3D Liver Tumor Segmentation in CT Images Using Improved ...downloads.hindawi.com/journals/bmri/2017/5207685.pdf · ResearchArticle 3D Liver Tumor Segmentation in CT Images Using Improved

Research Article3D Liver Tumor Segmentation in CT Images Using ImprovedFuzzy C-Means and Graph Cuts

Weiwei Wu1 Shuicai Wu2 Zhuhuang Zhou2 Rui Zhang2 and Yanhua Zhang1

1Faculty of Information Technology Beijing University of Technology Beijing 100124 China2College of Life Science and Bioengineering Beijing University of Technology Beijing 100124 China

Correspondence should be addressed to Shuicai Wu wushuicaibjuteducn

Received 14 December 2016 Accepted 18 June 2017 Published 26 September 2017

Academic Editor Cristiana Corsi

Copyright copy 2017 Weiwei Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Three-dimensional (3D) liver tumor segmentation from Computed Tomography (CT) images is a prerequisite for computer-aideddiagnosis treatment planning andmonitoring of liver cancer Despitemany years of research 3D liver tumor segmentation remainsa challenging task In this paper an efficient semiautomatic method was proposed for liver tumor segmentation in CT volumesbased on improved fuzzy C-means (FCM) and graph cuts With a single seed point the tumor volume of interest (VOI) wasextracted using confidence connected region growing algorithm to reduce computational costThen initial foregroundbackgroundregions were labeled automatically and a kernelized FCM with spatial information was incorporated in graph cuts segmentationto increase segmentation accuracy The proposed method was evaluated on the public clinical dataset (3Dircadb) which included15 CT volumes consisting of various sizes of liver tumors We achieved an average volumetric overlap error (VOE) of 2904 andDice similarity coefficient (DICE) of 083 with an average processing time of 45 s per tumor The experimental results showed thatthe proposed method was accurate for 3D liver tumor segmentation with a reduction of processing time

1 Introduction

Liver cancer is one of the most common types of cancerousdiseases worldwide with increasingly high morbidity [1]Early diagnosis and treatment are crucial to improve the sur-vival rate and the medical imaging techniques provide greathelp Among many different imaging modalities ComputedTomography (CT) is widely used for diagnosis of hepaticdisease as it can provide relatively high resolution imageswith accurate anatomical information [2]Three-dimensional(3D) segmentation of liver and tumors from CT images is animportant prerequisite for early diagnosis treatment plan-ning and monitoring of liver cancer [3] However manualsegmentation of liver tumors slice by slice is still routinelyused by radiologists in clinical practice which is laboriousand time-consuming due to the large amount of data and alsoprone to interobserver variability [4] The need for accurateand efficient tumor delineation leads to the development ofsemiautomatic or automatic tumor segmentation methods

3D liver tumor segmentation remains a challenging taskdue to the high variability of tumor shape size intensity

and the low contrast between tumor and surrounding livertissues [5] Many different approaches have been proposedto improve the tumor segmentation performance Recentpublications mainly included semiautomatic and automatictumor segmentation methods based on region growing orthresholding [6ndash8] clustering [9ndash11] level set [12 13] graphcuts [14 15] and machine learning [16ndash19]

Region growing thresholding or clustering methodshave been commonly used in medical image segmentationsince they are fast and easy to be implemented and have a rel-atively low computational cost However the main drawbackof these methods is that only intensity information is usedAs a result such methods are prone to boundary leakage onblurred tumor boundaries Thus prior knowledge or otheralgorithms were integrated to reduce undersegmentation oroversegmentation [7 8 11] Anter et al [7] proposed anautomatic tumor segmentationmethod using adaptive regiongrowing The initial seed points for region growing weredetected by applyingmarker-controlledwatershed algorithmZhou et al [8] presented a performance benchmarking study

HindawiBioMed Research InternationalVolume 2017 Article ID 5207685 11 pageshttpsdoiorg10115520175207685

2 BioMed Research International

of three semiautomatic methods for tumor segmentationincluding the two-dimensional (2D) region growing withknowledge-based constraints and the 3D Bayesian rule-based region growing method Kumar et al [9] developeda computer-aided diagnosis (CAD) system for tumor seg-mentation and classification The alternative fuzzy clusteringalgorithm was used in the segmentation stage which used anew distance function instead of the Euclidean metric Dasand Sabut [11] used adaptive thresholding morphologicalprocessing and a kernelized fuzzy C-means (FCM) algo-rithm to segment liver tumors from CT images Moghbel etal [10] proposed an automatic tumor segmentation schemebased on the supervised randomwalker approach FCMwithcuckoo optimization was applied for the labeling of pixels forthe final random walker segmentation

Active contour approaches such as fast marchingand level set algorithms are popular segmentation tech-niques However good initialization and speed functions arerequired in order to obtain accurate segmentation resultsespecially for tumors with heterogeneous intensities andweak boundaries Li et al [12] proposed a new level set modelintegrating edge- and region-based information with priorinformation FCMalgorithmwas applied for the probabilisticestimation of tumor tissues Le et al [13] proposed a semi-automatic method to segment liver tumors from MagneticResonance (MR) images where the fast marching algorithmwas used to generate the initial labeled regions and then otherunlabeled voxels were classified by the neural network Graphcutsmethods have also beenwidely applied formedical imagesegmentation [14 15] which can achieve global optimizationsolution Stawiaski et al [14] proposed an interactive seg-mentation method based on watershed and graph cuts Themethod achieved the highest accuracy compared to othersemiautomatic or automatic methods in the competitionof 2008 Liver Tumor Segmentation Challenge (LTSC08)which was held in conjunction with the Medical ImageComputing and Computer Assisted Intervention (MICCAI)2008 conference [20] Linguraru et al [15] presented anautomatic tumor segmentationmethod using graph cuts withHessian-based shape constraints biased to blob-like tumorsHowever the main drawback of such level set or graph cutsbased techniques is their relatively high computational costespecially for 3D volume data

