06262482

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 31, NO. 10, OCTOBER 2012 1965

Tumor Burden Analysis on Computed Tomographyby Automated Liver and Tumor SegmentationMarius George Linguraru*, William J. Richbourg, Jianfei Liu, Jeremy M. Watt, Vivek Pamulapati,

Shijun Wang, and Ronald M. Summers

Abstract—The paper presents the automated computation ofhepatic tumor burden from abdominal computed tomography(CT) images of diseased populations with images with inconsistentenhancement. The automated segmentation of livers is addressedfirst. A novel 3-D affine invariant shape parameterization isemployed to compare local shape across organs. By generatinga regular sampling of the organ’s surface, this parameterizationcan be effectively used to compare features of a set of closed3-D surfaces point-to-point, while avoiding common problemswith the parameterization of concave surfaces. From an initialsegmentation of the livers, the areas of atypical local shape aredetermined using training sets. A geodesic active contour correctslocally the segmentations of the livers in abnormal images. Graphcuts segment the hepatic tumors using shape and enhancementconstraints. Liver segmentation errors are reduced significantlyand all tumors are detected. Finally, support vector machines andfeature selection are employed to reduce the number of false tumordetections. The tumor detection true position fraction of 100%is achieved at 2.3 false positives/case and the tumor burden isestimated with 0.9% error. Results from the test data demonstratethe method’s robustness to analyze livers from difficult clinicalcases to allow the temporal monitoring of patients with hepaticcancer.

Index Terms—Cancer, contrast-enhanced computed tomog-raphy (CT), liver, parameterization, segmentation, shape, tumorburden.

I. INTRODUCTION

A CCORDING to the American Cancer Society, approxi-mately 26 190 new cases of liver cancer are expected to

occur in the U.S. in 2011 and more than 80% of them to be hepa-tocellular carcinomas [1]. The majority of primary liver cancershave their origins in alcohol-related cirrhosis and fatty liver dis-ease associated with obesity. Other major risk factors are hep-atitis B and C viruses. The incidence of liver cancer has beenincreasing by more than 3% yearly. About 19 590 liver cancer

Manuscript received June 26, 2012; accepted July 30, 2012. Date of publica-tion August 07, 2012; date of current version September 27, 2012. This workwas supported in part by the Intramural Research Program of the National In-stitutes of Health, Clinical Center. Asterisk indicates corresponding author.*M. G. Linguraru is with the Sheikh Zayed Institute for Pediatric Surgical

Innovation, Children’s National Medical Center, Washington, DC 20010 USA,and also with the Department of Radiology and Imaging Sciences, ClinicalCenter, National Institutes of Health, Bethesda, MD 20892 USA (e-mail: [email protected]).W. J. Richbourg, J. Liu, J. M. Watt, V. Pamulapati, S. Wang, and R. M. Sum-

mers are with the Imaging Biomarkers and Computer Aided Diagnosis Labo-ratory, Radiology and Imaging Sciences, Clinical Center, National Institutes ofHealth, Bethesda, MD 20892 USA (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMI.2012.2211887

deaths are expected in 2011 with incidence and mortality morethan twice as high in men as in women [1]. Early stage livercancer can sometimes be treated successfully with surgery andtransplantation. Patients whose tumors cannot be removed sur-gically may benefit from ablation, embolization or targeted drugtherapy. The overall five-year survival rate for patients withliver cancer is 14%.Liver metastases are hepatic cancers that have spread from

another primary source in the body. The liver is a prime candi-date for metastases from cancers in the breast, colon, prostate,lung, pancreas, stomach, esophagus, adrenal glands, or skin(melanoma) [32]. A hepatic metastasis can be found at the timeof the diagnosis of the primary cancer or appear later after theremoval of the primary tumor. The treatment and prognosis ofsecondary liver cancers vary largely depending on its sourceand stage. Systemic chemotherapy is usually used to treat themetastases, but ablation and embolization are also common,while surgery is a rarer option [9], [32]. Although secondaryliver cancer is generally untreatable, treatments may improvelife expectancy.Computed tomography (CT) is commonly adopted for

