research article functional region annotation of...

Research ArticleFunctional Region Annotation of Liver CT Image Based onVascular Tree

Yufei Chen1 Xiaodong Yue12 Caiming Zhong3 and Gang Wang14

1Research Center of CAD Tongji University Shanghai 200092 China2School of Computer Engineering and Science Shanghai University Shanghai 200444 China3College of Science and Technology Ningbo University Ningbo 315211 China4School of Statistics and Management Shanghai University of Finance and Economics Shanghai 200433 China

Correspondence should be addressed to Xiaodong Yue yswantflyshueducn

Received 2 June 2016 Revised 24 July 2016 Accepted 4 August 2016

Academic Editor Quan Zou

Copyright copy 2016 Yufei Chen 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

Anatomical analysis of liver region is critical in diagnosis and treatment of liver diseases The reports of liver region annotationare helpful for doctors to precisely evaluate liver system One of the challenging issues is to annotate the functional regions of liverthrough analyzing Computed Tomography (CT) images In this paper we propose a vessel-tree-based liver annotation method forCT imagesThe first step of the proposed annotationmethod is to extract the liver region including vessels and tumors from the CTscans And then a 3-dimensional thinning algorithm is applied to obtain the spatial skeleton and geometric structure of liver vesselsWith the vessel skeleton the topology of portal veins is further formulated by a directed acyclic graph with geometrical attributesFinally based on the topological graph a hierarchical vascular tree is constructed to divide the liver into eight segments accordingto Couinaud classification theory and thereby annotate the functional regions Abundant experimental results demonstrate thatthe proposed method is effective for precise liver annotation and helpful to support liver disease diagnosis

1 Introduction

As a noninvasive and painless medical test ComputedTomography (CT) imaging can provide volumetric imagedata for liver disease diagnosis which has been widely usedin hospitals [1 2] The Computer Aided Diagnosis (CAD) onliver is a complex task that depends on a good understandingof the whole liver system including the features of livervessels and lesions as well as the anatomical features on spe-cific patients [3ndash5] Automatically annotating the functionalsegments of liver is an effective way to support doctors tostudy and precisely evaluate the liver system Although therehave been limited research works on liver annotation [6ndash8] its implementation for real CAD applications is still anarduous task for the following reasons

Thefirst and fundamental step in liver annotation is organregion segmentation [9] Some methods segment organthroughmodeling the shape of liver region [10ndash13] Howeverbecause of the large variance of liver shapes among differentpatients it is difficult for shape-based methods to achieve

precise liver segmentation As another popular segmentationmethod the level set methods are very sensitive to livercontour initialization and suffer from iterative computationburden [14ndash16] In particular for the images with tumorsand vessels located near liver surface the level-set-basedsegmentation tends to be trapped into local optima and elim-inates tumors and vessels from main target Recent researchworks reveal that the graph cut models have a great potentialwith the advantages of global optimization and practicalefficiency for image segmentation [17] But for CT imagesof livers the graph cut models cannot handle well seriouslyblurred boundaries and are incapable of distinguishing theliver regions of similar intensities from neighboring organs[18 19]

Besides organ region segmentation vessel segmentationhas been another challenging task for liver annotation dueto the limitation of vascular imaging equipment and thecomplexity of liver vascular topology Florin et al [20] treatedthe vessel segmentation as a tracking problem where vesselswere iteratively tracked using information on centerlines

Hindawi Publishing CorporationBioMed Research InternationalVolume 2016 Article ID 5428737 13 pageshttpdxdoiorg10115520165428737

2 BioMed Research International

Hepatic vein

Portal vein

Figure 1 Couinaud classification of liver anatomy

and local features The method needs user interaction andrequires special routines to handle branch points Selle et al[21] presented an intensity-threshold-based method whichdefined an optimal intensity threshold through measuringregion growing This kind of methods mainly suits segment-ing large vessels Manniesing et al proposed a vessel segmen-tationmethod based onHessianmatrix which enhances livervessels and thereby extracts tubular structures from the organregion [22] The vesselness of the structure is determinedby its geometrical features obtained from the eigensystem ofHessian matrix [23]

The topology of liver vasculature is of importance forrecognizing functional segments Vessel skeleton is widelyused to present the topology of vasculature Generally speak-ing there are three types of vessel skeletonization methodsThe algorithms based on distance transformation describewell the local structure but cannot guarantee the connectivityand completeness of skeleton [24] The algorithms based onVoronoi diagram are capable of capturing the topology of theentire vasculature but the computation of Voronoi skeleton istime-consuming especially for themedical image containinglarge-size objects [25] Compared with the skeletonizationmethods above the thinning algorithms can extract thevessel skeleton efficiently and in the meantime preserve theconnectivity and completeness of the skeleton Moreover thethinning algorithm can also record the medial position ofthe skeleton which is very helpful to annotate the functionalregions [2 26] However only vessel skeletons withoutquantitativemeasurement are not sufficient to present the realtopology of vasculature [27] For example it is difficult forvessel skeletons to keep the important organ features suchas length blood flow direction and radius of subbranchWithout considering anatomical measurements the imper-fect vessel segmentation results may lead to cyclic skeleton

Obtaining the topology of liver vasculature we canpartition liver region into functional segments and makethe annotation Referring to the Couinaud classification ofliver anatomy hepatic and portal veins divide liver into eightfunctionally independent segments as shown in Figure 1 [28]Each segment has its own vascular inflow outflow and biliarydrainage In the center of each segment there is a branch ofthe portal vein hepatic artery and bile duct In the peripheryof each segment there is vascular outflow through the hepaticveins Middle hepatic vein divides the liver into right and leftlobes Right hepatic vein divides the right lobe into anterior

and posterior segments Left hepatic vein divides the left lobeinto amedial and lateral part Portal vein divides the liver intoupper and lower segments

Formulating the Couinaud classification of liver anatomyOliveira et al estimated the planes that best fit each of thethree branches of the hepatic veins and the plane that best fitsthe portal vein These four planes define the subdivision ofthe liver in the Couinaud segments [29] However the plane-based method does not consider the influence of vascularvariation to plane estimation and it ignores the fact that theseparation between liver segments should be a surface Selle etal segmented liver through computing the nearest neighborof different vessel branches [21] But the result depends on theuser defined parameter which should be manually adjustedunder different cases Schenk et al used a Laplace model toassign each liver cell to one of the vascular branches to formliver segments [30]Thismodel suffers from a great computa-tion burden and is not robust enough due to the dependenceon vascular branch calibration Huang et al designed a fastliver segment method based on the hepatic vessel tree [31]The method projects the liver and vessel tree to a plane andthe classification of liver is achieved by classifying pointsin the projection plane Although having high efficiencythe method based on hepatic vessel tree is not a completefunctional anatomywhich leads to the inconsistency betweenthe annotated liver segments and the actual blood-supplybranch

