themodel is essential for the
reliability of the numericalsimulation involved.
-
3 L.A.C. Jorge, R. Minghim, L. G. Nonato, c.r. Bíscegll, E.C.
Pcdrino, V.O. Roda, M.S.V. Puiva
An MRI experiment has as resul! a signal map of thehydrogen (I
H) present in the analyzed sa~~ making i.~t _possible to-
distinguiShdifferences indensity and mobil ityof I H nuclei. In
fruits, these signals essentially come frornI H in free water
molecules (:::::95%). When nuclei, whichhave magnetic moments, are
subjected to an externalmagnetic field, they align in different
energy levels. ForI H, the nuclear spin Y2 will have two possible
orientationswith respect to the external field: parallel or
anti-parallel.The difference in energy between these two levels
isproportional to the externa I magnetic field strength. Likeother
spectroscopic rnethods, the purpose is to inducetransitions between
energy levels to obtain a non-equilibrium state. Then, relaxation .
to equilibrium isobserved r.and recorded. MRI images are obtained
byapplying radio-frequency pulses at the Larmor frequency ofI H
nuclei, adequately cornbined- with magnetic fieldgradient pulses.
Such pulses provide the .Iocation of theplane under observation. as
well as its thickness and its I Hnuclei distribution.
The next severa I sections cover each step of the proccss
inturn. lt is not our intent to give detailed description of
theinelividual techniques employed, rather to offer anoverview of
the various techniques employed, and toretlect the work performed
in tuning and validating thesetechniqucs for the applications
presented. This is followedby the method used for validating the
volume reconstructedand by the results of the work.
320 Imaging
3.1 Magnetic resonance in fruits
3.2 Data Acquisition
The images used in this work were obtained with theVarian 2
Tesla Magnetic Rcsonunce Imaging System atEmbrapa Agricullure
Instrumentation, São Carlos (SP),Brazil. Forty-six equally spaced
magnetic resonanceimagcs of each fruit were collected in the
sagitalorientation. MRI images of intact and diseased fruits
wereacquired using a birdcage radio frequency coil, with adiameter
of 14 em and 30 em in length, at a proton resonantfrequency of 85.5
MHz. Data was acquired using the Spin-Echo Mulli Slice pulse
sequence, with a 2s repetition timeanel an a 0.0 15s echo time.
Sliees were 0.2 em thick withno gap betwecn slices. Acquisition
time for the completeset of 46 tornograms was approxirnately 12
minutes.Because the signal to noise ratio is high, a single-pass
issufficient for acquiring elata. Complex data points wereacquircd
from this systcm by a workstation, proelucing a256x256 pixels
image. A 20 Fourier transforrn convertedthe original image to a
magnetic resonance image. Twocxarnplcs of M RI images of mangos
with correspondingphotographs can be seen in figure I. A dark
region rneansabsence of I H, while the white regions inelicate
presence of"free" I H. The severa I gray shades indicate the
regions inwhich I H has 101V mobility. Experirnents were carried
outon mangos of the variety Tomrny Atkins tMongifera
indica, L.). The sarnc process was applieel to the val
idationphantoms (sce validation section), and to other fruits.
a) b)
c) d)
Fig: a) One MRI slice of a mango presenting an internalcollapse
disease. b) Digital photography of the mango slicein figure Ia. c)
One MRI slice of a healthy mango forcomparison. d) Digital
photography of the slice in figureIc.
4 lmage Segmentation
In 3D reconstruction, the boundary curves (eontours) of
theinterest region segmentation need to be deteeted to be usedas
inputs for constructing a three-dirnensional model,Describing the
interior ofthese areas is also use fuI.
The segmentation technique employed here is region-basedanel
relies on a homogeneity function to partition the imageinto
regions. The overall idea of this type of segmentationalgorithm is
to verify, frorn an initial chosen region (orseed) in the image, if
each neighboring pixel to this regionshould be added to it. The
process continues, until there areno more neighboring pixels to be
attached to the region. Inthe case of the images for the mango
collapse, sceds forinside ~nd outside regions were chosen
inelividually forcore, hole, anel pulp.