To deal with the variations of tumor shape size intensityand texture machine learning based methods were alsostudied Foruzan and Chen [19] employed the support vectormachine (SVM) and scattered data approximation algorithmsto obtain the initial tumor boundary and then refined thefinal lesion region by using a sigmoid edge model Kadouryet al [17] developed an automatic tumor segmentationframework by using themachine learning technique based ondiscriminant Grassmannian manifolds Nonlinear intensitydistributions of liver and tumor tissues were learned duringthe training phase Then a higher-order conditional randomfield (CRF) approach was applied to perform the tumorsegmentation Zhang et al [16] applied watershed transformon the liver region and then employed region-based clas-sification by SVM for tumor segmentation However formachine learning based methods a large amount of training

data with gold standards is required during the trainingprocess

Considering the clinical applicability and segmentationaccuracy as well as the processing time our goal was todevelop an efficient robust and accurate tumor segmen-tation method with low human interaction Thus in thispaper a semiautomatic method based on improved FCMand graph cuts was proposed to realize 3D liver tumorsegmentation from CT images With a single user-selectedseed point both the tumor volume of interest (VOI) andlabeled foregroundbackground regions for graph cuts seg-mentation were extracted using the confidence connectedregion growing algorithm To improve segmentation accu-racy a kernelized FCM algorithm with spatial informationwas incorporated when estimating the probabilistic modelsof tumors and liver tissues

The rest of this paper is organized as follows Section 2introduces the details of the proposed method Section 3presents the experimental results and the discussion isgiven in Section 4 Finally the conclusion is summarized inSection 5

2 Methods

The proposed liver tumor segmentation framework is illus-trated in Figure 1 It consists of four major steps (1) prepro-cessing (2) tumor VOI extraction (3) tumor segmentationand (4) postprocessing Together with the original input CTvolume the presegmented liver mask is required to extractthe liverVOI to reduce the computational costThe livermaskcan be obtained by using a 3D liver segmentation methodsuch as the one in our previous work [21]

21 Preprocessing In the preprocessing step firstly nonlivertissues were removed and the liver VOI 119868Liver was extractedfrom the original CT image using the liver mask Then 119868Liverwas smoothed by median filtering and resampled to isotropicvoxel of size 1 times 1 times 1mm by linear interpolation

To segment the tumor one seed point was manuallyselected on the middle tumor slice The middle tumor slicewas defined as an axial slice which contained a relativelylarge lesion region The seed point V119904 was selected near thecenter of the lesion To reduce interoperator variability anautomatic correction was applied by replacing the seed pointto the darkest voxel within a cube of 5 times 5 times 3 voxels centeredat the selected seed point

22 Tumor VOI Extraction Using Confidence ConnectedRegion Growing Based on the seed point the tumor VOI119868Tumor was extracted by defining a bounding box around thetumor Further analysis was conducted on 119868Tumor in order toreduce the computational complexity and processing timeThebounding boxwas computed using confidence connectedregion growing algorithm (CCRG) in the axial coronal andsagittal slices

The concept of CCRG is similar to conventional regiongrowing based methods [7 8] Through an iterative regiongrowing process that started from the seed point V119904 neigh-boring voxels v with intensities inside the defined range 119868V isin

BioMed Research International 3

Resampled liver VOI

Original CT volume

Liver mask

SmoothingResampling

Liver VOI extraction

Confidence connected region growing

Axial slice

Coronal slice

Sagittal slice

Tumor VOI extraction

Seed point Middle tumor slice

Tumor VOI bounding box

Initial seed mask

Sigmoid of gradient

magnitude

Forebackground probabilisticmodels using KFCMS

Graph cuts segmentation

Postp

roce

ssin

g

Segmented liver tumor

Preprocessing

Figure 1 The proposed liver tumor segmentation framework (VOI volume of interest KFCMS kernelized fuzzy C-means with spatialconstraints)

[119898119888 minus 119897120590119888 119898119888 + 119897120590119888] were included in the tumor region where119898119888 and120590119888 are themean and standard deviation of the intensityin the region and l is a user-defined multiplicative factor Aregion of radius 2 voxels was defined as the initial regionThenew inclusion range was acquired by recomputing119898119888 and 120590119888at each iteration of region growingThe expansion continueduntil nomore neighboring voxels were added to the region orthe maximum number of iterations was reached

As shown in Figure 2 the results of confidence connectedsegmentation were affected by the selection of multiplicativefactor l A fixed value of l might lead to undersegmentationfor large tumors while causing oversegmentation for smalltumors Thus to reduce undersegmentation and overseg-mentation errors we employed an iterative process by usingconfidence connected region growing under the value of lranging from 15 to 25 (Figure 3) The iteration stopped ifthe segmented tumor region area was close to that of theliver region or the distance between the seed point V119904 andthe centroid of the segmented tumor region was larger than20mm Then all of the segmented masks were added togenerate an integrated image 119868confiThe tumor regionwas thenextracted from 119868confi using binary thresholding with the lowthreshold defined as half of the maximum value in 119868confi

After computing the 3D bounding box of the tumorregion on the three cross-section slices the tumor VOI wasdefined by adding a safety margin of 15mm around the 3Dbounding box

23 Tumor Segmentation Based on Improved Fuzzy C-Meansand Graph Cuts

231 Initialization The graph cuts segmentation in thetumor VOI 119868Tumor was initialized by the initial seed mask thesigmoid of gradientmagnitude of 119868Tumor and the probabilisticdistributions of lesion and liver tissues (Figure 4)

To generate the initial foregroundbackground seedmask voxels located inside the confidence connected seg-mented tumor regions (see Section 23) were labeled to 255as foreground seeds while the voxels outside the liver regionor adjacent to the boundaries of tumor VOI were labeled to 0as background seeds

An intensity transform was applied on the gradientmagnitude of 119868Tumor according to the following sigmoidfunction

119868sg = (1 + exp(minus(119868119892 minus 120573119904)120572119904 ))minus1 (1)

where 119868119892 denotes the gradient magnitude of 119868Tumor 119868sg isthe sigmoid of 119868119892 120572119904 and 120573119904 are parameters that definethe mapping range of the input 119868119892 120572119904 determines the inputintensity window width and 120573119904 defines the window center

Gaussian mixture model (GMM) is commonly appliedto estimate the intensity distribution [21 22] However onlyintensity information is used in GMM without consideringspatial information In this paper a kernelized FCM algo-rithm with spatial information was employed to estimate theprobabilistic models of lesionliver tissues

232 Kernelized FCM with Spatial Constraints Let 119868 =(1198681 1198682 119868119873V) denote the intensities of the voxels in thetumor VOI and let 119862 = (1198881 1198882 119888119873119888) denote the clustercenters where119873V and119873119888 are the number of voxels and clus-ter centers respectively Fuzzy clustering based algorithmsassign voxels v to each cluster by minimizing the objectivefunction defined as follows [23 24]

119869 = 119873Vsum119895=1

119873119888sum119894=1

119906119898119891119894119895 10038171003817100381710038171003817119868119895 minus 119888119894100381710038171003817100381710038172 (2)


l = 15 l = 17 l = 19 l = 23

(a)

l = 15 l = 17 l = 19

(b)

l = 17 l = 21 l = 23

(c)