As mentioned above the topology of vasculature canguide the annotation of functional segments Howeverbecause of the high complexity of liver vasculature it ishard to generate a precise representation of vasculaturetopology and the computation of geometric structures ofall the vessels is always a time-consuming task In factfrom the view of anatomy the left and right portal veinbranches superiorly and inferiorly project into the centerof each segment to supply blood This means that thefunctional segments of liver can be recognized by onlyportal vein branches in it In the light of this finding weproposed a hierarchical vascular tree to present the topologyof portal veins The branches of hierarchical vascular treeof portal veins correspond to the functional segments ofliver Based on the obtained functional segments we annotatethe liver region and measure the organ attributes using astandard terminology [6] The visualization of annotationand the measurements can form a report of liver system forCAD The contributions of this paper are summarized asfollows

(1) Design a Vessel Tree to Present the Topology of Portal VeinsConnect the topological voxels in vessel skeleton to form agraph Prune redundant and irrelevant branches of graph togenerate a formal vessel tree which indicates the geometricstructures of portal veins and blood flow direction

(2) Extend the Vessel Tree to a Hierarchical One for LiverAnnotation The vessel tree is hierarchically divided into twolevels according to the radius of portal vein branches TheSecond Subtree branches are preserved to form functionalsegments

BioMed Research International 3

Liver segmentation

Liver CT image

Tumorsegmentation

Vesselsegmentation

Hessianenhancement

Vesselskeletonization

Vascular treegeneration

Liver annotation

Graphrepresentation

Functionalsegment

Hierarchicalvascular tree

Visualization

Couinaudclassification

Measurements

Liver region

Tumorregion

Vesselregion

LiverCAD

Liver region

Liver systemreports

Figure 2 Workflow of the proposed annotation method

This paper is organized as follows The workflow of theproposed vessel-tree-based liver annotation method for CTimages is described in Section 2 Section 3 gives a detailedintroduction of the proposed method which includes vesseltree generation liver segment and annotation In Section 4abundant experimental results validate the effectiveness ofthe proposed annotation methodThe paper work is summa-rized in Section 5

2 Methodology

In this section we describe the entire workflow of theproposed functional region annotation method for liver CTimagesTheworkflow consists of four stages At the first stagethe liver region containing vessels and tumors is segmentedfrom the CT image using an improved graph cut modelMore details of liver region segmentation can be found inour previous work [32] In the liver region the segmentationfor tumors and vessels is further performed Second a 3-dimensional thinning algorithm is applied to extract theskeleton of vessels from the segmented vessel region Basedon the skeleton the topological structure of the vessel systemis represented by a vascular tree Specifically the vascular treeis formulated by a directed acyclic graph and it can be furtherextended to a hierarchical version The hierarchical vasculartrees present the connectivity of vessels among the functionalsegments of liver According to the connectivity of vasculartrees the liver region can be divided into eight functionalsegments referring to Couinaud classification theory At thethird stage integrating the segmentation results of tumorsvessels and functional segments we can annotate the liverregion and measure the attributes of organ Finally a reportof liver system which includes the visualization of regionannotation and the measurements of functional segments

is generated to support doctors to precisely evaluate theliver system The core steps of the workflow are illustratedin Figure 2 the details will be further introduced in thefollowing section

3 Vessel-Tree-Based Liver Annotation

As introduced above the key step of liver annotation is to par-tition the liver region into multiple functional segments andthe topology of vasculature can provide prior information toguide the partition According to the Couinaud classificationtheory the liver system can be divided into eight functionalanatomies It is not necessary to analyze the geometricstructure of the entire vasculature the partition can beperformed through constructing a hierarchical vascular treeof portal veins The methodologies of constructing trees ofportal veins and annotating liver segments with hierarchicalvessel trees will be elaborated in this section

31 Vessel Tree Generation

311 Vessel Segmentation Vessel segmentation is a prelim-inary step for liver annotation In this step first the liversegmentation is performed on CT image and then the vesselsand tumors are further extracted from the segmented liverregion Precise segmentation of liver region is crucial to thesubsequent annotation and measurement In the proposedmethod we adopt a semisupervised approach for liver seg-mentation of CT scans The segmentation method is basedon a graph cut model integrated with domain knowledgewhich combines both boundary and regional cues in a globaloptimization framework Specifically the pixels in each CTscan are represented by a graph and the problem of regionsegmentation is casted to searching for the optimal cut on


graph The energy function of graph cut is constructed viaknowledge-based similaritymeasure and hard constraints aredefined to speed up the graph computation More details ofliver region segmentation can be found in our previous work[32] We use the same segmentation method to obtain thetumor region

Extracting vessels from liver region is a prerequisite forthe geometrical and structural analysis of vasculature whichis very important for liver disease diagnosis To segment theregions of vessels we use Hessian-based filter to enhance thecontrast of liver region 119868liverThe filter is good at searching fortubular-like structures For discriminating tubular-like struc-tures from blob-like and plate-like structures the eigenvaluesofHessianmatrix for filtering should satisfy condition1205821 asymp 01205822 ≪ 0 1205823 ≪ 0 [22] The vesselness measure of structures isdefined as follows

Vessel (120582)

=

0 if 1205822 ge 0 or 1205823 ge 0(1 minus 119890minus119877211988621205722) sdot 119890minus119877211988721205732 sdot (1 minus 119890minus1198772119888 21198882) otherwise

119877119886 =100381610038161003816100381612058221003816100381610038161003816100381610038161003816100381612058231003816100381610038161003816

119877119887 =100381610038161003816100381612058211003816100381610038161003816

radic10038161003816100381610038161205822 sdot 12058231003816100381610038161003816

119877119888 = radic12058221 + 12058222 + 12058223

(1)

where 120572 120573 119888 are the parameters to control the sensitivityof measure In the experiments we set 120572 = 03 120573 = 07119888 = 119868max2 Upper bound 119868max corresponds to the brightestintensity value of vessels that can be empirically definedAfter the Hessian filtering a 3D region growing algorithmis utilized on the filtered liver region to segment the livervasculature Some morphological operations are adopted tofill small cavities so as to make the vessel region continuousand smooth The segmented vessel region consists of portalveins and hepatic veins As introduced in Section 1 the portalveins are sufficient for distinguishing the functional segmentsof liver thus we preserve the connected component of portalvein as binary image 119868vessel in which 1 stands for pixels ofvasculature and 0 represents the background