The algorithm described in [27] ernploys a similarityfunction to
deciele if a neighbor pixel p should be addcd toa region R. This
function associate, to each pair of regionsRin and Rout, a real
value between O and I, where Rin andRout are the neighborhoods of p
located respectively insideand outside R. I f the value of the
sirnilarity function isclose to I, then p must be added to R. In
this work, thesimilarity function used was:
ctJ(R. R ) = I,n' uut (E(R. )-E(R »2 (I)
exp( /li ., OUI )0'-
Where E represents the mean of pixel values within eachregion
and 0'2 is the variance of the values in RmuRoul' Thealgorithm is
based on lhe concept of digital planar surfaces,dcfined as the
union of a set of 8-connected disjoint regions
-
'4 LA.C Jorge, R. Mingh im, L G. Nonato, C.L Bisccgli, E.C
Pcdrino, V.O. Roda, M.S.V. Paiva
planar cells [40]. To add a cell (or pixel) p to R,
thealgorithrn employs a set of Morse operators thal controlsthe
topology and the boundary curves of R. There is a setof 5 classes
of operators named k-handles used to eonstructthe surface by adding
one eell (-I$k$3). 11 can be proventhat given an object S with
Euler characteristic X(S) and ak-handle O" then X(SvO")=X(S)-k.
This property givescontrol over the topology of the region (and
boundary)during construction. With this capability, it is possible,
forinstance, to control the number of holes in a region. If thereis
previous knowledge of the expected shape of the regionunder
construction, as in the case of some of the problemsstudied, the
procedure is capable of 'filling out' undesirableholes in the
object thus eliminating noise. Other examplesof similarity
funetions and a precise definition of ali Morseoperators for
digital planar surfaces can be found in [27].
, Fig. 3 Model of the three objects of interest in the
mango,---- An_additLonaLadvantag~(Jhis
segmentatioD-algorilhnLis--reconsfructed from planar-MRl si
ices.
the fact that, at the same time that it separates regions in
theimage, it also provides well defined curves representingtheir
contours. Figure 2 illustrates segmentation of theimage in figure
Ia.
, . , -v ,
Fig: 2 Conlours\e'xtracted frorn irnage in figure Ia.
Before further processing, the bordering curves generated. were
simplified by point reduction, to avoid an excessivenumber of
geometric primitives in the final model. Thealgorithrn used takes
into account the curvature along thecontour [15].
5 3D Reconstructlon and Visuulizatlo n
The reconstruction ulgorithrn employed in this work wasbased on
Dclaunay 3D Reconstruction [26]. It begins bygcncrating a 3D
Delaunay triangulation [11] from theoriented set of contour points.
It then classifies the formedtetrahedrons as internal, external or
on the contours, inaccordance with their position. Next, reverse
tetrahedronsare identified. These are tetrahedrons that have just
oneedge in each slice, without being contour edges. Theyappcar
c\'cry time two contours are well positionedgcometrically [26],
giving an extremely useful heuristic forbranching and merging.
These reverse tetrahedrons aretherefore used to determine which
contours should beconnected. Then, externa I tetrahedrons
betweencornponcnts are eliminated to disconnect them. Thetechnique
also includes procedures to ensure the model isconsistent with the
original contours and avoid singularitiesso that thcy can be used
for nurnerical simulation. Adaptivercfincment however would be a
useful additional feature[30). lnteractive exploration benefits
from the algorithrnbecause the rcsulting mesh is not as large as
those createdby other methods. The technique was qualitatively
compared before with traditional isosurface
constructionapproachcs [28] and to other Delaunay
basedreconstruction lechniquesadvantages. Figure 3 showsthe mango
in this study.
[40], presenting somethe resulting model built for
The basie visualization software used is VTK - TheVisualization
Toolkit [33] whieh is an extensible librarythat implernents many
visualization methods.
Before proceeding to analyze the results of modeling
andvisualizing 3D structures in the diseased mango, avalidation
procedure was earried out using two real lifeobjeets, for whieh the
volume eould be caleulated with highprecision. This validation
procedure, described in the nextseetion, estimates the
reconstruetion error.
