Research Article Coronary Arteries Segmentation Based on...
Transcript of Research Article Coronary Arteries Segmentation Based on...
Research ArticleCoronary Arteries Segmentation Based on the 3D DiscreteWavelet Transform and 3D Neutrosophic Transform
Shuo-Tsung Chen123 Tzung-Dau Wang4 Wen-Jeng Lee5 Tsai-Wei Huang6
Pei-Kai Hung1 Cheng-Yu Wei78 Chung-Ming Chen1 and Woon-Man Kung79
1 Institute of Biomedical Engineering National Taiwan University Taipei 10617 Taiwan2Department of Applied Mathematics Tunghai University Taichung 40704 Taiwan3Sustainability Research Center Tunghai University Taichung 40704 Taiwan4Cardiovascular Center and Division of Cardiology Department of Internal MedicineNational Taiwan University Hospital Taipei 10048 Taiwan5Department of Medical Imaging National Taiwan University Hospital Taipei 10048 Taiwan6Department of Nursing College of Medicine and Nursing Hungkuang University Taichung 43302 Taiwan7Department of Exercise and Health Promotion College of Education Chinese Culture University Taipei 11114 Taiwan8Department of Neurology Chang Bing Show Chwan Memorial Hospital Changhua 50544 Taiwan9Department of Neurosurgery Lo-Hsu Foundation Lotung Poh-Ai Hospital Luodong Yilan 26546 Taiwan
Correspondence should be addressed to Chung-Ming Chen chungntuedutw andWoon-ManKung nskungwmyahoocomtw
Received 19 July 2014 Accepted 11 October 2014
Academic Editor Kuo-Sheng Hung
Copyright copy 2015 Shuo-Tsung Chen et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Purpose Most applications in the field of medical image processing require precise estimation To improve the accuracy ofsegmentation this study aimed to propose a novel segmentation method for coronary arteries to allow for the automatic andaccurate detection of coronary pathologiesMethodsThe proposed segmentationmethod included 2 parts First 3D region growingwas applied to give the initial segmentation of coronary arteries Next the location of vessel information HHH subband coefficientsof the 3DDWT was detected by the proposed vessel-texture discrimination algorithm Based on the initial segmentation 3DDWTintegrated with the 3D neutrosophic transformation could accurately detect the coronary arteries Results Each subbranch of thesegmented coronary arteries was segmented correctly by the proposed method The obtained results are compared with thoseground truth values obtained from the commercial software from GE Healthcare and the level-set method proposed by Yanget al 2007 Results indicate that the proposed method is better in terms of efficiency analyzed Conclusion Based on the initialsegmentation of coronary arteries obtained from 3D region growing one-level 3D DWT and 3D neutrosophic transformation canbe applied to detect coronary pathologies accurately
1 Introduction
Efficient and automatic image segmentation methods areuseful for the isolation and visualization of vessels in com-puted tomographic angiography (CTA) There are manyproposed methods for the segmentation of vessels [1ndash14] Avessel filter [1] can be used to enhance tubular structurehowever it cannot address the problem of the image forceand veins which can lead to a narrowed or broken seg-mentation of vessels Parametric shape models [2ndash5] do notdirectly allow for the detection of topological changes and
they usually obtain a seriously narrowed segmentation inthe neighborhood of a branch point in the vessel Level-setapproaches [6ndash13] are computationally expensive They alsosuffer from leakage at places where the intensity gradientsof the edges are relatively weak and are very sensitive tothe placement of the initial contour of the propagatingfront Metz et al [14] used the minimum cost path ofthe specified start and end points in vessel to detect thecoronary arteries centerlineThis is not an automaticmethoddetecting branches is difficult Friman [15] proposedmultiplehypothesis template tracking which follows the direction of
Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 798303 9 pageshttpdxdoiorg1011552015798303
2 BioMed Research International
centerline obtained in advance However it is difficult todetect small branches and vessels by using this method
In this study we propose a newmethod for automaticallyand correctly segmenting coronary arteries from CTA datasets In image preprocessing we detected the aorta auto-matically by using methods proposed in the literature [516] The proposed coronary arteries segmentation method issummarized as follows First of all we automatically obtainedthe seed point of a 3D region growing by the differencebetween the two adjacent slices due to the small changesof the aorta between two adjacent slices Next 3D regiongrowing was applied to initially search for the probablelocation of coronary arteries which was then dilated by 3voxels Based on the dilation of the probable location wedetected the coronary arteries accurately by applying the 3Ddiscrete wavelet transformation (DWT) and 3Dneutrosophictransformation to the CTA volume The location of vesselinformation in HHH subband coefficients was detectedby the proposed vessel-texture discrimination algorithmAccordingly HHH subband coefficients were used whichwere characterized and classified by 120572-means operation and119870-means clustering Finally the proposed method was testedon several CTA data sets and the experimental resultsindicated that the proposedmethod had a good performance
The rest of this study is organized as follows Section 2reviews some preliminaries and Section 3 uses 3D regiongrowing and 3DDWT to propose a newmethod for segment-ing coronary arteries Section 4 contains the experiments anddiscussion and the conclusions are drawn in Section 5
2 Preliminaries
In this section we will briefly introduce the concepts of DWTand provide an overview of some fundamental mathematicalconcepts that are used in this study
21 Region Growing Region growing is a simple well-developed region-based image segmentation technique [17]It postulates that neighboring voxels within the same regionhave similar intensity values and is also classified as a voxel-based image segmentation method since it involves theselection of initial seed points In other words this methodof segmentation examines neighboring voxels of initial seedpoints and determines whether neighboring voxels should beadded to the region Consequentially the general concept ofregion growing is to group voxels with the same or similarintensities to one region according to the given seed pointsand a homogeneity criterion
22 Discrete Wavelet Transform Wavelet transform isobtained by a single prototype function 120595(119909) which isregulated with scaling and shift parameters To construct120595(119909) a scaling function 120593(119909) is determined The discretenormalized scaling and wavelet basis functions are definedas
120593119894119899 (
119905) = 21198942
120593 (2119894119905 minus 119899)
120595119894119899 (
119905) = 21198942
120595 (2119894119905 minus 119899)
(1)
where 119894 and 119899 are the dilation and translation parametersOrthogonal wavelet basis functions not only provide a simplemethod to calculate coefficient expansion but also span 119871
2(R)
in signal processing As a result signal 119878(119905) isin 1198712(R) can
be expressed as a series expansion of orthogonal scalingfunctions and wavelets More specifically
119878 (119905) = sum
ℓ
1198881198950(ℓ) 1205931198950 119896
(119905) + sum
119896
infin
sum
119895=1198950
119889119895 (
119896) 120595119895119896 (119905) (2)
where 119888119895(ℓ) = int
R119878(119905)120593119895ℓ
(119905)119889119905 and 119889119895(119896) = int
R119878(119905)120595119895119896
(119905)119889119905
are the low-pass and high-pass coefficients respectively 1198950is
an integer to define an interval on which 119878(119905) is a piecewiseconstant The two-scale equations for scaling and waveletbasis function are given as follows
120593 (119905) = radic2 sum
119898isinZ
ℎ119898120593 (2119905 minus 119898) (3)
120595 (119905) = radic2 sum
119898isinZ
119892119898120593 (2119905 minus 119898) (4)
where 119892119898
= (minus1)119898ℎ1minus119898
The coefficient ℎ119898in (3) has to meet