imaging abdominal organs for diagnosis and preoperative plan-ning. The 3-D analysis of volumes, shapes, and enhancementsof abdominal organs, such as the liver, are common indicatorsof disorders and important markers for diagnosis and treatmentresponse evaluation of cancer [13], [58], [61]. Organ and tumorvolume measurements have been found to be important inmaking surgical decisions involving organ transplantation [5],[29]. Clinical cases can exhibit low contrast, imaging and mo-tion artifacts and large pathologies, which change the intensityand shape of organs. But it is in these unusual clinical casesthat potentially require surgical interventions that the currentfully automated 3-D segmentation techniques most often breakdown.In traditional clinical practice, 3-D organ analysis is per-

formed via time-consuming manual measurements, or as analternative the evaluation is incomplete, based on 2-D pro-jection images. There are several advantages that automatedmethods have over manual or interactive techniques. An impor-tant aspect is the reproducibility of results, which in automatedalgorithms are not subjected to user interaction. Moreover,automated techniques may be faster, readily available, andcan run in the background without interrupting the clinicalworkflow (do not require human presence).The automated computer-aided diagnosis (CAD) of livers

from medical scans can provide quantitative data. The imple-mentation of a robust and fully automated 3-D segmentation

U.S. Government work not protected by U.S. copyright.

1966 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 31, NO. 10, OCTOBER 2012

technique for liver and its tumors would allow radiologistsand surgeons to have easy and convenient access to organmeasurements and 3-D visualization. The proposed methodfor the automated segmentation of the liver, and detection,segmentation, and classification of tumors can be employed asan assisting diagnostic tool robust to morphological changesfrom normal and pathological anatomical variability, as well aspoor image quality or enhancement. The Sections II–IV of themanuscript present the state of the art in shape parameteriza-tion, liver segmentation and liver tumor analysis.

A. Shape Parameterization

Shape analysis is often performed via image-based registra-tion [34], [35] or landmark identification [36], [65], which relyon image-based metrics and landmark repeatability. To identifysubtle shape differences between two objects, a robust param-eterization of their surfaces is required in combination with aninvariant shape descriptor and a point-to-point correspondence.Previous methods for 3-D surface analysis have been pro-

posed in medical applications [14], but a reliable parameteri-zation of human organs remains challenging. In a more generalsense, the parameterization of star-shaped objects [2], [14] isrestrictive for irregular shapes in the abdomen. To avoid thisshortcoming, the method in [6] involves generating a bijectivemapping from the 3-D surface to the unit sphere as an explicitparametric representation and global description of surfaces ofsimply connected 3-D objects. A spherical harmonics-based pa-rameterization was also presented in [25] by dividing a givensurface into a set of basis functions. Spherical harmonics-basedparameterizations for brain [16], [60] and cardiac [23] applica-tion have been particularly popular. Spherical harmonics canintroduce aliasing that results in an inaccurate representationof difficult data and induce computational complexity. For theliver, corresponding points were initialized by the user in [31]to be incorporated in statistical shape models [21].

B. Liver Segmentation

A variety of methods have been proposed to segment the liverin recent years. This increased interest in the field reflects thedifficulty of liver segmentation for clinical applications. The fol-lowing paragraphs detail some of the most relevant publishedtechniques. A comprehensive review of CT-based liver seg-mentation techniques was done by Campadelli et al. [7], de-scribing methods that employed live wire, gray-level analysis,neural networks, model fitting, level sets, and probabilistic at-lases. Campadelli highlighted the advantages and drawbacksthat limit the use of such techniques in the clinic.For a straightforward comparison, in 2007 a liver segmen-

tation competition from mainly pathological CT data was heldin conjunction with the International Conference on Med-ical Image Computing and Computer Assisted Intervention(MICCAI) [22]. The Workshop on 3-D Segmentation in theClinic: A Grand Challenge provided a set-up for a segmenta-tion competition for automatic and semi-automatic extractionof the whole liver from CT scans. All data in the competi-tion were obtained using enhancement, as the use of contrastin CT acquisition helps differentiate the liver parenchymafrom surrounding abdominal soft tissue. Besides training and