6 Validation Regarding Volume Calculation
11 is important to know how reliable are the rnodelsobtai'ned by
reeonstruetion, although this is rarely discussedin the literature.
lmportant issues when judging reliabilityrefer to the aspect of the
model and of its individual cells.The most desirable features in a
modeling mesh are:absence of singularities, consistency with
original objectslicing, reduced number ofcells and cell aspect
ratio. Thesefeatures are intrinsic of the reconstruction method
[26]. Anadditional picce of information to validate its use for
anurnber of applications is its effectiveness for
volumecalculation. This would indicate adequacy of the moelel
todefine J..,ell the region inside the object boundaries. In
thecase of fruit diseases it would be possible to estimare
theportion affected.
A useful method for the purpose of vai idation employs anobject
with known geometry anel volume, callcd a'phantom'. Because the
exact internal dimensions of aparticular phantorn and the value of
its volume are known,it can be eompared with the volume calculated
from areconstructed version of the sarne phantorn. Due to thelarge
nurnber of approximations used in lhe reconstructionprocess,' a
certain degree of inaccuracy is expected. Ameasurernent of this
inaccuracy is the target of thevalidation procedure.
For the methodology presented here, two phantoms wereemployed,
to account for two different geornetrical forms.A cubical phantorn
(see figure 4) was designcd and builtusing small plates of
polymethylmethacrylate. A sphericalphantorn (a table-tennis ball)
was also used. Both phantornswere filled with 1% watcr solution of
Copper Sulphate
-
5 L.A.C. Jorge, R. Minghim, L. G. Nonato, c.r. Biscegli, E.C.
Pedrino, V.O. Roda, M.S.V. Paiva
(Cl;2S04), to lower the relaxation times TI and T2 belowlhe
values for tap water, imaged using the same M RIacquisition method
described above, and processed by thesame set 3-D reconstruction
procedures applicd to themango. The cubic phantom was built with a
designedvolume of 108.0 cm3, while the actua l amount of
watersolution of copper sulphate it was capable of holding
was107.84 em3. The sphere had an external diameter of 3.76em, with
an external volume of 27.83 cm3 and filledvolume of 25.95 cm3. 801h
phantoms were 'sliced' every0.2em with no gap between slices (same
approach as withlhe mango). No steps were taken to reduce error
during lhevarious phases of the procedure.
h J ib)a)
Fig. 4 Phantom, designed and built to validate volumecalculation
from rcconstructed models.
7 Results and Discussion
Applying MRI to investigate the internal quality of freshfruits
is a natural and very important extension of itshistorical
introduction in medicine as an imaging techniquefor diagnosis [13],
[21], [12], [25]. The main advantage ofMRI over other investiga
tive approaches is its non-invasiveand non-destructive nature,
Figure I a presents a sagitaltomography of a mango with tissue
eollapse. The core, thevoid, and the pulp are ali visible. Figure I
b presents adigital photograph of the same mango opened with
ahaeksaw approximately at the same location. Figures I cand I d
illuslrate a healthy mango for comparison. 8ecausethere is no
tissue collapse in the healthy mango, the darkgray regions around
the core (figure I c) are due to thewcak magnetic resonance signal
frorn the low mobility I Hof lhe externa I solid arid dry tissues
of the core. Due to lhenature of the segmentation proeess used
here, that grayregion, ir segmented, could be interactively
included eitherin the core 01' in the pulp region, at user 's
choice. Includingit in the core would be lhe correct choice.
The method employed here for segrnentation behavesparticularly
well when boundaries have uniform intensitiesover their complete
extent. For instance, the separationbetween hole and pulp to the
right of the core in figure I ais wcll capturcd by the method (see
figure 2), even wherethe actual boundary is just slightly visible
(that is, darkregions are visually mixed with clear regions).
Dependingon user needs, either of the attained properties (region
oreontour) can be used. In this case, we used ali the
contoursgenerated by the segmentation proeedure for every
slice,that is, the boundary curves presented in blaek in figure
2.
Frorn the contours cxtraeted in lhe whole set of slices, amodcl
was built for the parts of interest in the fruit, whiehwas furthcr
explorcd. One set of modcls, formed by
processing ali frames with three regions of interest (pulp,hole
and core), is presented in figure 5, and the triangularmesh of its
exterior part is shown in figure 6. Thisgeornctric rnodel was used
for interaction, analysis andcalculation. It is aetually composed
of tetrahedrons thoughon the screen only the boundary of the model
is displayed.Figure 7 shows a part of the reconstruction of one 01'
thephantoms to illustrate this property. Volume
calculationsinvolved summing lhe volumes of eaeh of its interna
Itetrahedrons,
Fig, 5 Reconstruction of the three parts of interest in
thediseased mango. a) Core b) Void caused by
physiologicaldisturbance. c) Pulp.