several conditions for the set of the wavelet basis functionto be unique and orthonormal and have a certain degree ofregularity
The coefficients ℎ119898and 119892
119898play a very crucial role in a
given DWT Performing the wavelet transformation does notrequire the explicit forms of 120593(119905) and 120595(119905) but only dependson ℎ119898and 119892
119898 The final output of the wavelet decomposition
includes a set of 119895-level wavelet coefficients One method toimplement DWT is to use a filter bank that provides perfectreconstruction DWT involves local analysis of frequency inspace and time domains and it provides multiscale imagedetails step by step If the scale becomes smaller every partbecomes more accurate and ultimately all imaging detailscan be focalized accurately If DWT is applied to a volumeit will produce the highest-frequency middle-frequency andlowest-frequency parts Figure 1 shows the results of applying3D DWT to a volume which includes eight parts LLLLLH LHL LHH HLL HLH HHL and HHH The lowest-frequency and highest-frequency parts are LLL and HHHrespectively [16 17]
23 119870-Means Clustering 119870-means clustering is a method ofcluster analysis which aims to partition 119899 observations into 119896
clusters in which each observation belongs to the cluster withthe nearest mean Given a set of observations (119909
1 1199092 119909
119899)
where each observation is a 119889-dimensional real vector 119896-means clustering aims to partition the 119899 observations into119896 (119896 le 119899) sets 119904
1 1199042 119904
119896 so as to minimize the within-
cluster sum of squares
arg min119896
sum
119894=1
sum
119909119895isin119904119894
10038171003817100381710038171003817119909119895minus 120583119894
10038171003817100381710038171003817
2
(5)
where 120583119894is the mean of points in 119904
119894
BioMed Research International 3
Rows
Columns
Slices
Original volume
LxLyLz
LxLyHz
LxHyLz
LxHyHz
HxLyLz
HxLyHz
HxHyLz
HxHyHz
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
Figure 1 The structure of applying 3D DWT to a volume
3 The Proposed Segmentation Method
In order to segment coronary arteries accurately from CTAdata sets 3D region growing was initially applied to searchfor the probable location of the coronary arteries Next weused the 3D DWT and 3D neutrosophic transformation toaccurately detect the coronary arteries
31 Initial Segmentation of Coronary Arteries This sectiondiscusses the initial segmentation of coronary arteries using3D region growing In image preprocessing we found theaorta automatically by using methods proposed in the liter-ature [5 16] The selection of the seed point of 3D regiongrowing was initially made to check which slice beganthe information of the coronary arteries Due to the smallchanges in aorta area between the two adjacent slices weautomatically obtained the seed points by the differencebetween the two adjacent slices
As shown in Figure 2 we use the difference between thetwo adjacent slices (a) and (b) to automatically obtain theseed points bounded by the blue line in (c) which indicatesthe boundary of coronary arteriesThe boundary of coronaryarteries denotes the high-frequency subband 119889
119895(119896) in (2)
when comparing vessel lumen and backgroundSince coronary arteries do not exhibit abrupt intensity
changes along their centerline [4] a rough tubular mask ofcoronary arteries can be easily constructed by 3D region
growing We chose a 26-connected neighborhood for ouradjacent pixel relationship and then the 3D region growingmethod was applied with a set of prespecified seed voxel(s)and grown from these seeds by merging neighboring voxelswhose properties were most similar to the premerged regionThe homogeneity criterion was defined as the differencebetween the intensity of the candidate voxel and the averageintensity of the premerged region The selection of the seedpoint was initially intended to check which slice began theinformation of the coronary arteries Next the homogeneitycriterion was applied to group voxels with the same or similarintensities into one region If the homogeneity criterion wassatisfied the candidate voxel was merged with the premergedregion The process was repeated until no more voxelswere assigned to the region and then the number of allmerged voxels was calculated In order to avoid leakagethe total number of merged voxels was limited to 12000otherwise 3D region growing was restarted by automaticallyusing an improved homogeneity criterion Finally the initialsegmentation of the coronary arteries in a volume wascompleted
32 Vessel-Texture Discrimination According to Parsevalrsquostheorem the energy in a signal 119878(119905) is given as follows [16 17]
int |119878(119905)|2119889119905 =
infin
sum
119897=minusinfin
|119888(119897)|2+
infin
sum
119895=0
infin
sum
119896=minusinfin
10038161003816100381610038161003816119889119895(119896)
10038161003816100381610038161003816
2
(6)
4 BioMed Research International
This equation implies that the energy of a signal is the sum-mation of low-frequency and high-frequency coefficientsDWT is a good analytic tool for image texture analysis orline-based patterns [18ndash21] Since a vessel is a type of 3D line-based pattern inCT volume we used 119897
2-normof thesewavelet
coefficients to find the energy of line-based patterns 1198972-norm
was defined as
119864 (119862) = 1198622=
119901
sum
119894=1
1003816100381610038161003816119888119894
1003816100381610038161003816
2 (7)
where the vector 119862 = [119888119894]1times119901
was the wavelet coefficients ofa frequency channelThe searching algorithm is summarizedas follows
Algorithm 1 (1) Transform a given vessel volume into fre-quency channels by a specified number of decompositionlevels We usually set the number to one in the first search
(2) Use (7) to calculate the average 1198972-norm of each
channel and maximum of 119864(119862) for the vessel volume(3) If the maximum of 119864(119862)was significantly greater than
another channelrsquos 119864(119862) the search was stopped Otherwisethe number of decomposition levels was increased followedby a repeat of step 1
By using the above algorithm we observed that the mostsignificant information of the vessel texture often appearedin the high frequency channels Thus we used the subbandHHH to detect vessels in this study
33 Accurate Detection of Coronary Arteries The initialsegmentation of coronary arteries in a volumewas completedby 3D region growing as described in Section 31 Sinceregion growing is a simple region-based image segmentationmethod it was only used to search for the initial locationof the coronary arteries We then accurately detected thecoronary arteries by applying DWT to each slice in thevolume as described in this subsection
First the initial location of the coronary arteries obtainedfrom 3D region growing was dilated by 3 voxels Nextwe used the Haar wavelet bases in (1) to transform thehost images into the orthogonal DWT domain by one-leveldecomposition Only HHH subbands were employed forfurther processes because most of the information on thecoronary arteries and boundarieswere in theHHHsubbandsWe calculated the mean energy using coefficients of HHHsubbands in a local window 119908 as follows
HHH (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
HHH (119897 119898 119899) (8)
where
119903 = round(119894 +
119908
2
)
119904 = round(119895 +
119908
2
)
119905 = round(119896 +
119908
2
)
(9)
Next the subbands HHH were characterized by 3 member-ship sets 119879 119865 and 119880 Consider
119879HHH (119894 119895 119896) =
HHH (119894 119895 119896) minusHHHmin
HHHmax minusHHHmin
119865HHH (119894 119895 119896) = 1 minus 119879HHH (119894 119895 119896)
119880HHH (119894 119895 119896) =
120575 (119894 119895 119896) minus 120575min120575max minus 120575min
(10)
where
HHHmin = min HHH (119894 119895 119896)
HHHmax = max HHH (119894 119895 119896)
120575 (119894 119895 119896) =
10038161003816100381610038161003816HHH (119894 119895 119896) minusHHH (119894 119895 119896)
10038161003816100381610038161003816
120575min = min 120575 (119894 119895 119896)
120575max = max 120575 (119894 119895 119896)
(11)