Figure 2 Comparison of confidence connected segmentation results under different values of multiplicative factor l Each row represents anexample of segmentation for tumor with varying size The orange contour indicates liver region and red point shows the tumor seed point

where119906119894119895 is a partitionmatrix that represents themembershipof the voxel in the ith cluster and119898119891 is a weighting factor thatcontrols the fuzziness of the resulting partitionThe objectivefunction is minimized through an iterative optimizationThemembership value in 119906119894119895 indicates the probability that a voxelbelongs to a specific cluster

In traditional FCM algorithm the membership matrixand cluster centers were updated by

119906119894119895 = (119873119888sum119896=1

( 10038171003817100381710038171003817119868119895 minus 1198881198941003817100381710038171003817100381710038171003817100381710038171003817119868119895 minus 11988811989610038171003817100381710038171003817)2(119898119891minus1))

minus1

119888119894 = sum119873V119895=1 119906119898119891119894119895 119868119895sum119873V119895=1 119906119898119891119894119895 (3)

Only intensity informationwas includedwithout consideringthe local spatial information To improve the robustness offuzzy classification spatial neighborhood information wasincorporated into the membership matrix [24] and the

Euclidean distance was replaced by the Gaussian kernel-induced distance measure [23 25] The membership matrixwas then updated by

1199061015840119894119895 = 119906119901119894119895ℎ119902119894119895sum119873119888119896=1

119906119901119896119895ℎ119902119896119895

(4)

where

ℎ119894119895 = sum119896isinNB(119868119895)

119906119894119896

119906119894119895 = (1 minus 119870 (119868119895 119888119894))minus1(119898119891minus1)sum119873119888119896=1

(1 minus 119870 (119868119895 119888119896))minus1(119898119891minus1) 119870 (119868 119888) = exp(minus119868 minus 119888221205901198912 )

(5)

Here119901 and 119902 are weighting factors determining the influenceof both functions NB(sdot) represents the neighboring window


Axial

Coronal

Sagittal

(a) (b) (c) (d)

x

y

x

z

y

z

middot middot middot



Figure 3 Illustration of tumor VOI extraction using confidence connected region growing (a) Confidence connected segmentation resultsunder l in the range [15 25] (b) The integrated image of (a) (c) The extracted tumor mask (d) The bounding box of tumor region (greenrectangle) the tumor mask (yellow contour) and the seed point (red point)

(a) (b) (c) (d) (e) (f)

Figure 4 Intermediate results of the initialization of graph cuts segmentation (a) The middle tumor slice (b) The sigmoid of gradientmagnitude (c) Probabilistic distribution of lesion (d) Probabilistic distribution of liver (e) Initial seedmask (f) Comparison of segmentationresults of the proposed method (yellow contour) and the ground truth (green contour)

and 120590119891 is the adjustable parameter of the Gaussian kernel119870(119868 119888) The new cluster centers were updated by

119888119894 = sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) 119868119895sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) (6)

For convenience the improved kernelized FCM algorithmwith spatial constraints was called KFCMS Details of theKFCMS algorithm are presented in Algorithm 1

As shown in Figures 4(c) and 4(d) the probabilisticmodels of lesion and liver were obtained using KFCMS Theprobability value of each voxel in tumor VOI was in range[0 1] and was mapped to grayscale for visualization

233 Graph Cuts Segmentation Tumor segmentation prob-lem can be formulated in terms of energy minimization andgraph cuts segmentation is an optimization process aimedto find optimal surface with minimal cost [26 27] In thispaper a graph was constructed on the tumor VOI whichconsisted of three types of nodes V = TNS and threetypes of undirected edges E = 119864119899 119864119905 119864119904 The sink nodeTrepresents a set of foreground seeds and the source node Sdenotes the background seeds The node set N correspondsto the voxels in 119868Tumor In the edge set 119864119899 the so-called n-linkedges connect all neighboring voxels In 119864119905 and 119864119904 the so-called t-link edges connect each voxel to the sink and sourcenode respectively


input the tumor seed point V119904 the tumor VOI 119868Tumoroutput the probabilistic models for tumor 119875fg(V) and liver 119875bkg(V)(1) Set the number of clusters119873119888 larr 2 weighting factor119898119891 larr 2 119901 larr 2 119902 larr 1

neighborhood window of radius 3 voxels the Gaussian parameter 120590119891 larr 8maximum number of iterations 119905119898 larr 10 and maximum error 120576119891 larr 001(2) Set the intensity of the seed point and the average intensity value of the liverregion as the initial cluster centers(3) for iteration 119905 larr 1 do(4) Calculate the membership matrix 1199061015840119894119895 according to (4)(5) Update the new cluster centers 119888119894 according to (6)(6) 119905 larr 119905 + 1 if 119905 lt 119905119898 119888119905119894 minus 119888119905minus1119894 gt 120576119891(7) end for(8) Generate probabilistic model for each cluster derived from 1199061015840119894119895

Algorithm 1 Kernelized FCM with spatial constraints (KFCMS)

For the node setN and a set of labelsL the goal is to finda labeling 119891 N rarr L by minimizing the following energyfunction 119864(119891)

119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)

where 119877(119891V) and 119861(119891V 119891119906) are the region term and boundaryterm respectively and 120574 is a weighting factor These termscorrespond to the weights of the two types of edgesE and aredefined as follows

For (VT) isin 119864119905119877 (119891V) =

infin V isin T0 V isin S119875fg (V) others

(8)

For (S V) isin 119864119904119877 (119891V) =

0 V isin Tinfin V isin S119875bkg (V) others

(9)

The regional term 119877(119891V) specifies the cost of assigning a labelto voxel v based on the probabilisticmodels119875fg(V) and119875bkg(V)of tumor and liver tissues (see Section 232)

119861 (119891V 119891119906) = 120575 (119891V 119891119906) sdot (((119868V minus 119868119906)2 + 1)minus1 + 120582119868sg) 120575 (119891V 119891119906) =

1 if119891V = 1198911199060 if119891V = 119891119906(10)

The boundary term 119861(119891V 119891119906) represents the penalty of dis-continuity between two adjacent voxels v and u by integratingboth the intensity and gradient information 119868sg (see Sec-tion 231)

After the graph was constructed the optimal tumorsurface can be obtained via the max-flowmin-cut algorithm[26 28] Details of the graph cuts algorithm are presented inAlgorithm 2