Fig. 6 Mesh for the exterior surfaee of the mango.
A model was created for each of the phantoms describedpreviously
(figure 8b and 8d) using the same seanningparameters as for the
mango (see figure 8a and 8e forparticular sliees). For MRI scanning
of the eubie phantorn,it was placed at a 45-degree inclination to
the equipmentaxis. The approximations imposed by the
reconstruetionprocess have a visual effeet in the resulting mcdcls,
whichc~n belobserved in figure 8b. For the cubic phantorn, 23slices
were generated, while for the sphere, 19 sliees wereprodueed.
Fig.7 Tetrahedrons in a reconstrueted object. A
shrinkingalgorithrn was used to split the individual
tetrahedronsapart.
-
· 6j-j·c.@·Q" ...• -101 xl
L.A.C. Jorge, R. Minghlm, L. G. Nonato, C.I. Biscegli, E.C.
Pcdrino, V.O. Roda, M.S.V. Paiva
a) b)
i i " 1i iA "" • '~I.I
oc) d)
Fig.S Phantom reconstruction. a) MRI of the cubicphantom. b)
reconstructed model for the cubic phantom. c)MRI of the spherical
pharuorn. d) reconstructed model forthe spherical phantom.
The volume of the reconstructed spherical phantom was0.15%
higher than the actual sphere and the volume of thecubical phantom
was 2.3% higher than the actual volumeof the original object
(25.988447 cm3 for the sphere and116.25 cm3 for the cubic object).
The number oftetrahedrons is an indication of the size of the rnesh
andtherefore of the time needed to calculate '
volumetricproperties. The number of tetrahedrons generated
here(2565 for the sphere, 7636 for the cube, and 11081 for thewhole
mango) can be handled easily by most computersrunning the software,
and the processing time for volumecalculation is not a significant
portion of the full processoThe void caused by the disease in the
studied case wascalculated to be 4.04% of the volume of the
mango.Because the pulp is 92.47% of the mango, the collapsedpart
would correspond to 4.37% of the volume of the pulp.The resulting
values for the volumes were consideredsatisfactory, taking into
account that crrors can occur inmany parts of image manipulation,
including acquisition(for instance, there is always a slice of the
object missingfrorn cach cnd of the image set). Thercfore, errors
of 0.15to 2.3% wcre found for the phantorns. So, if
thescgrnentation proccss for the application of fruit analysis
isacccptable, it is possible to have the sarne rates of errors
inthe reconstruction, especially because it was reduced noisein the
intcrrncdiate steps of rcconstruction. If moreaccuracy is nccded,
approximation crrors could be reducedby a series of extra
precautions during processing, such asmesh smoothing, active noise
rcduction and control ofapproxirnation crror.
An additional model, for the case of a cashew nut (seefigure 9)
was also built. The intention with this mede! is touse its
geometric represcntation to simulare forces on thenut during the
extraction of the almond. By studying itsbehavior under such
forces, it may be possible tomanufacture a device to irnprove the
unsatisfactory manualextraction process currently uscd.
a) b)
Fig.9 Reconstruction of a cashew nut and almond, a)boundary of
meshes of both nut and almond. b)Visualization of the cashew
nut.