That is a pixel could be represented as a neutrosophic domain119875(119905 119891 119906) which means the pixel is 119905 true 119891 false and 119906uncertain where 119905 varies in 119879 119891 varies in 119865 and 119906 varies in119880 In order to reduce the uncertainty 119906 120572-means operationwas employed as follows
119879 (120572) =
119879 if 119880 lt 120572
119879120572 if 119880 ge 120572
119865 (120572) =
119865 if 119880 lt 120572
119865120572 if 119880 ge 120572
119880120572(119894 119895 119896) =
120575119879(119894 119895 119896) minus 120575
119879min
120575119879max
minus 120575119879min
(12)
where the parameter 120572 is a positive number and
119879120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
119865120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119865 (119897 119898 119899)
120575119879(119894 119895 119896) =
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) minus 119879 (119894 119895 119896)
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
(13)
The inverse DWT was then applied to obtain a new volumewhich possessed the true subset Finally we applied119870-meansclustering (119870 = 3) in (2) to differentiate vessel lumen vesselboundary (true subset) and background The true subset 119879was retained respectively
BioMed Research International 5
(a) (b)
(c)
Figure 2 The 3D region growing seed points in (c) were automatically obtained by using the difference between the two areas bounded bythe blue lines in adjacent slices (a) and (b)
4 Experiments and Discussion
To test the proposed method CTA volumes obtained froma CT system were segmented for coronary arteries The slicethickness was 0625mm and the volume was 512lowast512lowast(sdot) indifferent data sets The window size 119908 was set to 3 whichwas enough to capture the local texture characteristics Theparameter 120572 was set to 02 We tested 20 data sets most ofwhich were segmented successfully except for a few smallbranches that were lost in 2 of the data sets due to the localfailure in region growing To evaluate the performance ofour segmented coronary arteries we compared our resultswith that obtained from the ground truth values obtainedfrom the commercial software from GE Healthcare and thelevel-set method We used the overlapping metric (OM) andHausdorff distance (119889
119867) to analyze the efficiency of each
method
41 The Segmenting Efficiency of 2D Imaging Figure 3(b)shows the results of 6 slices in 1 CTA volume obtainedusing the proposed method The areas bounded by the red
line are coronary arteries The segmenting efficiency wascomparedwith themanually delineated ground truth data119873
119877
in Figure 3(a) by using OM which was defined as
OM = 2(
119873119879cap 119873119877
119873119879+ 119873119877
) (14)
where 119873119879indicates the pixelsvoxels of the segmented coro-
nary arteries The OM was close to 1 when the segmenta-tion was well matched to the reference ground truth andapproached zero when the results had no similarity to thereference
In the 6 slices in Figure 3(b) the segmentation resultsshowed that the proposed method detected coronary arteriesaccurately As shown in Table 1 the average OM of theproposed method was 096
42The Segmenting Efficiency on a 3DVolume Thefirst focusof the comparisonwas the correctness of the 4main branchesthe right coronary artery (RCA) the left anterior descendingartery (LAD) the circumflex (CRX) and the first diagonal
6 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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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
2 BioMed Research International
centerline obtained in advance However it is difficult todetect small branches and vessels by using this method
In this study we propose a newmethod for automaticallyand correctly segmenting coronary arteries from CTA datasets In image preprocessing we detected the aorta auto-matically by using methods proposed in the literature [516] The proposed coronary arteries segmentation method issummarized as follows First of all we automatically obtainedthe seed point of a 3D region growing by the differencebetween the two adjacent slices due to the small changesof the aorta between two adjacent slices Next 3D regiongrowing was applied to initially search for the probablelocation of coronary arteries which was then dilated by 3voxels Based on the dilation of the probable location wedetected the coronary arteries accurately by applying the 3Ddiscrete wavelet transformation (DWT) and 3Dneutrosophictransformation to the CTA volume The location of vesselinformation in HHH subband coefficients was detectedby the proposed vessel-texture discrimination algorithmAccordingly HHH subband coefficients were used whichwere characterized and classified by 120572-means operation and119870-means clustering Finally the proposed method was testedon several CTA data sets and the experimental resultsindicated that the proposedmethod had a good performance
The rest of this study is organized as follows Section 2reviews some preliminaries and Section 3 uses 3D regiongrowing and 3DDWT to propose a newmethod for segment-ing coronary arteries Section 4 contains the experiments anddiscussion and the conclusions are drawn in Section 5
2 Preliminaries
In this section we will briefly introduce the concepts of DWTand provide an overview of some fundamental mathematicalconcepts that are used in this study
21 Region Growing Region growing is a simple well-developed region-based image segmentation technique [17]It postulates that neighboring voxels within the same regionhave similar intensity values and is also classified as a voxel-based image segmentation method since it involves theselection of initial seed points In other words this methodof segmentation examines neighboring voxels of initial seedpoints and determines whether neighboring voxels should beadded to the region Consequentially the general concept ofregion growing is to group voxels with the same or similarintensities to one region according to the given seed pointsand a homogeneity criterion
22 Discrete Wavelet Transform Wavelet transform isobtained by a single prototype function 120595(119909) which isregulated with scaling and shift parameters To construct120595(119909) a scaling function 120593(119909) is determined The discretenormalized scaling and wavelet basis functions are definedas
120593119894119899 (
119905) = 21198942
120593 (2119894119905 minus 119899)
120595119894119899 (
119905) = 21198942
120595 (2119894119905 minus 119899)
(1)
where 119894 and 119899 are the dilation and translation parametersOrthogonal wavelet basis functions not only provide a simplemethod to calculate coefficient expansion but also span 119871
2(R)
in signal processing As a result signal 119878(119905) isin 1198712(R) can
be expressed as a series expansion of orthogonal scalingfunctions and wavelets More specifically
119878 (119905) = sum
ℓ
1198881198950(ℓ) 1205931198950 119896
(119905) + sum
119896
infin
sum
119895=1198950
119889119895 (
119896) 120595119895119896 (119905) (2)
where 119888119895(ℓ) = int
R119878(119905)120593119895ℓ
(119905)119889119905 and 119889119895(119896) = int
R119878(119905)120595119895119896
(119905)119889119905
are the low-pass and high-pass coefficients respectively 1198950is
an integer to define an interval on which 119878(119905) is a piecewiseconstant The two-scale equations for scaling and waveletbasis function are given as follows
120593 (119905) = radic2 sum
119898isinZ
ℎ119898120593 (2119905 minus 119898) (3)
120595 (119905) = radic2 sum
119898isinZ
119892119898120593 (2119905 minus 119898) (4)
where 119892119898
= (minus1)119898ℎ1minus119898
The coefficient ℎ119898in (3) has to meet
several conditions for the set of the wavelet basis functionto be unique and orthonormal and have a certain degree ofregularity
The coefficients ℎ119898and 119892
119898play a very crucial role in a
given DWT Performing the wavelet transformation does notrequire the explicit forms of 120593(119905) and 120595(119905) but only dependson ℎ119898and 119892
119898 The final output of the wavelet decomposition