24 Postprocessing After completing the graph cuts segmen-tation postprocessing steps were conducted to refine thesegmentation result including connected region selectionby the seed point V119904 median filtering and morphologicaldilating Then the postprocessed result was resampled to theoriginal input CT resolution and size for further evaluation

3 Experimental Results

31 Datasets The proposed method was evaluated on thepublic clinical contrast-enhanced CT dataset (3Dircadb(httpwwwircadfrresearch3dircadb)) which contains 15CT volume images involving 120 liver tumors of differentsizes The pixel spacing slice thickness and number ofslices varied from 056 to 087mm 1 to 4mm and 74 to260 respectively with the in-plane resolution of 512 times 512pixels in all cases Tumors manually segmented by clinicalexperts were also provided and considered as ground truthTumors less than 5mm in diameter were not included in ourexperiment as they are too small and only visible in one ortwo slices which are not suitable for 3D segmentation As ourmethod was designed for the segmentation of single tumorsconnected tumors were also excluded

32 Evaluation To evaluate the performance of the proposedmethod quantitatively the five metrics used in the competi-tion of LTSC08 [20] and Dice similarity coefficient (DICE)were computed to measure the volumetric overlap or surfacedistance of the segmentation result compared to groundtruth The five metrics are volumetric overlap error (VOE)relative volume difference (RVD) average symmetric surfacedistance (ASD) rootmean square symmetric surface distance(RMSD) andmaximum symmetric surface distance (MaxD)For the detailed definitions of these statistic measures pleaserefer to [29 30] The value of DICE ranges from 0 to 1with a value of 0 indicating no overlap and 1 representingperfect segmentation For the other five metrics a value of0 represents perfect segmentation A negative value of RVDindicates undersegmentation A scoring system employedin LTSC08 assigned a score between 0 and 100 to eachmetrics to compute an overall score A score of 100 indicates


input the tumor VOI 119868Tumor the gradient magnitude 119868119892 the probabilistic modelsfor tumor 119875fg(V) and liver 119875bkg(V)output the binary tumor mask(1) Set parameters 120574 larr 2 120582 larr 001 120572119904 larr minus5(2) Generate initial seed mask Set 119868V larr 255 inside the confidence connected

segmented tumor regions (V isin T) and 119868V larr 0 outside the liver region oradjacent to the boundaries of 119868Tumor (V isin S)(3) Compute the mean value119898119892 of 119868119892 Set 120573119904 larr 119898119892 and then generate sigmoidof 119868119892 according to (1)(4) Construct the graph on 119868Tumor(5) for V119894 on 119868Tumor 119894 larr 0 do(6) Compute region cost according to (9)(7) Compute boundary cost according to (10) using the 6-neighborhoodsystem(8) 119894 larr 119894 + 1 if 119894 lt 119873V(9) end for(10) Find optimal tumor surface via the max-flowmin-cut algorithm Set 119868V larr 255for V isin T and 119868V larr 0 for V isin S

Algorithm 2 Graph cuts segmentation

Table 1 Quantitative evaluation of the proposed tumor segmentation method Results are represented as mean plusmn standard deviation (VOEvolumetric overlap error RVD relative volume difference ASD average symmetric surface distance RMSD root mean square symmetricsurface distance MaxD maximum symmetric surface distance DICE Dice similarity coefficient)

VOE () RVD () ASD (mm) RMSD (mm) MaxD (mm) DICE Diameter (mm)Small tumor 3590 plusmn 706 038 plusmn 2529 066 plusmn 023 099 plusmn 031 334 plusmn 127 078 plusmn 005 942 plusmn 211Max 4776 3799 125 174 632 086 1480Min 2411 minus3124 040 069 200 069 554Large tumor 2662 plusmn 711 minus311 plusmn 1105 074 plusmn 035 113 plusmn 054 457 plusmn 340 084 plusmn 005 1695 plusmn 920Max 4650 1825 240 327 2078 095 4538Min 878 minus1807 040 068 173 070 761Average 2904 plusmn 816 minus220 plusmn 1588 072 plusmn 033 110 plusmn 049 425 plusmn 303 083 plusmn 006 1499 plusmn 863

a perfect tumor segmentation and the manual segmentationof the average quality (VOE = 1294 RVD = 964 ASD =040mm RMSD = 072mm and MaxD = 40) is worth thescore of 90

In our experiments the parameters described in Sec-tion 23 were determined experimentally by consideringthe segmentation performance and computational cost Theproposed method was implemented in C++ and tested on a2GHz Intel Xeon E5-2620 PC workstation with 32GB RAM

33 Results The statistical results of the proposed methodare represented in Table 1 In this paper a tumor with anapproximate diameter larger than or equal to 10mm wasdefined as a large one and a small tumor had a diameterless than 10mm Our method achieved an average VOE andRVD of 2904 and minus220 an average ASD RMSD MaxDof 072mm 110mm and 425mm and an average DICE of083 respectively Figure 5 shows the scores of ourmethod forsmall tumor and large tumor segmentationThe average scoreof VOE for all tumors was 7756 For large tumors a VOE of2662 RVD of minus311 ASD of 074mm MaxD of 457mm

VOE RVD ASD RMSD MaxD

Small tumorLarge tumorAverage

50556065707580859095

100

Scor

e

Figure 5 Scores of segmentation results obtained by the proposedmethod (VOE volumetric overlap error RVD relative volumedifference ASD average symmetric surface distance RMSD rootmean square symmetric surface distance MaxD maximum sym-metric surface distance)


(a) (b) (c) (d) (e) (f) (g) (h)

Figure 6 Segmentation results obtained by the proposed method compared to ground truth manual segmentation Each column from (a) to(g) shows one case of tumor segmentation results in axial coronal and sagittal view and the 3D reconstruction result (h) 3D reconstructionof segmented tumors inside the liver The contoursurface of the ground truth is in green The contoursurface of the segmented tumor bythe proposed method is in yellow The liver surface is shown in brown

Table 2 Statistical performance of the proposed method compared to some other methods Results are represented as mean plusmn standarddeviation

Method Year Auto Dataset VOE () RVD () ASD (mm) RMSD (mm) MaxD (mm) DICE RuntimeStawiaski etal [14] 2008 Interactive LTSC08 2949 plusmn 1280 2387 plusmn 3472 150 plusmn 067 207 plusmn 089 830 plusmn 410 mdash 5ndash8mins

Li et al [12] 2012 Semi LTSC08 2631 plusmn 579 minus1064 plusmn 755 106 plusmn 038 mdash 866 plusmn 317 mdash 30 sKadoury etal [17] 2015 Auto LTSC08 252 plusmn 17 143 plusmn 28 14 plusmn 03 16 plusmn 04 69 plusmn 18 mdash 102 s