Besides providing 3D measurements, reconstructionmodels can also
provide internal views of the object underanalysis that would be
impossible to see unless the fruit hadbeen sliced, diced, or
actually cut in any way. For instance,
- figu re-I O shows-sorne manipulation of the model using
aninteractive technique implemented in the system. A'cursor' is
used to mark a path on the fruit surfaces, startingwith the externa
I object. When the path is closed, thesurface enclosed by it can be
'cut', and the cut can betreated as a separate object (figures 10a
to 10d). This objectcan be manipulated separately, or even deleted
from thescene. With this 'opening ', the user can actually
walkthrough the mango and explore its structures internally.The
process can be repeated for internal objects. Figure 10eillustrates
the view of the core through cuts in both theexterna I object and
the hole. This technology allowsnonphysical operations and insights
that would beimpossible in the real world, such as 'seeing a hole
in 3D',or even 'cutting a hole' to see the core. This
flexibilitycould be useful for a number of known or
novelapplications.
c)
@I ,Fig.IO Various levels of interaction with the
mangornodels.,
8 Conclusions
The methodology developed in this work represents aninnovative
contribution where the reliability of 3D modelconstruction is
importam. First, because it covers the wholeprocess from
acquisition to model manipulation, offeringdetailed instruction for
potential users. Second, because itvalidates the mcdel created
against volume calculation, aquality missing in other
reconstruction efforts which hasrestricted their use.
-
- 7 L.A.C. Jorge, R. Minghim, L. G. Nonato, C.I. Bisccgli, E.C.
Pedrino, V.O. Roda, M.S.V. Paiva
3. Boissonnat, J-D., 1988. Shape reconstruction frornplanar
cross sections, Computer Vision, Graphics andImage Processing,
44,1-29.
4. Bouman, c., 1995. Markov Randorn Fields andStochastie Image
Models. Tutorial presented at IEEEInter. Conf. on Image Processing,
Washington, 23-25.
5. Canny, 1., 1986. A cornputational approach 10 edgedetection,
IEEE Trans. Pauern Ana!. Maehine lntell.,8,679-698.
6. CIark, C.1., Burmeister, D.M., 1999. Magnetieresonanee
imaging of browning development in'Braeburn' appIe during
controlled-atmosphere storage
Many areas in agrieuIture ean benefit from the use of the under
high C02. Hortscience, 34(5), 915-919.developed methodology.
ExampIes include study of 7. Clark, C.1., Hockings, P.D., Joyce,
D.C., Mazucco,disease~ 'in fruits, analysis of structure of fruit
elements (as R.A., 1997. Application of magnetic resonancein the
cashew nut case), study of soil behavior and analysis imaging to
pre and post-harvest studies of fruits andof factors that influence
fat and w~ter content lJ1 meat, to vegetables. Post-harvest Biol
and Technol, 11, 1-21.mention a few. Forinstance, the accuracy of
the 3D mesh --8_ Cunha, M.M.,- Santos-Filho,H7P-"Nascimento,-S.A.IS
necessary to anow a reliable simulation of the forces (Org.), 2000.
Manga: Fitossanidade. Brasília, DF:applied on the cashew nut during
extraction of the almond. Embrapa Comunicação para Transferência
deThis work has just started with the reconstrucnon of Tecnologia
.. Chapt 5, 71-73.cashew models. In the case 01' soil, a ,study is
being planned 9. Ekoule, A. B., Peyrin, F. c., Odet, C. L., 1991.
Afor development of a metric .of 'porosity through the
Triangulation Algorithm frorn Arbitrary Shapedcalculation of volume
of capillaries reconstructed frorn soil Multiple Planar Contours,
ACM Trans. on Graph.,samples, As for the mango, the measurement of
volume of 10(2), 182-199.tissue collapse serves as starting point
for the development 10. Fitzpatrick, J. M., Sonka, M. (Eds.), 2000.
Handbookof a biophysical model that describes the phenomenon. of
Medical Imaging, Volume 2, Medical ImageThis model, together. with
additi~nal data on n~ango Proeessing and Analysis, SPIE Press,
Washington DC,plantations could support the description of the
evolution of USA.
the disturbanc~ and guide the manipulation of the problem lI.
Fortune, S., 1994. Voronoi Diagrams and Delaunaytherein.'
Triangulation. Computing in Euclidean Geometry. Ou,
D-Z., Hwang, F.K. (Eds.), World Scientific Pub.
Co.,193-233.Foster, M.A., 1984. Magnetic resonanee in medicineand
biology. Pergamon, Oxford, U.K.
13. Gadian, D.G., 1982. Nuclear magnetic resonance andits
applications to living systems. Oxford Univ. Press,Oxford, U.K.