312 Vessel Skeletonization To capture the topology of vas-culature first we should extract the vessel skeleton fromthe segmented vessel region Vessel skeletonization aims toreduce the foreground region of binary image 119868vessel to askeletal remnantThe skeletonization process should preservethe extent and connectivity of the original vessel regionTo satisfy these requirements we design a 3D thinningalgorithm to extract the skeleton of vessels The skeletonobtained through spatial thinning can preserve the geomet-ric structure of the original vessel region situate in themiddle of 119868vessel and be single-voxel wide Moreover thethinning-based skeletonization is robust to noisy voxels Thethinning algorithm is implemented through categorizing thevoxels

0 3 61 4

121610

14

22

13

72 5 8

9 15

17

2425

262320

211819

11

Figure 3 Neighborhood connectivity of a voxel

In 3D space a 3 times 3 times 3 lattice is built to examine thelocal connectivity of a voxel The 26-neighborhood and 6-neighborhood (marked as green) connectivity is shown inFigure 3 Given voxel V1198736(V) and11987326(V) respectively denotethe 6 neighbors and 26 neighbors of V For skeletonizationthe voxels can be categorized into four types Border Voxel119881119861 Line Voxel119881119871 Euler Invariant Voxel119881119864 and Simple Voxel119881119878 Next we expatiate the definitions of the voxels of differenttypes

Definition 1 (BorderVoxel) Given vessel voxel V isin 119881vessel if atleast one of its 6 neighbors has the value of 0 that is belongingto background the voxel is considered as Border Voxel

119881119861 = V | Number (1198736 (V) = 0) ge 1 V isin 119881vessel 119881vessel = V | 119868vessel (V) = 1

(2)

Definition 2 (Line Voxel) Given vessel voxel V isin 119881vessel ifmore than one of its 26 neighbors have the value of 1 that isbelonging to vessels the voxel is considered as Line Voxel

119881119871 = V | Number (11987326 (V) = 1) gt 1 V isin 119881vessel 119881vessel = V | 119868vessel (V) = 1

(3)

Definition 3 (Euler Invariant Voxel) Given vessel voxel V isin119881vessel if Euler characteristic 120594 will not change when remov-ing V from 119881vessel the voxel is considered Euler Invariant

119881119864 = V | 120594 (119881vessel cap 11987326 (V))minus 120594 (119881vessel cap 11987326 (V) cup V) = 0 V isin 119881vessel

120594 = 119874 minus 119867 + 119862119881vessel = V | 119868vessel (V) = 1

(4)

where 119874 119867 and 119862 are respectively the numbers of con-nected objects holes and cavities in the image

Definition 4 (Simple Voxel) Given vessel voxel V isin 119881vessel ifthe connectivity in its 26 neighborhoods keeps being invari-ant when removing V from 119881vessel the voxel is considered asSimple Voxel


119881vessel = V | 119868vessel (V) = 1 (5)


Fc Ec Vc

Figure 4 Topological voxels in vessel skeleton

From the definitions above we can find that the voxelsof border and lines and Euler invariant and simple voxels areredundant for preserving the topology of vasculature Thusthe skeletonization can be performed through iterativelydeleting all those four kinds of voxels from vessel regionuntil no more change occurs The output of skeletonizationis binary image 119868skeleton that contains a single-voxel wideskeleton marked as 1 noted as 119881skeleton

313 Graph Representation To better understand the topol-ogy of vasculature the structure of liver vessels represented byskeleton is further formulated by a graph The graph consistsof a set of vertexes (topological voxels) and connecting edges

Definition 5 (topological voxels) Topological voxels consistof end-voxels and branch-voxels end-voxel is the voxel in119881skeleton with only one skeleton neighbor and branch-voxel isthe skeleton voxel having more than two skeleton neighbors

As shown in Figure 4 end-voxels can be easily found bycounting the skeleton number in its 26 neighborhoods whichare marked as yellow However for branch-voxels there arefour candidates that have more than two neighbors (markedin red and green) Among all the possible branch-voxelcandidates the real branch-voxel should have the highestconnectivity with all its neighboring branches as the redvoxels shown in Figure 4 The connectivity of neighboringbranches can be quantified by the following cost function

Vcandidate

= V | Number (11987326 (V) = 1) ge 2 V isin 119881skeleton cost (V)= 1199084sumNeighborVoxel + 1199083sum119865119888 + 1199082sum119864119888+ 1199081sum119881119888 (1199084 gt 1199083 gt 1199082 gt 1199081)

branch-voxel

= Vbranch | cost (Vbranch) = max cost (Vcandidate)

(6)

where sumNeighborVoxel means the number of candidatesneighbor sum119865119888 sum119864119888 and sum119881119888 are respectively the numberof face-connected edge-connected and vertex-connectedcandidates The voxels of three connected types are alsomarked in Figure 4 In our implementation the weightingfactors are set as 1199084 = 4 1199083 = 3 1199082 = 2 1199081 = 1

Connecting the topological voxels with the correspond-ing edges we can construct an undirected graph to presentthe geometric structure of vessel system Based on the graphof topological voxels it is convenient for us to measure thegeometric attributes of vessel system The measurements aresummarized in Table 1

314 Tree Generation To simulate the structure of vascula-ture and indicate the blood flow we transform the topologicalgraph of vessel system into vessel trees First we convert theundirected graph to a directed one through breadth-first-searching from the vessel root The root of graph 119881root is themain portal vein which can be specified as the end-voxel withlargest radius summation of it and its branches It is definedas follows

119877 (V) = Radius (V) +MeanRadius (edge (V)) 119881root = V0 | 119877 (V0) = max 119877 (V) V isin end-voxel

(7)

Since the segmented vessel region contains internalcavities holes and bays the generated graph is alwayscyclic There are basically two kinds of loops in the graphredundant branches (with self-loops) and irrelevant branches(with cycles) The redundant branches are easily removed bydeleting branches in which all the skeleton voxels share thesamenearest topological voxel Removing irrelevant brancheswill be a more complex task According to anatomy theoryat each ramification point the blood inflow should be equalto outflow Based on this we can match the vessels onblood routine and remove the irrelevant ones Specificallythe outflow of branches should match the inflow of root veinand the blood flow can be approximated with cross-sectionalarea of veins which is square of radius Figure 5 illustratesa vessel system including one root vein and a branch of fivevessels Among all the connected cyclic edges marked in lightblue we should find a combination set of them that makesoutflow most closely match inflow The vessels out of thecombination set are considered as irrelevant branches andshould be removed