Moghbel etal [10] 2016 Auto 3Dircadb 2278 plusmn 1215 859 plusmn 1878 mdash mdash mdash 075 plusmn 015 30 sslice

Foruzan andChen [19] 2016 Semi 3Dircadb 3061 plusmn 1044 1597 plusmn 1204 418 plusmn 960 509 plusmn 1071 1255 plusmn 1707 082 plusmn 007 154 s

Our method Semi 3Dircadb 2904 plusmn 816 minus220 plusmn 1588 072 plusmn 033 110 plusmn 049 425 plusmn 303 083 plusmn 006 45 s

and DICE of 084 were obtained For small tumors a higherVOE of 3590 and a lower DICE of 078 were obtainedwhich led to lower accuracy scores

As shown in Table 2 the average running time of theproposed method taken to do seed point selection tumorVOI extraction and graph cuts segmentation was 45 s Fora particular tumor the running time varied with the tumorsize For a large tumor with approximately 45mm in diame-ter the time for VOI extraction and graph cuts segmentationwas 3 s and 28 s respectivelyThe time for selecting themiddletumor slice and the tumor seed point was typically less than30 s

Table 2 shows the comparative results of the proposedmethod with previous methods [10 12 14 17 19] Themethods of Li et al [12] Stawiaski et al [14] and Kadouryet al [17] were evaluated on the dataset provided by thecompetition of LTSC08 which included 4 CT volumes with10 tumors However the LTSC08 dataset is not available nowThe methods of Moghbel et al [10] and Foruzan and Chen[19] were evaluated using the 3Dircadb dataset involving

120 tumors The 3Dircadb dataset includes more challengingcases than the LTSC08 dataset does Compared with otherprevious methods our method improved the time efficiencyof liver tumor segmentation while maintaining accuracy

Figure 6 shows a typical example of one patientrsquos CTvolume data consisting of 7 tumors with different sizesintensities and positions It can be seen that our methodachieved comparable results to the ground truth manualsegmentation in most cases However relatively large under-segmentation and oversegmentation errors occurred whenthe tumor presented ambiguous or low contrast boundaries(Figures 6(e) and 6(g)) More examples of challenging casesare presented in Figure 7

4 Discussion

In this paper we proposed a new semiautomatic method tosegment liver tumors from CT volume images It consists oftwo major steps (1) tumor VOI extraction using confidenceconnected region growing algorithm with one single seed


(a)

(b)

(c)

Figure 7 Some challenging cases Each row shows a case of tumor segmentation results in sequential slices and 3D visualization Thecontoursurface of the ground truth is in green The contoursurface of the segmented tumor by the proposed method is in yellow

point (2) tumor segmentation based on KFCMS and graphcuts algorithms

The proposed method was evaluated on the 3Dircadbdataset Experimental results showed that the segmentationaccuracy of ourmethodwas comparable to that of themanualsegmentation for most cases (Figure 6) while the efficiencyof segmentation was improved significantly with an averageprocessing time less than one minute per tumor (Table 2) Asshown in Table 1 and Figure 5 small tumors were prone tohave higher volumetric overlap errors than large tumorsThiswas because for small tumors a small discrepancy betweenthe segmentation and the ground truth could lead to a consid-erably increased error Figure 7 shows the undersegmentationand oversegmentation results on challenging cases whichhad lower accuracy scores than averageThe undersegmenta-tion and oversegmentation errors were mainly due to the lowcontrast or weak boundaries of tumors Large tumors withinhomogeneous intensity adjacent to the boundary of liverwere also prone to be undersegmented

Compared with previous approaches (Table 2) the pro-posed method can achieve accurate 3D liver tumor segmen-tation in a fast manner Among the graph based methodsStawiaski et al [14] constructed a region adjacency graph onsubregions of watershed transform and applied graph cutsfor tumor segmentation Kadoury et al [17] applied a high-order graphical model with potential functions based ondiscriminant Grassmannian manifolds learning Kadouryrsquosmethod achieved one of the highest accuracies in Table 2and the average segmentation time per tumor was 102 swith the average training time of 6 hours For Staviaskirsquosmethod it took a long time to segment a tumor including1 minute to define the tumor VOI manually 1-2 minutesto mark seed points for graph cuts segmentation in threeorthogonal slices and 2ndash5 minutes to refine the segmentedtumor contours in an interactive way Unlike Staviaskirsquos andKadouryrsquos methods user interaction was reduced to markone single seed point in our method and then the tumorVOI extraction and graph cuts initialization processes were

conducted automatically and efficiently Fuzzy probabilisticmodels and gradient informationwere introduced to improvethe accuracy and robustness of our method

Among the semiautomatic methods Li et al [12] usedlevel sets method integrating FCM based regional infor-mation and gradient based boundary information Foruzanand Chen [19] obtained initial tumor contours using super-vised watershed SVM and scattered data approximationfor largesmall tumors and then refined the contours basedon sigmoid edge model For Lirsquos method an average timeof 30 s was taken per tumor in a given tumor VOI whichwas defined by two user-selected seed points in the tumorand surrounding liver regions The average time of Foruzanrsquosmethod was 154 s per tumor including seed points selectiontraining tumor contour extraction and refinement Severalseed points for the tumor liver and other background weremarked in the middle tumor slice through user interac-tion [19] Compared with Lirsquos and Foruzanrsquos methods weemployed confidence connected region growingwith one sin-gle seed point in three orthogonal slices to extract the tumorVOI rapidly The kernelized FCM with spatial constraintsinstead of FCM and the sigmoid of gradient magnitudewere incorporated in the energy function as regional andedge information No training process was needed for theinitialization of our graph cuts based method

Among all the methods in Table 2 Moghbel et al [10]proposed an automatic hybrid method based on FCM withcuckoo optimization and random walkers It achieved thehighest accuracy and the average time was 30 s per sliceapproximately 16 minutes per case The performance of ourmethod on the 3Dircadb dataset was comparable to thatof Foruzan and the tumor segmentation procedure wasperformed in a fast way with low computational cost