14. Gonzalez, J.J., ValIe, R.C., Bobroff, S., Biasi,
W.V.,Mitcham, E.1., McCarthy, M.1., 2001. Detection andmonitoring
of interna I browning development in "Fuj i"applcs us ing MRI.
Post-harvest Biol. and Techno!., 22,179-188.
15. Hamann B., Chen J-L., 1994. Data point selectian
forpiebewise linear curve approximation. CornpurerAided Geometric
Design, 11, 289-30 I.
16. Haris K., Efstratiadis S., 1998. Hybrid ImageSegrnentation
Using watersheds and Fast Region
17. Merging. IEEE. Trans. on lrnage Processing, 7(
12),1684-1699.
18. Kato Z., 1994. Multi-scale Markovian Modelisation inComputer
Vision with Application to SPOT ImagcSegmentation, PhD Thesis,
Universtity ofNice.
19. Kim, Y., Horii, S. C. (Eds.), 2000. Handbook ofMedical
Imaging, Volume 3, Display and PACS, SPIEPress, Washington DC,
USA.Lorensen, W. E., Cline, H. E., 1987. Marching Cubes:A
high-resolution 3D surface construction algorithm.ACM SIGGRAPH
ComputerGraphics21(4), 163-168.Mansfield, P., Morris, P.G., 1982.
NMR imaging inbiomedicine. Academie Press, New York.Van Metter, R.
L., Beutel, J., Kundel, H. L. (Eds.),2000. Handbook of Medical
Imaging, Volume I.
The qualities inherent of the segmentation andreconstruction
methods were favorable here. In thesegmentation algorithm, the
topological control over thesurface construction speeds up the
reconstruction processoBy having an idea of the shape of the
objects undergoingreeonstruction it was possible to eliminare noisy
regions inthe data while maintaining the actual 'holes' that were
partof' lhe structure under analysis. ln the volumereconstruction
step, the topological tests and the quality ofthe mesh formed gave
robustness and good definition ofthe object formed.
Being the only methodology for 3D reconstructioneurrently that
had the volume caleulation validated, it isexpected that the
eontribution presented here wilI haveapplication in Il,lany other
fields of science. This aspect,added to the intrinsic qualities of
the volumetric modelgenerated by the reconstruction rnethod, alIows
forexpansion of its use for other applications, such as
medica!.
It must be noticed that the methodology requires goodquality
irnages for its accuraey, reason why the use of MRIis important as
the acquisition rnethod, Low quality imagesthat produced noise on
the boundary of the regions ofinterest would generate impreeise
coruour definition,impairing the creation of rcliable models.
Besides providing a fulI methodology for datamanipulation frorn
image to interaction, this work gives acontribution for the
discussion of validation ofreconstruction methods, particularly in
the case wherevolume calculation is of concern.
References
I .. Beutel, 1., Kundel, H., Van Metter, R. L. (Eds.),
2000,Handbook of Medical Imaging, I, Physics andPsychophysics, SPI
E Press.
2. Baraldi A., Parmiggiani F., 1996. Single linkageregion
growing algorithrns based on the vector degreeof match. IEEE Trans.
on Geoscience and RemeteSensing, 34(1),137-148.
12.
20.
21.
22.
-
L.A.C. Jorge, R. Minghim, L. G. Nonato, c.r, Blsccgti, E.C.
Pedrino, V.O. Roda, M.S.V. raiva
Nonato, L.G., Castelo, A., Minghim, R.,
Batista,~~---J.E.S.-,---200 I
b~Mor-se-operators-foF-digital-planar----R..Minghim, L.G ...Nonato
- --
surfaces and their application to image segmentation.
Departamento de Ciências de,Computação e Estatística, ICMC·IEEE
Transactions on Image Processing 13(2):216- USP, Avenida
Trabalhador Sao-carlense, 400 - C. P. 668. 13560-227 2004 ' 970,
São Carlos, SP, Brazil
, . E-mail:
[email protected];gnonatoCã)iclllc.usp.brNonato, L.G.,
Minghim, R., Shimabukuro, M.H.,2000. Qual itative Analysis of two
ReconstructionTechniques and their application in Dentistry.
Journalof Electronic Imaging, 9(4), 385-393.PaI, N., PaI, S., 1993.