includes a set of 119895-level wavelet coefficients One method toimplement DWT is to use a filter bank that provides perfectreconstruction DWT involves local analysis of frequency inspace and time domains and it provides multiscale imagedetails step by step If the scale becomes smaller every partbecomes more accurate and ultimately all imaging detailscan be focalized accurately If DWT is applied to a volumeit will produce the highest-frequency middle-frequency andlowest-frequency parts Figure 1 shows the results of applying3D DWT to a volume which includes eight parts LLLLLH LHL LHH HLL HLH HHL and HHH The lowest-frequency and highest-frequency parts are LLL and HHHrespectively [16 17]
23 119870-Means Clustering 119870-means clustering is a method ofcluster analysis which aims to partition 119899 observations into 119896
clusters in which each observation belongs to the cluster withthe nearest mean Given a set of observations (119909
1 1199092 119909
119899)
where each observation is a 119889-dimensional real vector 119896-means clustering aims to partition the 119899 observations into119896 (119896 le 119899) sets 119904
1 1199042 119904
119896 so as to minimize the within-
cluster sum of squares
arg min119896
sum
119894=1
sum
119909119895isin119904119894
10038171003817100381710038171003817119909119895minus 120583119894
10038171003817100381710038171003817
2
(5)
where 120583119894is the mean of points in 119904
119894
BioMed Research International 3
Rows
Columns
Slices
Original volume
LxLyLz
LxLyHz
LxHyLz
LxHyHz
HxLyLz
HxLyHz
HxHyLz
HxHyHz
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
Figure 1 The structure of applying 3D DWT to a volume
3 The Proposed Segmentation Method
In order to segment coronary arteries accurately from CTAdata sets 3D region growing was initially applied to searchfor the probable location of the coronary arteries Next weused the 3D DWT and 3D neutrosophic transformation toaccurately detect the coronary arteries
31 Initial Segmentation of Coronary Arteries This sectiondiscusses the initial segmentation of coronary arteries using3D region growing In image preprocessing we found theaorta automatically by using methods proposed in the liter-ature [5 16] The selection of the seed point of 3D regiongrowing was initially made to check which slice beganthe information of the coronary arteries Due to the smallchanges in aorta area between the two adjacent slices weautomatically obtained the seed points by the differencebetween the two adjacent slices
As shown in Figure 2 we use the difference between thetwo adjacent slices (a) and (b) to automatically obtain theseed points bounded by the blue line in (c) which indicatesthe boundary of coronary arteriesThe boundary of coronaryarteries denotes the high-frequency subband 119889
119895(119896) in (2)
when comparing vessel lumen and backgroundSince coronary arteries do not exhibit abrupt intensity
changes along their centerline [4] a rough tubular mask ofcoronary arteries can be easily constructed by 3D region
growing We chose a 26-connected neighborhood for ouradjacent pixel relationship and then the 3D region growingmethod was applied with a set of prespecified seed voxel(s)and grown from these seeds by merging neighboring voxelswhose properties were most similar to the premerged regionThe homogeneity criterion was defined as the differencebetween the intensity of the candidate voxel and the averageintensity of the premerged region The selection of the seedpoint was initially intended to check which slice began theinformation of the coronary arteries Next the homogeneitycriterion was applied to group voxels with the same or similarintensities into one region If the homogeneity criterion wassatisfied the candidate voxel was merged with the premergedregion The process was repeated until no more voxelswere assigned to the region and then the number of allmerged voxels was calculated In order to avoid leakagethe total number of merged voxels was limited to 12000otherwise 3D region growing was restarted by automaticallyusing an improved homogeneity criterion Finally the initialsegmentation of the coronary arteries in a volume wascompleted
32 Vessel-Texture Discrimination According to Parsevalrsquostheorem the energy in a signal 119878(119905) is given as follows [16 17]
int |119878(119905)|2119889119905 =
infin
sum
119897=minusinfin
|119888(119897)|2+
infin
sum
119895=0
infin
sum
119896=minusinfin
10038161003816100381610038161003816119889119895(119896)
10038161003816100381610038161003816
2
(6)
4 BioMed Research International
This equation implies that the energy of a signal is the sum-mation of low-frequency and high-frequency coefficientsDWT is a good analytic tool for image texture analysis orline-based patterns [18ndash21] Since a vessel is a type of 3D line-based pattern inCT volume we used 119897
2-normof thesewavelet
coefficients to find the energy of line-based patterns 1198972-norm
was defined as
119864 (119862) = 1198622=
119901
sum
119894=1
1003816100381610038161003816119888119894
1003816100381610038161003816
2 (7)
where the vector 119862 = [119888119894]1times119901
was the wavelet coefficients ofa frequency channelThe searching algorithm is summarizedas follows
Algorithm 1 (1) Transform a given vessel volume into fre-quency channels by a specified number of decompositionlevels We usually set the number to one in the first search
(2) Use (7) to calculate the average 1198972-norm of each
channel and maximum of 119864(119862) for the vessel volume(3) If the maximum of 119864(119862)was significantly greater than
another channelrsquos 119864(119862) the search was stopped Otherwisethe number of decomposition levels was increased followedby a repeat of step 1
By using the above algorithm we observed that the mostsignificant information of the vessel texture often appearedin the high frequency channels Thus we used the subbandHHH to detect vessels in this study
33 Accurate Detection of Coronary Arteries The initialsegmentation of coronary arteries in a volumewas completedby 3D region growing as described in Section 31 Sinceregion growing is a simple region-based image segmentationmethod it was only used to search for the initial locationof the coronary arteries We then accurately detected thecoronary arteries by applying DWT to each slice in thevolume as described in this subsection
First the initial location of the coronary arteries obtainedfrom 3D region growing was dilated by 3 voxels Nextwe used the Haar wavelet bases in (1) to transform thehost images into the orthogonal DWT domain by one-leveldecomposition Only HHH subbands were employed forfurther processes because most of the information on thecoronary arteries and boundarieswere in theHHHsubbandsWe calculated the mean energy using coefficients of HHHsubbands in a local window 119908 as follows
HHH (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
HHH (119897 119898 119899) (8)
where
119903 = round(119894 +
119908
2
)
119904 = round(119895 +
119908
2
)
119905 = round(119896 +
119908
2
)
(9)
Next the subbands HHH were characterized by 3 member-ship sets 119879 119865 and 119880 Consider
119879HHH (119894 119895 119896) =
HHH (119894 119895 119896) minusHHHmin
HHHmax minusHHHmin
119865HHH (119894 119895 119896) = 1 minus 119879HHH (119894 119895 119896)
119880HHH (119894 119895 119896) =
120575 (119894 119895 119896) minus 120575min120575max minus 120575min
(10)
where
HHHmin = min HHH (119894 119895 119896)
HHHmax = max HHH (119894 119895 119896)
120575 (119894 119895 119896) =
10038161003816100381610038161003816HHH (119894 119895 119896) minusHHH (119894 119895 119896)
10038161003816100381610038161003816
120575min = min 120575 (119894 119895 119896)
120575max = max 120575 (119894 119895 119896)
(11)
That is a pixel could be represented as a neutrosophic domain119875(119905 119891 119906) which means the pixel is 119905 true 119891 false and 119906uncertain where 119905 varies in 119879 119891 varies in 119865 and 119906 varies in119880 In order to reduce the uncertainty 119906 120572-means operationwas employed as follows
119879 (120572) =
119879 if 119880 lt 120572
119879120572 if 119880 ge 120572
119865 (120572) =
119865 if 119880 lt 120572