The process of determining irrelevant cyclic branches canbe formally defined by the following equations

Diff (119890comb) =100381610038161003816100381610038161003816Radius (119890in)

2

minussumRadius (119890out noncyclic)2 minussumRadius (119890comb)2

100381610038161003816100381610038161003816

119890branch = arg min119890

Diff (119890comb) 119890comb sube 119890outcyclic

119890irrelevant = 119890 | 119890 isin 119890out cyclic and 119890 notin 119890branch

(8)

where 119890out cyclic = 1198901out cyclic 119890119898out cyclic consists of all119898 connected cyclic branches and 119890comb denotes a possiblecombination set of cyclic branches Diff(119890comb) measure theblood difference between inflow of root vein and outflow ofbranches 119890branch is the combination set whose blood flowmatches the inflow of root vein The branches not containedin 119890branch are considered as irrelevant cyclic vessel branches


Table 1 Graph attributes description

Attributes Description

Vertex Coordinate(V) 3D coordinate values of each vertex VRadius(V) The distance from vertex V to its nearest surface voxel of 119868vessel

Edge

Length(119890) The actual length of the branchDistance(119890) The Euclidean distance between the two vertexes

MeanRadius(119890) Themean radius of the branch MeanRadius(119890) = radicVolume(119890)(120587 sdot Length(119890))Volume(119890) is the voxel numbers in 119890

Angle(119890) The angle from the parent edge to 119890No(119890) The edge belonging to which part of vascular system (portalhepatic vein)

eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic

120587 middot Radius(ein)2 asymp sum 120587 middot Radius(eout_noncyclic)

2+sum 120587 middot Radius(eout_cyclic)

2

Figure 5 Determining irrelevant vessel branches

Through removing the redundant branches and irrelevantbranches vascular tree 119879vessel of portal vessels is generatedwhich consists of a set of vertexes 119881vessel and directed edges119864vessel to indicate the blood flow

32 Liver Segment and Annotation321 Hierarchical Vascular Tree Considering the blood flowin vasculature we can further extend the vessel tree tohierarchical vascular tree As introduced above vasculartree is formulated by a directed acyclic graph 119879vessel =(119881vessel 119864vessel) the edge direction represents the blood flowAccording to blood-supply amount of branches the vasculartree can be hierarchically divided into two levels The FirstSubtree has the branches of large mean radius and generallydenotes the main vessel of liver portal vein Compared withFirst Subtree the Second Subtree denotes the branch ofsmaller mean radius which is widely distributed in liversegments

According to the physiological characteristics of vascula-ture [33] First Subtree generally consists of limited numberof main vessels and Second Subtree involves abundant minorvessels of smaller radius Based on this we can categorizevessel trees through modeling the distribution of vesselradius For implementation we utilize a mixture of Gaus-sian distributions (GMM) to approximate the vessel radiusdistribution Figure 6 illustrates the radius statistics of allthe vessel tree branches Min and Max denote the minimumand maximum radius respectively Obviously there are two

Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)

Figure 6 Radius statistics of vessel tree branches

clusters in the histogram one centers at small radius andanother one locates in the interval of big radius Havingmanysmall branches of similar radius Second Subtree correspondsto the cluster with higher peak centered at small radius Onthe other side First Subtree is represented by the smallercluster centered at large radius Suppose that the radiusdistributions of two clusters are Gaussian and have forms1198732(1205832 1205902) and 1198731(1205831 1205901) let 120583 = 1205832 the radius rangeof Second Subtree is [Min 2120583 minus Min] and the threshold 120579that separates First and Second Subtree can be computedas 120579 = 2120583 minus Min For easy implementation the thresholdcan be set default as 120579 asymp 05 times Max In real applicationsthe threshold can also be online tuned referring to 3Dvisualization


Figure 7 Liver region extraction and visualization

Based on the distribution of branch radius we candetermine the subtree of vessels at different levels

Definition 6 (First and Second Subtree) Given vascular tree119879vessel = (119881vessel 119864vessel) and threshold 120579 for each edge 119890 isin119864vessel if 120579 lt Radius(119890) le Max edge 119890 belongs to the FirstSubtree Otherwise if Min le Radius(119890) le 120579 119890 belongs to theSecond Subtree

As introduced in Section 1 only the connecting branchesin Second Subtree will be preserved for the subsequent liverannotation Among those branches theMicro Subtree whichrepresents the trivial structure of vessel systemwill be furtherremoved

Definition 7 (Micro Subtree) Given a tree in Second Subtreeif the number of vertexes in the tree is no more than five thatis |119881vessel| le 5 the tree is considered as Micro Subtree

The blood flow of Second Subtree actually presentsthe circulation of vessel system and thereby indicates thestructure of functional segments We use 119870-means++ tocluster the root vertexes of the preserved Second Subtrees andthe root clustering will induce a partition of liver region Eachcluster of vessel trees corresponds to a functional segmentof liver Since all the vertexes in the same tree belong tothe same blood-supply branch they are definitely in thesame segment Anatomically the liver is divided into eightsegments according toCouinaud classificationTherefore thenumber of the vessel tree clusters is set as 119870 = 8 Afterclustering we complete the branch division of vascular tree

322 Liver Annotation Based on the branch division ofhierarchical vascular tree the liver voxels are iterativelyclassified into eight parts using aminimum distance classifier[34] Let 119861 stand for the divided branches in vascular tree 119861119894119894 = 1 2 8 is 119894th subtree with vertexes 119881119861119894 For each voxelV in liver region 119868liver the classifier computes the minimumdistance between V and 119861119894 to determine which branchsupplies blood to V see Definition 8 Through classifying thevoxels to different vessel branches the functional segments ofliver are partitioned

Definition 8 (Branch Distance) For any pair of voxels Vliver isin119868liver and Vbranch isin 119861 Dist(Vliver Vbranch) is the Euclide-an distance between the two voxels Based on the voxel

distance we can define the distance between Vliver andbranch 119861119894 as MinDist(Vliver 119861119894) = MinDist(Vliver Vbranch) Theliver voxel Vliver will be classified into 119896th branch if 119896 =arg min119894(MinDist(Vliver 119861119894))