testing data, the competition also provided ground truth andtools for the quantitative evaluation of results. A variety oftechniques were presented and their performance evaluatedthrough a combination of metrics, including volume overlapand error, root-mean square error, and average surface distance.Amongst the ten automatic and six interactive methods forliver segmentation, the interactive methods achieved some ofthe best segmentation results [3], [10]. Statistical shape modelswere the best fully automated liver segmentation methods andperformed competitively with the semi-automatic techniques.In particular, a combination of shape-constrained statisticaldeformable models based on a heuristic intensity model hadthe best performance among automated methods [28]. Othernotable participations in the competition employed regiongrowing [47], a technique sensitive to liver abnormalities, and asemantic formulation of knowledge and context [49], but withrelatively low segmentation overlap.Several other approaches to segment the liver should be men-

tioned. A model-based segmentation was also employed in asupervised segmentation using graph representation in [51]. Ashape-constrained graph-cut approach segmented abdominal or-gans including the liver in [35], but mainly normal anatomy. Thegraph was initialized from training data statistics and constraintson shape, from Parzen windows, and location, from a proba-bilistic atlas, were used for segmentation. Shape densities andboundary appearance models were used in [63] with high ac-curacy. A fast hierarchical model using marginal space learningwas introduced in [33], but segmentation outliers were excludedfrom validation. Finally, a multilevel statistical shape model(ML-SSM) and principal component analysis (PCA) were usedin [42], but required heavy manual initialization.

C. Hepatic Tumor Analysis

In 2008, another segmentation competition followed inconjunction with MICCAI, this time addressing the segmenta-tion of liver tumors from CT data [11]. CT images covered arange of pathologies and were acquired with contrast enhance-ment to allow the differentiation of tumors from healthy liverparenchyma. Data and evaluation tools were made available tothe participants. One interactive, five semi-automatic and fourautomatic methods for tumor segmentation were evaluated.The evaluation of the techniques was performed using similarmetrics to the liver segmentation competition. As in the case ofthe liver, the highest scoring technique was interactive, usingclassic graph cuts and the watershed algorithm to accuratelysegment tumors [59]. The most successful semi-automatic ap-proaches scored similarly and employed adaptive thresholdingand morphological processing [40], voxel classification andpropagational learning [66], and a level set with fuzzy pixelclassification [56]. Tumors were best automatically segmentedvia machine learning and classification techniques, namelyusing cognition network technology [50] and ensemble seg-mentation trained using AdaBoost [55].Other recent notable approaches to segment hepatic lesions

employed intensity distribution combined with hidden Markovfields in [20]. The method is interactive and the tumor volumeestimation error was over 23%. The semi-automatic segmenta-tion of tumors based on support vector machines and affinity

LINGURARU et al.: TUMOR BURDEN ANALYSIS ON COMPUTED TOMOGRAPHY BY AUTOMATED LIVER AND TUMOR SEGMENTATION 1967

Fig. 1. Schematic of the automated technique for tumor burden analysis. The green and red boxes show the input and output data, respectively. The blue boxesrepresent the modules of the algorithm starting with the initial liver segmentation (Section II-A), continuing with shape analysis (Section II-B) and the correctedliver segmentation (Section II-C), and the segmentation and classification of tumors (Sections II-D and II-E).

constraint propagation was addressed in [15] with results com-parable to the reports from the MICCAI competition. Machinelearning was also used for the detection of liver cancers basedon linear discriminant analysis [64].CAD and surgical planning would benefit from fully auto-

mated 3-D segmentation of both the liver and liver tumors, aswell as the organ’s vasculature [18], [54]. Methods for the con-current segmentations of liver structures are mainly interactive[45]. Exceptionally, both the liver and its tumors were automat-ically segmented with a combination of statistical models, ac-tive contours and expectation maximization in [38]; the methodstruggled with pathological cases. In an integrated approach, atechnique that uses a combination of thresholding, mathemat-ical morphology and distance maps to automatically delineatethe liver and related structures was shown to be beneficial toradiologists when compared with traditional reading of the CTscan [57].