The contributions of the proposed method are as follows(1) User interaction was reduced significantly compared tothe traditional graph cuts method Only one seed pointwas required to be marked close to the center of tumor inthe middle tumor slice An automatic correction was also


conducted to reduce interoperator variability in choosing theseed point (2)The tumor VOI was extracted adaptively usingconfidence connected region growing in the three orthogonalslices to reduce computational cost Initial tumor regions onthe three slices were obtained based on the integrated imagesof CCRG segmentations to improve the robustness of tumorVOI extraction (3) Image intensity and spatial and gradientinformation corresponding to the probabilistic distributionsestimated by KFCMS and the sigmoid of gradientmagnitudewere incorporated in the energy function to improve theperformance of graph cuts segmentation (4) The proposedmethod was efficient while maintaining accuracy Such afast segmentation method might be used for practical appli-cations like trajectory planning for radiofrequency ablationwithout significantly increasing the processing time whichinvolves segmentations of all relevant organsstructures [31]

One limitation of our method is that it mainly focusedon liver tumors with hypointensity For tumors with hyper-intensity some parts of the method shall be adjusted likethe automatic correction of seed point in the VOI extractionstep Also the evaluation experiments should be extended toinclude more types of liver lesions To deal with challengingcases of tumorswith low contrast and ambiguous boundariesour method may be enhanced by incorporating more textureinformation and a contour refinement process in future

5 Conclusion

This paper presented a semiautomatic method for 3D tumorsegmentation in CT images using improved FCM and graphcuts algorithms Low interaction was required and the tumorVOI was extracted to reduce computational cost Probabilis-tic distributions estimated by KFCMS and sigmoid of gradi-ent magnitude were incorporated into the energy function ofgraph cutsWhile being faster thanmost of previousmethodswith an average computational time of 45 s per tumor theproposed method achieved accurate segmentation results Infuture improvements for reducing undersegmentation andoversegmentation errors shall be conducted to enhance theperformance of the proposed method on challenging casesDatasets withmore types of tumors for evaluation are needed

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant nos 81127006 and 71661167001)

References

[1] J Ferlay I Soerjomataram R Dikshit et al ldquoCancer incidenceand mortality worldwide sources methods and major patternsin GLOBOCAN 2012rdquo International Journal of Cancer 2014

[2] P Campadelli E Casiraghi and A Esposito ldquoLiver segmen-tation from computed tomography scans a survey and a new

algorithmrdquoArtificial Intelligence inMedicine vol 45 no 2-3 pp185ndash196 2009

[3] L Massoptier and S Casciaro ldquoA new fully automatic androbust algorithm for fast segmentation of liver tissue andtumors from CT scansrdquo European Radiology vol 18 no 8 pp1658ndash1665 2008

[4] G Li X Chen F Shi W Zhu J Tian and D Xiang ldquoAutomaticliver segmentation based on shape constraints and deformablegraph cut inCT imagesrdquo IEEETransactions on Image Processingvol 24 no 12 pp 5315ndash5329 2015

[5] L Rusko and A Perenyi ldquoAutomated liver lesion detection inCT images based on multi-level geometric featuresrdquo Interna-tional Journal of Computer Assisted Radiology and Surgery vol9 no 4 pp 577ndash593 2014

[6] A Zygomalas D Karavias D Koutsouris et al ldquoComputer-assisted liver tumor surgery using a novel semiautomatic anda hybrid semiautomatic segmentation algorithmrdquo Medical andBiological Engineering and Computing vol 54 no 5 pp 711ndash7212016

[7] A M Anter M A ElSoud A E Hassanien et al ldquoAutomaticcomputer aided segmentation for liver and hepatic lesions usinghybrid segmentations techniquesrdquo in Proceedings of the 2013Federated Conference on Computer Science and InformationSystems pp 193ndash198 2013

[8] J-Y Zhou D W K Wong F Ding et al ldquoLiver tumoursegmentation using contrast-enhanced multi-detector CT dataPerformance benchmarking of three semiautomated methodsrdquoEuropean Radiology vol 20 no 7 pp 1738ndash1748 2010

[9] S S Kumar R S Moni and J Rajeesh ldquoContourlet transformbased computer-aided diagnosis system for liver tumors oncomputed tomography imagesrdquo in Proceedings of the 2011 -International Conference on Signal Processing CommunicationComputing andNetworking Technologies ICSCCN-2011 pp 217ndash222 ind July 2011

[10] M Moghbel S Mashohor R Mahmud and M Iqbal BinSaripan ldquoAutomatic liver tumor segmentation on computedtomography for patient treatment planning and monitoringrdquoEXCLI Journal vol 15 pp 406ndash423 2016

[11] A Das and S K Sabut ldquoKernelized Fuzzy C-means Clusteringwith Adaptive Thresholding for Segmenting Liver Tumorsrdquo inProceedings of the 2nd International Conference on IntelligentComputing Communication and Convergence ICCC 2016 pp389ndash395 ind January 2016

[12] B N Li C K Chui S Chang and S H Ong ldquoA new unifiedlevel set method for semi-automatic liver tumor segmentationon contrast-enhanced CT imagesrdquo Expert Systems with Applica-tions vol 39 no 10 pp 9661ndash9668 2012

[13] T-N Le P T Bao and H T Huynh ldquoLiver Tumor Segmenta-tion from MR Images Using 3D Fast Marching Algorithm andSingle Hidden Layer Feedforward Neural Networkrdquo BioMedResearch International vol 2016 Article ID 3219068 2016

[14] J Stawiaski E Decenciere and F Bidault ldquoInteractive livertumor segmentation using graph-cuts and watershedrdquo TheMIDAS Journal - Grand Challenge Liver Tumor Segmentation(MICCAI Workshop) pp 1ndash12 2008

[15] M G Linguraru W J Richbourg J Liu et al ldquoTumor burdenanalysis on computed tomography by automated liver andtumor segmentationrdquo IEEE Transactions on Medical Imagingvol 31 no 10 pp 1965ndash1976 2012

[16] X Zhang J Tian D Xiang X Li and K Deng ldquoInteractiveliver tumor segmentation from ct scans using support vector


classification with watershedrdquo in Proceedings of the 33rd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society EMBS 2011 pp 6005ndash6008 usa September2011

[17] S Kadoury E Vorontsov andA Tang ldquoMetastatic liver tumoursegmentation from discriminant Grassmannian manifoldsrdquoPhysics in Medicine and Biology vol 60 no 16 pp 6459ndash64782015

[18] W Li F Jia and Q Hu ldquoAutomatic Segmentation of LiverTumor in CT Images with Deep Convolutional Neural Net-worksrdquo Journal of Computer and Communications vol 03 no11 pp 146ndash151 2015

[19] A H Foruzan and Y-W Chen ldquoImproved segmentation oflow-contrast lesions using sigmoid edge modelrdquo InternationalJournal of Computer Assisted Radiology and Surgery vol 11 no7 pp 1267ndash1283 2016