Integrating the functional segments of liver and the organfeatures obtained from the topological graph of vessels wecan generate the report of liver annotation The annotationreport consists of the functional region visualization andthe clinical features to describe the characteristics of liversystem Moreover the clinical features can be categorizedinto two groups Global features mainly include the size ofliver vessels and lesions as well as the ratio of each segmentto liver Individual features usually consist of anatomicallocations such as the spatial relationship among vasculaturelesions and liver and also the segment in which the lesionresides The annotation results are helpful for doctors toachieve precise evaluation of liver system and reduce the riskof operation

4 Experimental Results

In the experiments we expect to validate the effectiveness ofthe proposed vessel-tree-based liver annotation methodTheexperiments consist of the tests of vessel tree generation andliver annotation In the test of vessel tree generation we verifythe vessel skeletonization algorithm and the construction ofdirected acyclic graph to present the topology of vasculatureIn the test of liver annotation we focus on validating thestrategy of partitioning the liver region into functional seg-ments based on hierarchical vascular trees The experimentsare performed on CT dataset stored in format of DICOMimages Each volume has an in-plane resolution of 512 times 512pixelsThemodel was implemented based on the toolkits ITK(httpsitkorg) and VTK (httpwwwvtkorg) and wasintegrated into theMITK framework (httpwwwmitkorg)as a plugin The computer for program development hasan Intel(R) Core(TM)2 Quad CPU (266GHz) and 325GBRAM

41 Test of Vessel Tree Generation Applying the improvedgraph cut model to the treated abdominal CT volumeswe can efficiently produce the reliable segmentation resultsof liver region An example is given in Figure 7 The firstcolumn is one of the original CT slices The following twocolumns show the result of liver region segmentation The


(a)

(b) (c)

Figure 8 Skeletonization results and visualization

average running time for around 70 slices is about 20 s Moreexperimental analysis can be found in our previous work[32]The second and third columns present the segmentationof vessel and tumor in liver region on the same slice Theregions of vessels and tumors are marked in green andblue respectively Integrating the segmentation results ofa series of CT slices we can form the 3D visualizationof the whole liver region see the last column We renderthe liver region in red tumors in yellow and vessels ingreen (both portal vein and hepatic vein) The visualiza-tion indicates that the adopted segmentation method iseffective in extracting the liver region from original CTimages

Based on the segmented vessel regions we can con-struct the skeleton and further the topological graph ofvasculature Various kinds of skeletonization algorithmswereapplied to build up the vessel skeletons including distancetransform algorithms Voronoi diagram algorithms andthinning algorithms Figure 8(a) shows the vessel skeletonsobtained by different skeletonization algorithms The first

column presents three CT images of liver region The secondcolumn illustrates the segmentation of vessel regions Thelast three columns show the vessel skeletons generated bydistance transform algorithm Voronoi diagram algorithmand thinning algorithm respectively We find that the thin-ning algorithm that we use for model implementation canguarantee the connectivity and completeness of the structureof vessel system Figures 8(b) and 8(c) show 3D visualizationof the portal veins and the corresponding skeleton extractedby thinning algorithm

Compared with the efficiency of different skeletonizationalgorithms in 2D space the average computing time ofthree algorithms are respectively 048 s 062 s and 016 sper slice Taking a CT volume of 124 slices for testing thecomputing time of distance transform algorithm is 3211 s thethinning algorithm costs 1579 s and the Voronoi diagramalgorithm runs out of memory To sum up the thinningalgorithm generates the vessel skeleton in a short time andin the meantime preserves the topology and connectivity ofvasculature


(a) (b) (c)

(d) (e) (f)

Figure 9 Liver vessel tree generation and visualization

Table 2 Liver segments attributes

SegI SegII SegIII SegIV SegV SegVI SegVII SegVIII119873seg 53062 78287 169190 115116 58760 144737 152095 157323119881seg (mL) 5306 7829 16919 11512 5876 14474 15210 15732119877seg () 571 843 1822 1240 633 1559 1638 1694119877tumor () 897 0 395 0 476 0 0 0

As introduced in Section 3 with vessel skeletons we canconstruct a directed acyclic graph to present the topologyof vasculature Figure 9 shows the graph representation ofthe geometric structure of liver portal veins (a) exhibits theportal veins segmented from liver region The skeleton resultof the portal veins is given in (b) (c) illustrates the directedacyclic graph with the topological voxels marked in red andthe tree root marked in blue Zooming in a local part of liverregion (d) and (e) present the portal veins of local vesselsystem and its skeleton (f) shows the induced topologicalgraph We can find that the proposed method can preciselyexpress the geometric structure of vasculature even for theminor vessel branches The time cost for constructing thewhole vessel tree is just 15 s

42 Test of Liver Segment and Annotation According to theblood flow the vessel trees can be divided into two levelsThe First Subtree represents the main vessels of liver portalveins and the Second Subtree denotes the minor branchesin vasculature A liver vessel tree constructed in experimentsis shown in Figure 10(a) The tree has 192 vertexes markedin green and 191 edges marked in red Through measuringthe radius of vessels the branches of the tree are categorizedinto two groups 26 branches belonging to First Subtreeand 165 branches belonging to Second Subtree The SecondSubtree is shown in Figure 10(b) After removing the MicroSubtree we obtain the final tree as shown in Figure 10(c)The preserved branches of tree are further clustered into 8

classes using 119870-means++ algorithm Figure 10(d) illustratesthe clustering results in which the clusters of branches aremarked by different colors From the view of anatomy eachcluster of vessel branches indicates a functional segmentThus through clustering the vessel branches the liver regioncan be anatomically divided into eight segments as shown inFigure 11 To achieve complete analysis the liver segmentsare exhibited from four different views in visceral surfacehepatic side hepatic septal and right lope The time cost ofthe whole process is 5 s

Based on the functional segments we can compute thebasic organ attributes of liver system such as voxel number ofsegment119873seg segment volume 119881seg volume ratio of segmentto liver 119877seg and proportion of tumors in segment 119877tumorDenoting eight functional segments by SegIsimSegVIII theorgan attributes of liver segments shown in Figure 11 are listedin Table 2

Besides basic organ attributes we can also compute theattributes of liver lopes to support diagnosis Table 3 showsthe annotation results including the volume informationof leftright liver and four liver lopes It can be inferredfrom Table 3 that the left lope which consists of functionalsegments SegIIsimSegIV occupies 3905 of the liver regionand the right lope of segments SegVsimSegVIII dominates5524 The statistics are consistent with the anatomicaldistribution of liver region

At the final step of the proposed workflow we shouldintegrate the visualization of liver region the topological


(a) (b) (c)

(d)