119865120572 if 119880 ge 120572
119880120572(119894 119895 119896) =
120575119879(119894 119895 119896) minus 120575
119879min
120575119879max
minus 120575119879min
(12)
where the parameter 120572 is a positive number and
119879120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
119865120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119865 (119897 119898 119899)
120575119879(119894 119895 119896) =
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) minus 119879 (119894 119895 119896)
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
(13)
The inverse DWT was then applied to obtain a new volumewhich possessed the true subset Finally we applied119870-meansclustering (119870 = 3) in (2) to differentiate vessel lumen vesselboundary (true subset) and background The true subset 119879was retained respectively
BioMed Research International 5
(a) (b)
(c)
Figure 2 The 3D region growing seed points in (c) were automatically obtained by using the difference between the two areas bounded bythe blue lines in adjacent slices (a) and (b)
4 Experiments and Discussion
To test the proposed method CTA volumes obtained froma CT system were segmented for coronary arteries The slicethickness was 0625mm and the volume was 512lowast512lowast(sdot) indifferent data sets The window size 119908 was set to 3 whichwas enough to capture the local texture characteristics Theparameter 120572 was set to 02 We tested 20 data sets most ofwhich were segmented successfully except for a few smallbranches that were lost in 2 of the data sets due to the localfailure in region growing To evaluate the performance ofour segmented coronary arteries we compared our resultswith that obtained from the ground truth values obtainedfrom the commercial software from GE Healthcare and thelevel-set method We used the overlapping metric (OM) andHausdorff distance (119889
119867) to analyze the efficiency of each
method
41 The Segmenting Efficiency of 2D Imaging Figure 3(b)shows the results of 6 slices in 1 CTA volume obtainedusing the proposed method The areas bounded by the red
line are coronary arteries The segmenting efficiency wascomparedwith themanually delineated ground truth data119873
119877
in Figure 3(a) by using OM which was defined as
OM = 2(
119873119879cap 119873119877
119873119879+ 119873119877
) (14)
where 119873119879indicates the pixelsvoxels of the segmented coro-
nary arteries The OM was close to 1 when the segmenta-tion was well matched to the reference ground truth andapproached zero when the results had no similarity to thereference
In the 6 slices in Figure 3(b) the segmentation resultsshowed that the proposed method detected coronary arteriesaccurately As shown in Table 1 the average OM of theproposed method was 096
42The Segmenting Efficiency on a 3DVolume Thefirst focusof the comparisonwas the correctness of the 4main branchesthe right coronary artery (RCA) the left anterior descendingartery (LAD) the circumflex (CRX) and the first diagonal
6 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
Submit your manuscripts athttpwwwhindawicom
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Disease Markers
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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OncologyJournal of
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Oxidative Medicine and Cellular Longevity
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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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
BioMed Research International 3
Rows
Columns
Slices
Original volume
LxLyLz
LxLyHz
LxHyLz
LxHyHz
HxLyLz
HxLyHz
HxHyLz
HxHyHz
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
LA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
HA darr
Figure 1 The structure of applying 3D DWT to a volume
3 The Proposed Segmentation Method
In order to segment coronary arteries accurately from CTAdata sets 3D region growing was initially applied to searchfor the probable location of the coronary arteries Next weused the 3D DWT and 3D neutrosophic transformation toaccurately detect the coronary arteries
31 Initial Segmentation of Coronary Arteries This sectiondiscusses the initial segmentation of coronary arteries using3D region growing In image preprocessing we found theaorta automatically by using methods proposed in the liter-ature [5 16] The selection of the seed point of 3D regiongrowing was initially made to check which slice beganthe information of the coronary arteries Due to the smallchanges in aorta area between the two adjacent slices weautomatically obtained the seed points by the differencebetween the two adjacent slices
As shown in Figure 2 we use the difference between thetwo adjacent slices (a) and (b) to automatically obtain theseed points bounded by the blue line in (c) which indicatesthe boundary of coronary arteriesThe boundary of coronaryarteries denotes the high-frequency subband 119889
119895(119896) in (2)
when comparing vessel lumen and backgroundSince coronary arteries do not exhibit abrupt intensity
changes along their centerline [4] a rough tubular mask ofcoronary arteries can be easily constructed by 3D region
growing We chose a 26-connected neighborhood for ouradjacent pixel relationship and then the 3D region growingmethod was applied with a set of prespecified seed voxel(s)and grown from these seeds by merging neighboring voxelswhose properties were most similar to the premerged regionThe homogeneity criterion was defined as the differencebetween the intensity of the candidate voxel and the averageintensity of the premerged region The selection of the seedpoint was initially intended to check which slice began theinformation of the coronary arteries Next the homogeneitycriterion was applied to group voxels with the same or similarintensities into one region If the homogeneity criterion wassatisfied the candidate voxel was merged with the premergedregion The process was repeated until no more voxelswere assigned to the region and then the number of allmerged voxels was calculated In order to avoid leakagethe total number of merged voxels was limited to 12000otherwise 3D region growing was restarted by automaticallyusing an improved homogeneity criterion Finally the initialsegmentation of the coronary arteries in a volume wascompleted
32 Vessel-Texture Discrimination According to Parsevalrsquostheorem the energy in a signal 119878(119905) is given as follows [16 17]
int |119878(119905)|2119889119905 =
infin
sum
119897=minusinfin
|119888(119897)|2+
infin
sum
119895=0
infin
sum
119896=minusinfin
10038161003816100381610038161003816119889119895(119896)
10038161003816100381610038161003816
2
(6)
4 BioMed Research International
This equation implies that the energy of a signal is the sum-mation of low-frequency and high-frequency coefficientsDWT is a good analytic tool for image texture analysis orline-based patterns [18ndash21] Since a vessel is a type of 3D line-based pattern inCT volume we used 119897
2-normof thesewavelet
coefficients to find the energy of line-based patterns 1198972-norm
was defined as
119864 (119862) = 1198622=
119901
sum
119894=1
1003816100381610038161003816119888119894
1003816100381610038161003816
2 (7)
where the vector 119862 = [119888119894]1times119901
was the wavelet coefficients ofa frequency channelThe searching algorithm is summarizedas follows
Algorithm 1 (1) Transform a given vessel volume into fre-quency channels by a specified number of decompositionlevels We usually set the number to one in the first search
(2) Use (7) to calculate the average 1198972-norm of each
channel and maximum of 119864(119862) for the vessel volume(3) If the maximum of 119864(119862)was significantly greater than
another channelrsquos 119864(119862) the search was stopped Otherwisethe number of decomposition levels was increased followedby a repeat of step 1
By using the above algorithm we observed that the mostsignificant information of the vessel texture often appearedin the high frequency channels Thus we used the subbandHHH to detect vessels in this study