[20] X Deng and G Du ldquoEditorial 3D segmentation in the clinica grand challenge II-liver tumor segmentationrdquo The MIDASJournal - Grand Challenge Liver Tumor Segmentation (MICCAIWorkshop) pp 1ndash4 2008

[21] WWu Z Zhou SWu and Y Zhang ldquoAutomatic liver segmen-tation on volumetric CT images using supervoxel-based graphcutsrdquo Computational and Mathematical Methods in MedicineArticle ID 9093721 Art ID 9093721 14 pages 2016

[22] C Rother V Kolmogorov andA Blake ldquoldquoGrabCutrdquo interactiveforeground extraction using iterated graph cutsrdquoACMTransac-tions on Graphics vol 23 no 3 pp 309ndash314 2004

[23] S Chen andD Zhang ldquoRobust image segmentation using FCMwith spatial constraints based on new kernel-induced distancemeasurerdquo IEEE Transactions on Systems Man and CyberneticsB Cybernetics vol 34 no 4 pp 1907ndash1916 2004

[24] K-S Chuang H-L Tzeng S Chen J Wu and T-J ChenldquoFuzzy c-means clustering with spatial information for imagesegmentationrdquo Computerized Medical Imaging and Graphicsvol 30 no 1 pp 9ndash15 2006

[25] D-Q Zhang and S-CChen ldquoAnovel kernelized fuzzyC-meansalgorithm with application in medical image segmentationrdquoArtificial Intelligence in Medicine vol 32 no 1 pp 37ndash50 2004

[26] Y Boykov and V Kolmogorov ldquoAn experimental comparisonof min-cutmax-flow algorithms for energy minimization invisionrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 26 no 9 pp 1124ndash1137 2004

[27] Y Boykov and G Funka-Lea ldquoGraph cuts and efficient N-Dimage segmentationrdquo International Journal of Computer Visionvol 70 no 2 pp 109ndash131 2006

[28] Y Li J Sun C-K Tang andH-Y Shum ldquoLazy snappingrdquoACMTransactions on Graphics vol 23 no 3 pp 303ndash308 2004

[29] T Heimann B van Ginneken M A Styner et al ldquoComparisonand evaluation of methods for liver segmentation from CTdatasetsrdquo IEEE Transactions on Medical Imaging vol 28 no 8pp 1251ndash1265 2009

[30] A A Taha and A Hanbury ldquoMetrics for evaluating 3Dmedicalimage segmentation Analysis selection and toolrdquo BMC Medi-cal Imaging vol 15 no 1 article no 29 2015

[31] C Schumann C Rieder S Haase et al ldquoInteractive multi-criteria planning for radiofrequency ablationrdquo InternationalJournal of Computer Assisted Radiology and Surgery vol 10 no6 pp 879ndash889 2015

Submit your manuscripts athttpswwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


of three semiautomatic methods for tumor segmentationincluding the two-dimensional (2D) region growing withknowledge-based constraints and the 3D Bayesian rule-based region growing method Kumar et al [9] developeda computer-aided diagnosis (CAD) system for tumor seg-mentation and classification The alternative fuzzy clusteringalgorithm was used in the segmentation stage which used anew distance function instead of the Euclidean metric Dasand Sabut [11] used adaptive thresholding morphologicalprocessing and a kernelized fuzzy C-means (FCM) algo-rithm to segment liver tumors from CT images Moghbel etal [10] proposed an automatic tumor segmentation schemebased on the supervised randomwalker approach FCMwithcuckoo optimization was applied for the labeling of pixels forthe final random walker segmentation

Active contour approaches such as fast marchingand level set algorithms are popular segmentation tech-niques However good initialization and speed functions arerequired in order to obtain accurate segmentation resultsespecially for tumors with heterogeneous intensities andweak boundaries Li et al [12] proposed a new level set modelintegrating edge- and region-based information with priorinformation FCMalgorithmwas applied for the probabilisticestimation of tumor tissues Le et al [13] proposed a semi-automatic method to segment liver tumors from MagneticResonance (MR) images where the fast marching algorithmwas used to generate the initial labeled regions and then otherunlabeled voxels were classified by the neural network Graphcutsmethods have also beenwidely applied formedical imagesegmentation [14 15] which can achieve global optimizationsolution Stawiaski et al [14] proposed an interactive seg-mentation method based on watershed and graph cuts Themethod achieved the highest accuracy compared to othersemiautomatic or automatic methods in the competitionof 2008 Liver Tumor Segmentation Challenge (LTSC08)which was held in conjunction with the Medical ImageComputing and Computer Assisted Intervention (MICCAI)2008 conference [20] Linguraru et al [15] presented anautomatic tumor segmentationmethod using graph cuts withHessian-based shape constraints biased to blob-like tumorsHowever the main drawback of such level set or graph cutsbased techniques is their relatively high computational costespecially for 3D volume data

To deal with the variations of tumor shape size intensityand texture machine learning based methods were alsostudied Foruzan and Chen [19] employed the support vectormachine (SVM) and scattered data approximation algorithmsto obtain the initial tumor boundary and then refined thefinal lesion region by using a sigmoid edge model Kadouryet al [17] developed an automatic tumor segmentationframework by using themachine learning technique based ondiscriminant Grassmannian manifolds Nonlinear intensitydistributions of liver and tumor tissues were learned duringthe training phase Then a higher-order conditional randomfield (CRF) approach was applied to perform the tumorsegmentation Zhang et al [16] applied watershed transformon the liver region and then employed region-based clas-sification by SVM for tumor segmentation However formachine learning based methods a large amount of training

data with gold standards is required during the trainingprocess

Considering the clinical applicability and segmentationaccuracy as well as the processing time our goal was todevelop an efficient robust and accurate tumor segmen-tation method with low human interaction Thus in thispaper a semiautomatic method based on improved FCMand graph cuts was proposed to realize 3D liver tumorsegmentation from CT images With a single user-selectedseed point both the tumor volume of interest (VOI) andlabeled foregroundbackground regions for graph cuts seg-mentation were extracted using the confidence connectedregion growing algorithm To improve segmentation accu-racy a kernelized FCM algorithm with spatial informationwas incorporated when estimating the probabilistic modelsof tumors and liver tissues

The rest of this paper is organized as follows Section 2introduces the details of the proposed method Section 3presents the experimental results and the discussion isgiven in Section 4 Finally the conclusion is summarized inSection 5