Figure 10 Hierarchical vascular tree generation and division

1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23

Figure 11 Liver segments and visualization

structure of vessel tree the partition of functional segmentsand organ attributes to form a report of liver annotationAs shown in Figure 12(a) 3D visualization of liver regionintuitively exhibits the spatial relationship between vascu-lature lesions and liver segments For example we caneasily observe the blood-supply branches of each segmentin right liver lobe Figure 12(b) shows the spatial relation-ship between tumor portal vein and functional segments

Moreover from the visualization results of liver vasculatureand functional segments can be separated transformedrotated and scaled for complete analysis as shown inFigure 12(c) Abundant experimental results reveal that theproposed vessel-tree-based liver annotation method canprovide visual and measurable information for liver sys-tem evaluation and thereby it is effective in supportingdiagnosis


Table 3 Liver annotation results

Liver Ratio ()Caudal lobe SegI 571

Left lobeLeft lateral lobe SegII 2665

3905SegIII

Left medial lobe SegIVa 1240SegIVb

Right lobeRight anterior lobe SegVIII 2327

5524SegV

Right posterior lobe SegVII 3197SegVI

(a) (b) (c)

Figure 12 Three-dimensional visualization of liver

5 Conclusion

In this paper we proposed a vessel-tree-based liver annota-tion method for CT images At the first step of workflowthe regions of liver vessels and tumors are segmented fromCT scans And then a 3D thinning algorithm is appliedto obtain the skeleton of liver vessels Through searchingfor topological voxels the skeleton of the portal veins isimproved to a directed acyclic graph that is vessel tressto present the topology of vasculature According to theblood flow the vessel trees are categorized into First andSecond Subtrees and the structure of Second Subtrees canindicate the organization of functional segments of liverIn the light of this finding we cluster the Second Subtreesto partition the liver region into eight functional segmentsaccording to Couinaud classification of liver anatomy Basedon the partitioned functional regions the organ attributesare computed to form quantitative descriptions of liver Atthe final step of workflow we integrate the visualizationof liver region the topological structure of vessel tree thepartition of functional segments and organ attributes to forma report of liver annotation Experimental results validate theeffectiveness of proposed vessel-tree-based liver annotationmethod Our future work will focus on using individualfeatures such as locational description and shape featuresfor liver annotationThe liver annotation based on individualorgan features is helpful to recognize whether the tumor isbenign or malignant

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the Natural Science Foundationof China (nos 61103070 and 61573235) the FundamentalResearch Funds for theCentral Universities and theKey Lab-oratory of Embedded System and Service Computing Min-istry of Education Tongji University (no ESSCKF201303)

References

[1] P Campadelli E Casiraghi and A Esposito ldquoLiver segmen-tation from computed tomography scans a survey and a newalgorithmrdquoArtificial Intelligence inMedicine vol 45 no 2-3 pp185ndash196 2009

[2] K Palagyi J Tschirren E A Hoffman and M SonkaldquoAssessment of intrathoracic airway trees methods and in vivovalidationrdquo in Computer Vision and Mathematical Methods inMedical and Biomedical Image Analysis ECCV 2004WorkshopsCVAMIA and MMBIA Prague Czech Republic May 15 2004Revised Selected Papers vol 3117 of Lecture Notes in ComputerScience pp 341ndash352 Springer Berlin Germany 2004

[3] S S Kumar and D Devapal ldquoSurvey on recent CAD systemfor liver disease diagnosisrdquo in Proceedings of the Interna-tional Conference on Control Instrumentation Communicationand Computational Technologies ((ICCICCT rsquo14) pp 763ndash766Kanyakumari India July 2014

[4] F BMofrad R A Zoroofi A A Tehrani-Fard S Akhlaghpoorand Y Sato ldquoClassification of normal and diseased liver shapesbased on spherical harmonics coefficientsrdquo Journal of MedicalSystems vol 38 no 5 article 20 pp 1ndash9 2014

[5] U R Acharya O Faust F Molinari S V Sree S P Junnarkarand V Sudarshan ldquoUltrasound-based tissue characterization


and classification of fatty liver disease a screening and diag-nostic paradigmrdquo Knowledge-Based Systems vol 75 pp 66ndash772015

[6] A Kumar S Dyer C Li P H Leong and J Kim ldquoAutomaticannotation of liver CT images the submission of the BMETgroup to ImageCLEFmed 2014rdquo in Proceedings of the CLEFWorking Notes pp 428ndash437 Sheffield UK September 2014

[7] I Nedjar S Mahmoudi A Chikh K Abi-yad and Z Boua aldquoAutomatic annotation of liver CT image ImageCLEFmed2015rdquo in Proceedings of the Working Notes (CLEF rsquo15) pp 8ndash11Toulouse France September 2015

[8] F Gimenez J Xu Y Liu et al ldquoAutomatic annotation ofradiological observations in liver CT imagesrdquo in Proceedingsof the AMIA Annual Symposium American Medical InformaticsAssociation pp 257ndash263 Chicago Ill USA November 2012

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

[10] D Kainmuller T Lange and H Lamecker ldquoShape constrainedautomatic segmentation of the liver based on a heuristicintensity modelrdquo in Proceedings of the MICCAI Workshop 3DSegmentation in the Clinic A Grand Challenge pp 109ndash116Brisbane Australia October 2007

[11] T Heimann S Munzing H P Meinzer and I Wolf ldquoAShape-guided deformable model with evolutionary algorithminitialization for 3D soft tissue segmentationrdquo in Proceedingsof the Information Processing in Medical Imaging pp 1ndash12Kerkrade The Netherlands January 2007

[12] S Zhang Y Zhan M Dewan J Huang D N Metaxas and XS Zhou ldquoTowards robust and effective shape modeling sparseshape compositionrdquo Medical Image Analysis vol 16 no 1 pp265ndash277 2012

[13] H Ling S K Zhou Y Zheng B Georgescu M Suehling andD Comaniciu ldquoHierarchical learning-based automatic liversegmentationrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo08) pp 1ndash8Anchorage Alaska USA June 2008

[14] A Zidan N I Ghali A E Hassanien H Hefny and JHemanth ldquoLevel set-based CT liver computer aided diagnosissystemrdquo International Journal of Imaging andRobotics vol 9 no1 pp 26ndash36 2012

[15] C Li C Xu C Gui and M D Fox ldquoDistance regularized levelset evolution and its application to image segmentationrdquo IEEETransactions on Image Processing vol 19 no 12 pp 3243ndash32542010

[16] N Xu N Ahuja and R Bansal ldquoObject segmentation usinggraph cuts based active contoursrdquo Computer Vision and ImageUnderstanding vol 107 no 3 pp 210ndash224 2007