33 Accurate Detection of Coronary Arteries The initialsegmentation of coronary arteries in a volumewas completedby 3D region growing as described in Section 31 Sinceregion growing is a simple region-based image segmentationmethod it was only used to search for the initial locationof the coronary arteries We then accurately detected thecoronary arteries by applying DWT to each slice in thevolume as described in this subsection
First the initial location of the coronary arteries obtainedfrom 3D region growing was dilated by 3 voxels Nextwe used the Haar wavelet bases in (1) to transform thehost images into the orthogonal DWT domain by one-leveldecomposition Only HHH subbands were employed forfurther processes because most of the information on thecoronary arteries and boundarieswere in theHHHsubbandsWe calculated the mean energy using coefficients of HHHsubbands in a local window 119908 as follows
HHH (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
HHH (119897 119898 119899) (8)
where
119903 = round(119894 +
119908
2
)
119904 = round(119895 +
119908
2
)
119905 = round(119896 +
119908
2
)
(9)
Next the subbands HHH were characterized by 3 member-ship sets 119879 119865 and 119880 Consider
119879HHH (119894 119895 119896) =
HHH (119894 119895 119896) minusHHHmin
HHHmax minusHHHmin
119865HHH (119894 119895 119896) = 1 minus 119879HHH (119894 119895 119896)
119880HHH (119894 119895 119896) =
120575 (119894 119895 119896) minus 120575min120575max minus 120575min
(10)
where
HHHmin = min HHH (119894 119895 119896)
HHHmax = max HHH (119894 119895 119896)
120575 (119894 119895 119896) =
10038161003816100381610038161003816HHH (119894 119895 119896) minusHHH (119894 119895 119896)
10038161003816100381610038161003816
120575min = min 120575 (119894 119895 119896)
120575max = max 120575 (119894 119895 119896)
(11)
That is a pixel could be represented as a neutrosophic domain119875(119905 119891 119906) which means the pixel is 119905 true 119891 false and 119906uncertain where 119905 varies in 119879 119891 varies in 119865 and 119906 varies in119880 In order to reduce the uncertainty 119906 120572-means operationwas employed as follows
119879 (120572) =
119879 if 119880 lt 120572
119879120572 if 119880 ge 120572
119865 (120572) =
119865 if 119880 lt 120572
119865120572 if 119880 ge 120572
119880120572(119894 119895 119896) =
120575119879(119894 119895 119896) minus 120575
119879min
120575119879max
minus 120575119879min
(12)
where the parameter 120572 is a positive number and
119879120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
119865120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119865 (119897 119898 119899)
120575119879(119894 119895 119896) =
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) minus 119879 (119894 119895 119896)
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
(13)
The inverse DWT was then applied to obtain a new volumewhich possessed the true subset Finally we applied119870-meansclustering (119870 = 3) in (2) to differentiate vessel lumen vesselboundary (true subset) and background The true subset 119879was retained respectively
BioMed Research International 5
(a) (b)
(c)
Figure 2 The 3D region growing seed points in (c) were automatically obtained by using the difference between the two areas bounded bythe blue lines in adjacent slices (a) and (b)
4 Experiments and Discussion
To test the proposed method CTA volumes obtained froma CT system were segmented for coronary arteries The slicethickness was 0625mm and the volume was 512lowast512lowast(sdot) indifferent data sets The window size 119908 was set to 3 whichwas enough to capture the local texture characteristics Theparameter 120572 was set to 02 We tested 20 data sets most ofwhich were segmented successfully except for a few smallbranches that were lost in 2 of the data sets due to the localfailure in region growing To evaluate the performance ofour segmented coronary arteries we compared our resultswith that obtained from the ground truth values obtainedfrom the commercial software from GE Healthcare and thelevel-set method We used the overlapping metric (OM) andHausdorff distance (119889
119867) to analyze the efficiency of each
method
41 The Segmenting Efficiency of 2D Imaging Figure 3(b)shows the results of 6 slices in 1 CTA volume obtainedusing the proposed method The areas bounded by the red
line are coronary arteries The segmenting efficiency wascomparedwith themanually delineated ground truth data119873
119877
in Figure 3(a) by using OM which was defined as
OM = 2(
119873119879cap 119873119877
119873119879+ 119873119877
) (14)
where 119873119879indicates the pixelsvoxels of the segmented coro-
nary arteries The OM was close to 1 when the segmenta-tion was well matched to the reference ground truth andapproached zero when the results had no similarity to thereference
In the 6 slices in Figure 3(b) the segmentation resultsshowed that the proposed method detected coronary arteriesaccurately As shown in Table 1 the average OM of theproposed method was 096
42The Segmenting Efficiency on a 3DVolume Thefirst focusof the comparisonwas the correctness of the 4main branchesthe right coronary artery (RCA) the left anterior descendingartery (LAD) the circumflex (CRX) and the first diagonal
6 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
Submit your manuscripts athttpwwwhindawicom
Stem CellsInternational
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MEDIATORSINFLAMMATION
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Disease Markers
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BioMed Research International
OncologyJournal of
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Research and TreatmentAIDS
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Parkinsonrsquos Disease
Evidence-Based Complementary and Alternative Medicine
Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom
4 BioMed Research International
This equation implies that the energy of a signal is the sum-mation of low-frequency and high-frequency coefficientsDWT is a good analytic tool for image texture analysis orline-based patterns [18ndash21] Since a vessel is a type of 3D line-based pattern inCT volume we used 119897
2-normof thesewavelet
coefficients to find the energy of line-based patterns 1198972-norm
was defined as
119864 (119862) = 1198622=
119901
sum
119894=1
1003816100381610038161003816119888119894
1003816100381610038161003816
2 (7)
where the vector 119862 = [119888119894]1times119901
was the wavelet coefficients ofa frequency channelThe searching algorithm is summarizedas follows
Algorithm 1 (1) Transform a given vessel volume into fre-quency channels by a specified number of decompositionlevels We usually set the number to one in the first search
(2) Use (7) to calculate the average 1198972-norm of each
channel and maximum of 119864(119862) for the vessel volume(3) If the maximum of 119864(119862)was significantly greater than
another channelrsquos 119864(119862) the search was stopped Otherwisethe number of decomposition levels was increased followedby a repeat of step 1
By using the above algorithm we observed that the mostsignificant information of the vessel texture often appearedin the high frequency channels Thus we used the subbandHHH to detect vessels in this study
33 Accurate Detection of Coronary Arteries The initialsegmentation of coronary arteries in a volumewas completedby 3D region growing as described in Section 31 Sinceregion growing is a simple region-based image segmentationmethod it was only used to search for the initial locationof the coronary arteries We then accurately detected thecoronary arteries by applying DWT to each slice in thevolume as described in this subsection
First the initial location of the coronary arteries obtainedfrom 3D region growing was dilated by 3 voxels Nextwe used the Haar wavelet bases in (1) to transform thehost images into the orthogonal DWT domain by one-leveldecomposition Only HHH subbands were employed forfurther processes because most of the information on thecoronary arteries and boundarieswere in theHHHsubbandsWe calculated the mean energy using coefficients of HHHsubbands in a local window 119908 as follows
HHH (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