2 Methods

The proposed liver tumor segmentation framework is illus-trated in Figure 1 It consists of four major steps (1) prepro-cessing (2) tumor VOI extraction (3) tumor segmentationand (4) postprocessing Together with the original input CTvolume the presegmented liver mask is required to extractthe liverVOI to reduce the computational costThe livermaskcan be obtained by using a 3D liver segmentation methodsuch as the one in our previous work [21]

21 Preprocessing In the preprocessing step firstly nonlivertissues were removed and the liver VOI 119868Liver was extractedfrom the original CT image using the liver mask Then 119868Liverwas smoothed by median filtering and resampled to isotropicvoxel of size 1 times 1 times 1mm by linear interpolation

To segment the tumor one seed point was manuallyselected on the middle tumor slice The middle tumor slicewas defined as an axial slice which contained a relativelylarge lesion region The seed point V119904 was selected near thecenter of the lesion To reduce interoperator variability anautomatic correction was applied by replacing the seed pointto the darkest voxel within a cube of 5 times 5 times 3 voxels centeredat the selected seed point

22 Tumor VOI Extraction Using Confidence ConnectedRegion Growing Based on the seed point the tumor VOI119868Tumor was extracted by defining a bounding box around thetumor Further analysis was conducted on 119868Tumor in order toreduce the computational complexity and processing timeThebounding boxwas computed using confidence connectedregion growing algorithm (CCRG) in the axial coronal andsagittal slices

The concept of CCRG is similar to conventional regiongrowing based methods [7 8] Through an iterative regiongrowing process that started from the seed point V119904 neigh-boring voxels v with intensities inside the defined range 119868V isin


Resampled liver VOI

Original CT volume

Liver mask

SmoothingResampling



Axial slice

Coronal slice

Sagittal slice




Initial seed mask

Sigmoid of gradient

magnitude



Postp

roce

ssin

g


Preprocessing













119869 = 119873Vsum119895=1

119873119888sum119894=1

119906119898119891119894119895 10038171003817100381710038171003817119868119895 minus 119888119894100381710038171003817100381710038172 (2)


l = 15 l = 17 l = 19 l = 23

(a)

l = 15 l = 17 l = 19

(b)

l = 17 l = 21 l = 23

(c)




119906119894119895 = (119873119888sum119896=1


minus1

119888119894 = sum119873V119895=1 119906119898119891119894119895 119868119895sum119873V119895=1 119906119898119891119894119895 (3)



1199061015840119894119895 = 119906119901119894119895ℎ119902119894119895sum119873119888119896=1

119906119901119896119895ℎ119902119896119895

(4)

where

ℎ119894119895 = sum119896isinNB(119868119895)

119906119894119896



(5)



Axial

Coronal

Sagittal

(a) (b) (c) (d)

x

y

x

z

y

z





(a) (b) (c) (d) (e) (f)



119888119894 = sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) 119868119895sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) (6)









119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)


For (VT) isin 119864119905119877 (119891V) =


(8)

For (S V) isin 119864119904119877 (119891V) =


(9)



1 if119891V = 1198911199060 if119891V = 119891119906(10)


















50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Resampled liver VOI

Original CT volume

Liver mask

SmoothingResampling



Axial slice

Coronal slice

Sagittal slice




Initial seed mask

Sigmoid of gradient

magnitude



Postp

roce

ssin

g


Preprocessing













119869 = 119873Vsum119895=1

119873119888sum119894=1

119906119898119891119894119895 10038171003817100381710038171003817119868119895 minus 119888119894100381710038171003817100381710038172 (2)


l = 15 l = 17 l = 19 l = 23

(a)

l = 15 l = 17 l = 19

(b)

l = 17 l = 21 l = 23

(c)




119906119894119895 = (119873119888sum119896=1


minus1

119888119894 = sum119873V119895=1 119906119898119891119894119895 119868119895sum119873V119895=1 119906119898119891119894119895 (3)



1199061015840119894119895 = 119906119901119894119895ℎ119902119894119895sum119873119888119896=1

119906119901119896119895ℎ119902119896119895

(4)

where

ℎ119894119895 = sum119896isinNB(119868119895)

119906119894119896



(5)



Axial

Coronal

Sagittal

(a) (b) (c) (d)

x

y

x

z

y

z





(a) (b) (c) (d) (e) (f)



119888119894 = sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) 119868119895sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) (6)









119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)


For (VT) isin 119864119905119877 (119891V) =


(8)

For (S V) isin 119864119904119877 (119891V) =


(9)



1 if119891V = 1198911199060 if119891V = 119891119906(10)


















50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















l = 15 l = 17 l = 19 l = 23

(a)

l = 15 l = 17 l = 19

(b)

l = 17 l = 21 l = 23

(c)




119906119894119895 = (119873119888sum119896=1


minus1

119888119894 = sum119873V119895=1 119906119898119891119894119895 119868119895sum119873V119895=1 119906119898119891119894119895 (3)



1199061015840119894119895 = 119906119901119894119895ℎ119902119894119895sum119873119888119896=1

119906119901119896119895ℎ119902119896119895

(4)

where

ℎ119894119895 = sum119896isinNB(119868119895)

119906119894119896



(5)



Axial

Coronal

Sagittal

(a) (b) (c) (d)

x

y

x

z

y

z





(a) (b) (c) (d) (e) (f)



119888119894 = sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) 119868119895sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) (6)









119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)


For (VT) isin 119864119905119877 (119891V) =


(8)

For (S V) isin 119864119904119877 (119891V) =


(9)



1 if119891V = 1198911199060 if119891V = 119891119906(10)


















50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Axial

Coronal

Sagittal

(a) (b) (c) (d)

x

y

x

z

y

z





(a) (b) (c) (d) (e) (f)



119888119894 = sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) 119868119895sum119873V119895=1 1199061015840119898119891119894119895 119870(119868119895 119888119894) (6)









119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)


For (VT) isin 119864119905119877 (119891V) =


(8)

For (S V) isin 119864119904119877 (119891V) =


(9)



1 if119891V = 1198911199060 if119891V = 119891119906(10)


















50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















119864 (119891) = sumVisinN

119877 (119891V) + 120574 sum(V119906)isin119864119899

119861 (119891V 119891119906) (7)


For (VT) isin 119864119905119877 (119891V) =


(8)

For (S V) isin 119864119904119877 (119891V) =


(9)



1 if119891V = 1198911199060 if119891V = 119891119906(10)


















50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



























50556065707580859095

100

Scor

e



(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















(a) (b) (c) (d) (e) (f) (g) (h)













4 Discussion



(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















(a)

(b)

(c)












5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















5 Conclusion




Acknowledgments


References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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