[17] A Delong A Osokin H N Isack and Y Boykov ldquoFastapproximate energy minimization with label costsrdquo Interna-tional Journal of Computer Vision vol 96 no 1 pp 1ndash27 2012

[18] L Massoptier and S Casciaro ldquoFully automatic liver seg-mentation through graph-cut techniquerdquo in Proceedings of theEngineering in Medicine and Biology Society pp 5243ndash5246Lyon France August 2007

[19] T Kitrungrotsakul X-H Han and Y-W Chen ldquoLiver segmen-tation using superpixel-based graph cuts and restricted regionsof shape constrainsrdquo in Proceedings of the IEEE International

Conference on Image Processing (ICIP rsquo15) pp 3368ndash3371 IEEEQuebec Canada September 2015

[20] C Florin N Paragios and J Williams ldquoParticle filters a quasi-monte carlo solution for segmentation of coronariesrdquo in Pro-ceedings of theMedical Image Computing and Computer-AssistedIntervention (CMICCAI rsquo05) pp 246ndash253 Palm Springs CalifUSA October 2005

[21] D Selle B Preim A Schenk and H-O Peitgen ldquoAnalysis ofvasculature for liver surgical planningrdquo IEEE Transactions onMedical Imaging vol 21 no 11 pp 1344ndash1357 2002

[22] R Manniesing M A Viergever and W J Niessen ldquoVesselenhancing diffusion A scale space representation of vesselstructuresrdquo Medical Image Analysis vol 10 no 6 pp 815ndash8252006

[23] P T H Truc M A U Khan Y-K Lee S Lee and T-SKim ldquoVessel enhancement filter using directional filter bankrdquoComputer Vision and Image Understanding vol 113 no 1 pp101ndash112 2009

[24] W H Hesselink and J B T M Roerdink ldquoEuclidean skeletonsof digital image and volume data in linear time by the integermedial axis transformrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 30 no 12 pp 2204ndash2217 2008

[25] A Beristain and M Grana ldquoPruning algorithm for Voronoiskeletonsrdquo Electronics Letters vol 46 no 1 pp 39ndash41 2010

[26] T-C Lee R L Kashyap and C-N Chu ldquoBuilding skele-ton models via 3-D medial surfaceaxis thinning algorithmsrdquoCVGIP Graphical Models and Image Processing vol 56 no 6pp 462ndash478 1994

[27] D Fan A Bhalerao andRWilson ldquoComparative assessment ofretinal vasculature using topological and geometric measuresrdquoin Medical Imaging 2005 Image Processing vol 5747 of Pro-ceedings of SPIE pp 1104ndash1111 San Diego Calif USA February2005

[28] L Rusko and G Bekes ldquoLiver segmentation for contrast-enhanced MR images using partitioned probabilistic modelrdquoInternational Journal of Computer Assisted Radiology andSurgery vol 6 no 1 pp 13ndash20 2011

[29] D A B Oliveira R Q Feitosa and M M Correia ldquoAutomaticcouinaud liver and veins segmentation from CT imagesrdquo inProceedings of the International Conference on Bio-InspiredSystems and Signal pp 249ndash252 Madeira Portugal January2008

[30] A Schenk S Zidowitz H Bourquain et al ldquoClinical relevanceof model based computer-assisted diagnosis and therapyrdquo inMedical Imaging vol 6915 of Proceedings of SPIE San DiegoCalif USA March 2008

[31] S-H Huang B-L Wang M Cheng W-L Wu X-Y Huangand Y Ju ldquoA fast method to segment the liver according toCouinaudrsquos classificationrdquo in Medical Imaging and InformaticsX Gao H Muller M J Loomes R Comley and S Luo Edsvol 4987 of Lecture Notes in Computer Science pp 270ndash276Springer 2008

[32] Y Chen Z Wang J Hu W Zhao and Q Wu ldquoThe domainknowledge based graph-cut model for liver CT segmentationrdquoBiomedical Signal Processing and Control vol 7 no 6 pp 591ndash598 2012

[33] HKHahn B PreimD Selle andH-O Peitgen ldquoVisualizationand interaction techniques for the exploration of vascular


structuresrdquo inProceedings of the Visualization (VIS rsquo01) pp 395ndash578 IEEE San Diego Calif USA October 2001

[34] H G Debarba D J Zanchet D Fracaro A Maciel andA N Kalil ldquoEfficient liver surgery planning in 3D based onfunctional segment classiffication and volumetric informationrdquoin Proceedings of the Engineering in Medicine and BiologySociety pp 4797ndash4800 Buenos Aires Argentina August 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology


Molecular Biology International

GenomicsInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


BioinformaticsAdvances in

Marine BiologyJournal of



Signal TransductionJournal of


BioMed Research International

Evolutionary BiologyInternational Journal of



Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


Hepatic vein

Portal vein

Figure 1 Couinaud classification of liver anatomy

and local features The method needs user interaction andrequires special routines to handle branch points Selle et al[21] presented an intensity-threshold-based method whichdefined an optimal intensity threshold through measuringregion growing This kind of methods mainly suits segment-ing large vessels Manniesing et al proposed a vessel segmen-tationmethod based onHessianmatrix which enhances livervessels and thereby extracts tubular structures from the organregion [22] The vesselness of the structure is determinedby its geometrical features obtained from the eigensystem ofHessian matrix [23]

The topology of liver vasculature is of importance forrecognizing functional segments Vessel skeleton is widelyused to present the topology of vasculature Generally speak-ing there are three types of vessel skeletonization methodsThe algorithms based on distance transformation describewell the local structure but cannot guarantee the connectivityand completeness of skeleton [24] The algorithms based onVoronoi diagram are capable of capturing the topology of theentire vasculature but the computation of Voronoi skeleton istime-consuming especially for themedical image containinglarge-size objects [25] Compared with the skeletonizationmethods above the thinning algorithms can extract thevessel skeleton efficiently and in the meantime preserve theconnectivity and completeness of the skeleton Moreover thethinning algorithm can also record the medial position ofthe skeleton which is very helpful to annotate the functionalregions [2 26] However only vessel skeletons withoutquantitativemeasurement are not sufficient to present the realtopology of vasculature [27] For example it is difficult forvessel skeletons to keep the important organ features suchas length blood flow direction and radius of subbranchWithout considering anatomical measurements the imper-fect vessel segmentation results may lead to cyclic skeleton