A review on image segmentationtechniques. Pattern Recognition, 26,
1277-1294.Shewchuk, J. R., 1998. Tetrahedral Mesh Generationby
Delaunay Refinement. Proceeding of 14th. AnnualSimposium on
Computational Geometry, ACM Press,86-96.
31. Shirnabukuro, M. H., Minghim, R., Licciardi,P.R.D.B., 1998.
Implementing VisualizationProcedures in Dental Applications,
Proceedings of
. Information Visualization '98, London, UK, IEEE CSPress,
pp.25-31.
32. Shinagawa, Y., Kunii, T. L., 1991. The homotopymodel: a
generalized model for smooth surfacegeneration from cross sectional
data, The VisualComputer, 7, 72-86, 1991.
33. Schrõedcr, W.J., Martin, K., Lorensen, W., 1998.
TheVisualization Toolkit, An Object-Oricnted Approachto 3D
Graphics. 2nd cd. Prentice-Hall EnalewoodCliffs, NJ. ' ~
34. Singh, A. Goldgof, E., Terzopoulos, E. (Eds.),
1998.Dcformablc Models in Medicallmage Analysis, IEEECS Press.
35. Treece, G. M, Prager, R. W., Gee, A. H., 1998.Regularised
Marching Tetrahedra: ImprovedEsosurface Extraction, CUED/F-INFENG
TechnicaIRcport 333, Cambridge University
EngineeringDepartment.
36. Thomas, P., Kannan, A., Dgwekar, V.H.,Ramamurthy, M.S.,
1995. Non-destructive detection ofseed weevil-infested mango fruits
by X-ray imaging.Post-harvest BioI and TechnoI, 5,161-165.
37. Wang, c.v., Wang, P.C., 1989. Nondestructivedetection of
core breakdown in "Bartlett" pears withnuclear magnetic resonance
imaging. Hortscience,24(1),106-109.
38. Wang, c.v., Wang, P.c., Faust, M., 1988. Non-destructive
detection of watercore in apple withnuclear magnetic resonance
imaging. ScientiaHorticulturae, 35, 227-234.
Physics and Psychophysies, SPIE Press, WashingtonDC, USA.
23. Meyers O., Skinner, S., Sloan, K., 1992. Surface
fromContours, ACM Trans. on Graphics, II (3),228-258.
24. Monga, O., Deriche, R., Malandain, G., Cocquerez,J.P., 1991.
Recursive filtering and edge tracking: Twoprimary tools for 3D edge
detection. lmage Vis.Comput., 9(4), 203-214.
25. Morris, P.G., 1986. Nuclear magnetic resonance 111. medicine
and biology. Oxford Un]v. Press, Oxford,U.K.
26. Nonato, L.G., Minghim, R., Oliveira, M. C. F.,Tavares, G.,
200 I a. A Novel Approach for Delaunay3D Reconstruction with a
comparative analysis in theLight of Applications. Computer Graphics
Forum.,20(2),161-174.
27.
28.
29.
30.
39. Xu, c., Pharn, D.L. and Prince, J.L., 2000.
1mageSegmentation using Deformable Models. 111Fitzpatrick, J. M.,
Sonka, M. (Eds.), Handbook ofMedical1maging, 2, chapt. 3. SPIE
Press.
40. Nonato, L.G., Castelo, A., Campos, J.E.P.P., Biscaro,H.H.,
Minghim, R. Topological TetrahedronCharacterization with
Application in VolumeReconstruction. International journal of
shapemodeling, II (2): 189-216,2005 .
L.A.C. Jorge, C.I. BiscegliEmbrapa Instrumentação Agropecuária,
Rua 15 de Novembro,1452, C.P. 741, 13560-970, São Carlos, sr -
BrazilTe!.: +55-16-33742477Fax: +55-16-33725958E-mail:
lucio(ri)cnpdia.embrapa.br;[email protected]
V.O ..Roda, E.C. Pedrino, M.S.V. PaivaDepartamento de Engenharia
Elétrica, EESC-USPAvenida Trabalhador São-carlense, 400 - 13566-590
- São Carlos,sr, BrazilTe!.: +55-16-33739371FAX:
+55-16-33739372E-mail:
valentin@se!.eesc.lIsp.br;[email protected];[email protected]
mailto:[email protected]