HHH (119897 119898 119899) (8)
where
119903 = round(119894 +
119908
2
)
119904 = round(119895 +
119908
2
)
119905 = round(119896 +
119908
2
)
(9)
Next the subbands HHH were characterized by 3 member-ship sets 119879 119865 and 119880 Consider
119879HHH (119894 119895 119896) =
HHH (119894 119895 119896) minusHHHmin
HHHmax minusHHHmin
119865HHH (119894 119895 119896) = 1 minus 119879HHH (119894 119895 119896)
119880HHH (119894 119895 119896) =
120575 (119894 119895 119896) minus 120575min120575max minus 120575min
(10)
where
HHHmin = min HHH (119894 119895 119896)
HHHmax = max HHH (119894 119895 119896)
120575 (119894 119895 119896) =
10038161003816100381610038161003816HHH (119894 119895 119896) minusHHH (119894 119895 119896)
10038161003816100381610038161003816
120575min = min 120575 (119894 119895 119896)
120575max = max 120575 (119894 119895 119896)
(11)
That is a pixel could be represented as a neutrosophic domain119875(119905 119891 119906) which means the pixel is 119905 true 119891 false and 119906uncertain where 119905 varies in 119879 119891 varies in 119865 and 119906 varies in119880 In order to reduce the uncertainty 119906 120572-means operationwas employed as follows
119879 (120572) =
119879 if 119880 lt 120572
119879120572 if 119880 ge 120572
119865 (120572) =
119865 if 119880 lt 120572
119865120572 if 119880 ge 120572
119880120572(119894 119895 119896) =
120575119879(119894 119895 119896) minus 120575
119879min
120575119879max
minus 120575119879min
(12)
where the parameter 120572 is a positive number and
119879120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
119865120572(119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119865 (119897 119898 119899)
120575119879(119894 119895 119896) =
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) minus 119879 (119894 119895 119896)
1003816100381610038161003816100381610038161003816
119879 (119894 119895 119896) =
1
119908 times 119908 times 119908
119903
sum
119897=119894
119904
sum
119898=119895
119905
sum
119899=119896
119879 (119897 119898 119899)
(13)
The inverse DWT was then applied to obtain a new volumewhich possessed the true subset Finally we applied119870-meansclustering (119870 = 3) in (2) to differentiate vessel lumen vesselboundary (true subset) and background The true subset 119879was retained respectively
BioMed Research International 5
(a) (b)
(c)
Figure 2 The 3D region growing seed points in (c) were automatically obtained by using the difference between the two areas bounded bythe blue lines in adjacent slices (a) and (b)
4 Experiments and Discussion
To test the proposed method CTA volumes obtained froma CT system were segmented for coronary arteries The slicethickness was 0625mm and the volume was 512lowast512lowast(sdot) indifferent data sets The window size 119908 was set to 3 whichwas enough to capture the local texture characteristics Theparameter 120572 was set to 02 We tested 20 data sets most ofwhich were segmented successfully except for a few smallbranches that were lost in 2 of the data sets due to the localfailure in region growing To evaluate the performance ofour segmented coronary arteries we compared our resultswith that obtained from the ground truth values obtainedfrom the commercial software from GE Healthcare and thelevel-set method We used the overlapping metric (OM) andHausdorff distance (119889
119867) to analyze the efficiency of each
method
41 The Segmenting Efficiency of 2D Imaging Figure 3(b)shows the results of 6 slices in 1 CTA volume obtainedusing the proposed method The areas bounded by the red
line are coronary arteries The segmenting efficiency wascomparedwith themanually delineated ground truth data119873
119877
in Figure 3(a) by using OM which was defined as
OM = 2(
119873119879cap 119873119877
119873119879+ 119873119877
) (14)
where 119873119879indicates the pixelsvoxels of the segmented coro-
nary arteries The OM was close to 1 when the segmenta-tion was well matched to the reference ground truth andapproached zero when the results had no similarity to thereference
In the 6 slices in Figure 3(b) the segmentation resultsshowed that the proposed method detected coronary arteriesaccurately As shown in Table 1 the average OM of theproposed method was 096
42The Segmenting Efficiency on a 3DVolume Thefirst focusof the comparisonwas the correctness of the 4main branchesthe right coronary artery (RCA) the left anterior descendingartery (LAD) the circumflex (CRX) and the first diagonal
6 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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
BioMed Research International 5
(a) (b)
(c)
Figure 2 The 3D region growing seed points in (c) were automatically obtained by using the difference between the two areas bounded bythe blue lines in adjacent slices (a) and (b)
4 Experiments and Discussion
To test the proposed method CTA volumes obtained froma CT system were segmented for coronary arteries The slicethickness was 0625mm and the volume was 512lowast512lowast(sdot) indifferent data sets The window size 119908 was set to 3 whichwas enough to capture the local texture characteristics Theparameter 120572 was set to 02 We tested 20 data sets most ofwhich were segmented successfully except for a few smallbranches that were lost in 2 of the data sets due to the localfailure in region growing To evaluate the performance ofour segmented coronary arteries we compared our resultswith that obtained from the ground truth values obtainedfrom the commercial software from GE Healthcare and thelevel-set method We used the overlapping metric (OM) andHausdorff distance (119889
119867) to analyze the efficiency of each
method
41 The Segmenting Efficiency of 2D Imaging Figure 3(b)shows the results of 6 slices in 1 CTA volume obtainedusing the proposed method The areas bounded by the red
line are coronary arteries The segmenting efficiency wascomparedwith themanually delineated ground truth data119873
119877
in Figure 3(a) by using OM which was defined as
OM = 2(
119873119879cap 119873119877
119873119879+ 119873119877
) (14)
where 119873119879indicates the pixelsvoxels of the segmented coro-
nary arteries The OM was close to 1 when the segmenta-tion was well matched to the reference ground truth andapproached zero when the results had no similarity to thereference
In the 6 slices in Figure 3(b) the segmentation resultsshowed that the proposed method detected coronary arteriesaccurately As shown in Table 1 the average OM of theproposed method was 096
42The Segmenting Efficiency on a 3DVolume Thefirst focusof the comparisonwas the correctness of the 4main branchesthe right coronary artery (RCA) the left anterior descendingartery (LAD) the circumflex (CRX) and the first diagonal
6 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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 BioMed Research International
(a) Ground truth data (b) The segmented results
Figure 3 Comparison of the 2D segmentation (b) with respect to the ground truth data (a)
artery (DA) Figures 4 and 5 show the detected coronaryarteries in the CTA volume obtained from the GE Health-care and the proposed method and the proposed methodsegmented these 4 main branches correctly compared to the4 main branches in Figure 5
Another test of performance is the correctness of theremaining branches Due to the multiresolution of the DWTeach subbranch in Figures 3 and 5 was correctly segmentedFurthermore the coronary arteries obtained from the pro-posed method were much better than those obtained from
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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
BioMed Research International 7
Figure 4The 3D coronary arteries manually edited by a radiologistusing an AW workstation (GE Healthcare Wisconsin USA)
200
150
100
100100
50
50
50150
150
Figure 5 The 3D coronary arteries in the CTA volume obtainedfrom the proposed method
Table 1 Comparison of the 2D image segmentation results
Yang et al [11] method Proposed methodMean OM 068 096
the level-set method which had several leakages as seen inFigure 6