Obtaining the topology of liver vasculature we canpartition liver region into functional segments and makethe annotation Referring to the Couinaud classification ofliver anatomy hepatic and portal veins divide liver into eightfunctionally independent segments as shown in Figure 1 [28]Each segment has its own vascular inflow outflow and biliarydrainage In the center of each segment there is a branch ofthe portal vein hepatic artery and bile duct In the peripheryof each segment there is vascular outflow through the hepaticveins Middle hepatic vein divides the liver into right and leftlobes Right hepatic vein divides the right lobe into anterior

and posterior segments Left hepatic vein divides the left lobeinto amedial and lateral part Portal vein divides the liver intoupper and lower segments

Formulating the Couinaud classification of liver anatomyOliveira et al estimated the planes that best fit each of thethree branches of the hepatic veins and the plane that best fitsthe portal vein These four planes define the subdivision ofthe liver in the Couinaud segments [29] However the plane-based method does not consider the influence of vascularvariation to plane estimation and it ignores the fact that theseparation between liver segments should be a surface Selle etal segmented liver through computing the nearest neighborof different vessel branches [21] But the result depends on theuser defined parameter which should be manually adjustedunder different cases Schenk et al used a Laplace model toassign each liver cell to one of the vascular branches to formliver segments [30]Thismodel suffers from a great computa-tion burden and is not robust enough due to the dependenceon vascular branch calibration Huang et al designed a fastliver segment method based on the hepatic vessel tree [31]The method projects the liver and vessel tree to a plane andthe classification of liver is achieved by classifying pointsin the projection plane Although having high efficiencythe method based on hepatic vessel tree is not a completefunctional anatomywhich leads to the inconsistency betweenthe annotated liver segments and the actual blood-supplybranch

As mentioned above the topology of vasculature canguide the annotation of functional segments Howeverbecause of the high complexity of liver vasculature it ishard to generate a precise representation of vasculaturetopology and the computation of geometric structures ofall the vessels is always a time-consuming task In factfrom the view of anatomy the left and right portal veinbranches superiorly and inferiorly project into the centerof each segment to supply blood This means that thefunctional segments of liver can be recognized by onlyportal vein branches in it In the light of this finding weproposed a hierarchical vascular tree to present the topologyof portal veins The branches of hierarchical vascular treeof portal veins correspond to the functional segments ofliver Based on the obtained functional segments we annotatethe liver region and measure the organ attributes using astandard terminology [6] The visualization of annotationand the measurements can form a report of liver system forCAD The contributions of this paper are summarized asfollows

(1) Design a Vessel Tree to Present the Topology of Portal VeinsConnect the topological voxels in vessel skeleton to form agraph Prune redundant and irrelevant branches of graph togenerate a formal vessel tree which indicates the geometricstructures of portal veins and blood flow direction

(2) Extend the Vessel Tree to a Hierarchical One for LiverAnnotation The vessel tree is hierarchically divided into twolevels according to the radius of portal vein branches TheSecond Subtree branches are preserved to form functionalsegments


Liver segmentation

Liver CT image

Tumorsegmentation

Vesselsegmentation

Hessianenhancement



Liver annotation

Graphrepresentation

Functionalsegment


Visualization


Measurements

Liver region

Tumorregion

Vesselregion

LiverCAD

Liver region

Liver systemreports



2 Methodology










Vessel (120582)

=


119877119886 =100381610038161003816100381612058221003816100381610038161003816100381610038161003816100381612058231003816100381610038161003816

119877119887 =100381610038161003816100381612058211003816100381610038161003816

radic10038161003816100381610038161205822 sdot 12058231003816100381610038161003816

119877119888 = radic12058221 + 12058222 + 12058223

(1)



0 3 61 4

121610

14

22

13

72 5 8

9 15

17

2425

262320

211819

11





(2)



(3)




(4)




119881vessel = V | 119868vessel (V) = 1 (5)


Fc Ec Vc






Vcandidate


branch-voxel


(6)





(7)




2


100381610038161003816100381610038161003816




(8)






Edge




eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic



2





Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)


















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Liver segmentation

Liver CT image

Tumorsegmentation

Vesselsegmentation

Hessianenhancement



Liver annotation

Graphrepresentation

Functionalsegment


Visualization


Measurements

Liver region

Tumorregion

Vesselregion

LiverCAD

Liver region

Liver systemreports



2 Methodology










Vessel (120582)

=


119877119886 =100381610038161003816100381612058221003816100381610038161003816100381610038161003816100381612058231003816100381610038161003816

119877119887 =100381610038161003816100381612058211003816100381610038161003816

radic10038161003816100381610038161205822 sdot 12058231003816100381610038161003816

119877119888 = radic12058221 + 12058222 + 12058223

(1)



0 3 61 4

121610

14

22

13

72 5 8

9 15

17

2425

262320

211819

11





(2)



(3)




(4)




119881vessel = V | 119868vessel (V) = 1 (5)


Fc Ec Vc






Vcandidate


branch-voxel


(6)





(7)




2


100381610038161003816100381610038161003816




(8)






Edge




eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic



2





Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)


















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




Vessel (120582)

=


119877119886 =100381610038161003816100381612058221003816100381610038161003816100381610038161003816100381612058231003816100381610038161003816

119877119887 =100381610038161003816100381612058211003816100381610038161003816

radic10038161003816100381610038161205822 sdot 12058231003816100381610038161003816

119877119888 = radic12058221 + 12058222 + 12058223

(1)



0 3 61 4

121610

14

22

13

72 5 8

9 15

17

2425

262320

211819

11





(2)



(3)




(4)




119881vessel = V | 119868vessel (V) = 1 (5)


Fc Ec Vc






Vcandidate


branch-voxel


(6)





(7)




2


100381610038161003816100381610038161003816




(8)






Edge




eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic



2





Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)


















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Fc Ec Vc






Vcandidate


branch-voxel


(6)





(7)




2


100381610038161003816100381610038161003816




(8)






Edge




eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic



2





Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)


















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





Edge




eout_cyclicein

eout_cyclic

eout_cyclic

eout_noncyclic

eout_noncyclic



2





Num

ber

Second Subtree

Min Max Radius

First Subtree

120579120583

N2(1205832 1205902)

N1(1205831 1205901)


















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology
















(a)

(b) (c)







(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b) (c)

(d) (e) (f)











(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b) (c)

(d)


1

2 3

4

3

1

8

7

7

6

8

8

4 5

5 6

1

23








3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





3905SegIII



5524SegV


(a) (b) (c)


5 Conclusion


Competing Interests


Acknowledgments


References















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology










































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

research article functional region annotation of...

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