In addition to the OM the difference between thesegmented vessel surface and themanually delineated groundtruth datawasmeasured by theHausdorffdistance [22]whichwas defined as follows
119889119867 (119883 119884) = maxsup
119909isin119883
inf119910isin119884
119889 (119909 119910) sup119910isin119884
inf119909isin119883
119889 (119909 119910) (15)
where 119883 and 119884 are the vertices of the mesh surfaces of thearteries corresponding to the segmentation results and theground truth and 119889(119909 119910) measure the Euclidean distancebetween points 119909 and 119910 belonging to vertices 119883 and 119884
150
150150
200
200
250
100
100
100
50
50
50
3D coronary tree
Figure 6 The 3D coronary arteries in the CTA volume obtainedfrom the level-set approach
Table 2 Comparison of the 3D segmentation results
Yang et al [11] method Proposed methodMean OM 060 092Mean 119889
119867(119883 119884) 108 068
Table 3 Comparison of the cross-sectional diameter
Ground truth Yang et al [11] method Proposed method47 44 48
Table 2 lists the mean OM and mean Hausdorff distance forthe proposed method and the method of Yang et al [11] Theresults show that the proposed method was much better thanthat of Yang et al [11] in terms of both OM and Hausdorffdistance
43 DiameterMeasurement In this subsection we computedthe diameters of segmented coronary arteries using theproposed method and the method of Yang et al Manyefficient algorithms have been proposed to extract the tubecenterline We applied the algorithm proposed by Lee etal [23] to extract the centerline of the segmented coronaryarteries Using these extracted centerlines we obtained thecross sections of the segmented coronary arteries as shownin Figure 7 By computing the area 119860 of each cross sectionthe diameter 119903 was estimated as follows
119903 asymp radic119860
120587
(16)
Table 3 shows the estimated diameter of the same crosssection for the proposed method and the method of Yang etal [11] The diameter of the proposed method was closer tothe diameter in ground truth data at the same cross sectionthan to that obtained from the method of Yang et al
44 Experimental Environment and Execution Time Theproposed method was implemented in MATLAB (R2011a)on a standard specification PC with a 32GHz CPU and12GB RAM The average execution time was 58 seconds to
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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
8 BioMed Research International
(a) (b)
Figure 7 (a) The cross section of the segmented coronary arteries (b) Magnified view of (a)
extract the entire coronary tree compared to approximately47 seconds for themethod by Yang et al for the same process
5 Conclusions
Accurate extraction of coronary arteries is important to assessartery lesions in clinical practice In this study we proposea novel method to segment coronary arteries automaticallyBased on the initial segmentation obtained from 3D regiongrowing one-level 3D DWT and 3D neutrosophic transfor-mation were applied to detect coronary arteries accuratelyThe location of vessel information in HHH subband coef-ficients of DWT was successfully detected by the proposedvessel-texture discrimination algorithm Accordingly theHHH subband coefficients were used and characterized andclassified by 3D neutrosophic transformation and 119870-meansclustering The experimental results verify the efficiency ofthe proposed method
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study was supported by the National Taiwan UniversityHospital and theNational ScienceCouncil Taiwan under theNSC Grant NSC 98-2221-E-002-098-MY3
References
[1] A F Frangi W J Niessen K L Vincken and M A ViergeverldquoMultiscale vessel enhancement filteringrdquo in Medical ImageComputing andComputer-Assisted InterventationmdashMICCAIrsquo98vol 1496 of Lecture Notes in Computer Science pp 130ndash137Springer Berlin Germany 1998
[2] P J Yim J J Cebral R Mullick H B Marcos and P L ChoykeldquoVessel surface reconstruction with a tubular deformablemodelrdquo IEEE Transactions on Medical Imaging vol 20 no 12pp 1411ndash1421 2001
[3] D Nain A Yezzi and G Turk ldquoVessel segmentation using adriven flow shaperdquo in Proceeding of International Conferenceon Medical Image Computing Computer-Assisted Intervention-MICCAI 2004 vol 3216 of Lecture Notes in Computer Sciencepp 51ndash59 2004
[4] H Tek Y Zheng M A Gulsun and G Funka-Lea ldquoAnautomatic system for segmenting coronary arteries from CTArdquoin Proceedings of the MICCAI Workshop on Computing andVisualization for Intravascular Imaging (MICCAI-CVII rsquo11) pp47ndash54 2011
[5] A Hennemuth T Boskamp D Fritz et al ldquoOne-click coronarytree segmentation in CT angiographic imagesrdquo InternationalCongress Series vol 1281 pp 317ndash321 2005
[6] Y Yang A Tannenbaum and D Giddens ldquoKnowledge-based3D segmentation and reconstruction of coronary arteries usingCT imagesrdquo in Proceedings of the 26th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo04) vol 1 pp 1664ndash1666 San Francisco CalifUSA September 2004
[7] H Shikata G McLennan E A Hoffman and M SonkaldquoSegmentation of pulmonary vascular trees from thoracic 3DCT imagesrdquo International Journal of Biomedical Imaging vol2009 Article ID 636240 11 pages 2009
[8] T Brox and J Weickert ldquoLevel set segmentation with multipleregionsrdquo IEEE Transactions on Image Processing vol 15 no 10pp 3213ndash3218 2006
[9] W K Pratt Digital Image Processing John Wiley amp Sons LosAltos Calif USA 4th edition 2007
[10] L Wang L He A Mishra and C Li ldquoActive contours drivenby local Gaussian distribution fitting energyrdquo Signal Processingvol 89 no 12 pp 2435ndash2447 2009
[11] Y Yang A Tannenbaum D Giddens and A Stillman ldquoAuto-matic segmentation of coronary arteries using bayesian drivenimplicit surfacesrdquo in Proceedings of the 4th IEEE InternationalSymposium on Biomedical Imaging From Nano to Macro (ISBIrsquo07) pp 189ndash192 April 2007
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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
BioMed Research International 9
[12] Y Wang and P Liatsis An Automatic Method for Segmentationof Coronary Arteries X-Ray in Coronary CT Imaging IEEEComputer Society Developments in E-Systems Engineering2010
[13] Y Wang and P Liatsis ldquoAutomatic segmentation of coronaryarteries inCT imaging in the presence of kissing vessel artifactsrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 4 pp 782ndash788 2012
[14] C T Metz M Schaap A C Weustink N R Mollet T VanWalsum and W J Niessen ldquoCoronary centerline extractionfrom CT coronary angiography images using a minimum costpath approachrdquo Medical Physics vol 36 no 12 pp 5568ndash55792009
[15] O Friman M Hindennach C Kuhnel and H-O PeitgenldquoMultiple hypothesis template tracking of small 3D vesselstructuresrdquo Medical Image Analysis vol 2010 no 14 pp 160ndash171 2010
[16] S C Saur C Kuhnel T Boskamp G Szekely and P C CattinldquoAutomatic ascending aorta detection in CTA datasetsrdquo inBildverarbeitung fur die Medizin 2008 pp 323ndash327 SpringerBerlin Germany 2008
[17] T Pavlidis and Y-T Liow ldquoIntegrating region growing and edgedetectionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 12 no 3 pp 225ndash233 1990
[18] M Unser ldquoLocal linear transforms for texture measurementsrdquoSignal Processing vol 11 no 1 pp 61ndash79 1986
[19] T Chang and C C J Kuo ldquoTexture analysis and classificationwith tree-structured wavelet transformrdquo IEEE Transactions onImage Processing vol 2 no 4 pp 429ndash441 1993
[20] M Unser ldquoTexture classification and segmentation usingwavelet framesrdquo IEEE Transactions on Image Processing vol 4no 11 pp 1549ndash1560 1995
[21] Z-Z Wang and J-H Yong ldquoTexture analysis and classificationwith linear regressionmodel based on wavelet transformrdquo IEEETransactions on Image Processing vol 17 no 8 pp 1421ndash14302008
[22] R T Rockefellar and R J-BWetsVariational Analysis vol 317Springer New York NY USA 1988
[23] T C Lee R L Kashyap and C N Chu ldquoBuilding skeletonmodels via 3-D medial surface axis thinning algorithmsrdquoGraphical Models and Image Processing vol 56 no 6 pp 462ndash478 1994
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