D. Tumor Burden

The tumor burden, the percentage of total tumor in the liver,is commonly used to monitor the evolution of disease in patientswith hepatic cancer. The measure of tumor burden can be usedfor developing treatment protocols [27]. Tumor burden also pro-vides meaningful comparison between different treatment reg-imens, and has been shown to be accurate as an assessment ofprognosis. An accurate assessment allows both physicians andpatients to make better therapeutic choices earlier [17].The quantification of tumor burden with CT and magnetic

resonance (MR) imaging is being used with increasing fre-quency to assess the effectiveness of cytotoxic anticancer drugs[46]. Tumor sizes are typically estimated from measuring themaximum tumor diameters in the transverse plane; often, thelargest perpendicular tumor diameters are also taken into con-sideration [12]. Pre-treatment and post-treatment cross productsare compared to categorize treatment response. Considerableinter-observer variation among radiologists in CT linear tumormeasurement has been reported [24], especially for ill-definedand irregular lesions common in hepatic cancers.Computer-aided detection and segmentation techniques can

supply precise tumor volumes. Automated volumetric measure-ments reduce the inter-observer variability in estimating the sizeof lesions that are confluent and irregular. Another advantageof volumetric measurements is the calculation of overall tumorburden in an organ, which eliminates the arbitrary guideline ofmeasuring five indicator lesions per organ. For the liver, a CAD

system should be sufficiently accurate to segment both the liverand liver tumors from typical variable clinical data to correctlyestimate the tumor burden.

E. Our Approach

We first present a novel automated technique to segment dis-eased livers from everyday CT data with inconsistent contrast-enhancement and imaging artifacts. A robust parameterizationof 3-D surfaces, like those of abdominal organs, is proposedfor the comparison of objects by point-to-point correspondence.3-D objects are represented by parallel planes that intersect thesurface of objects in closed planar curves. This spatial repre-sentation avoids common problems with the surface parameter-ization of concave objects. To compare local shape features oftwo organs we employ a shape descriptor invariant under rota-tion and scale and robust to noise. Once shape ambiguities aredetected on an initial segmentation of the liver, a shape-drivengeodesic active contour improves the segmentation significantlyeven in severe cases.From the segmented liver, graph cuts are employed to de-

tect and segment hepatic tumors using shape and enhancementconstraints. Features are extracted for the tumor candidates andclassification is performed using support vector machines. Thesegmentation techniques are evaluated using several databases,some public, for an adequate comparison with the exiting liter-ature. The liver tumor burden is computed from the segmentedliver and tumors. The automated liver analysis technique allowsmonitoring and diagnosing patients with abnormal livers underpoor image quality and inconsistent enhancement, and providesassessments for treatment and disease evolution.

II. METHODS AND MATERIALS

A schematic showing the pipeline of the technique is illus-trated in Fig. 1. The study included 101 CT scans from 68 pa-tients from a variety of public and clinical sources. The acqui-sition and analysis of clinical data at the National Institutes ofHealth was approved by the NIH Institutional Review Boardand informed consent was waived. The use of the public caseswas approved by the NIH Office of Human Subjects research.The groups of data are described in detail below.The main clinical test set consisted of 50 abdominal CT scans

collected from 17 patients with prostate cancer at single/mul-tiple time-points on five different scanners at our institution.Image resolution was 0.63–0.92 mm in the axial view with


5-mm-slice thickness. Images were acquired prior to and fol-lowing intravenous contrast administration; contrast data wereobtained at varying enhancement times from early-arterialto late portal venous phases. Additional to the inconsistentenhancement, cases with imaging and movement artifacts werepresent in the database. The volumes of the 50 test livers wereavailable from clinical reports (estimated by image processingtechnologists supervised by experienced radiologists). Thesemanual measurements were performed on enhanced and non-contrast data (though only a few latter cases were present in theclinical test set) independently from this study and no segmen-tation results were available with the exception of the numericalvalue of the volume. The liver volume ranged from 1.07 to4.08 L, including cases with mild and severe hepatomegaly.Twenty-two of the 50 clinical test cases presented tumors ofhighly variable size. Tumors were manually segmented in 14of the clinical cases (79 tumors) with metastatic liver cancerby a research fellow supervised by an experienced radiologist.The tumor size varied from 10.0 to 206.4 mm in the largestdiameter. All manually segmented tumors were analyzed oncontrast-enhanced images, as tumors are poorly visible (or eveninvisible to the eye) without enhancement.The liver shape training set consisted of 27 scans from 27

patients acquired clinically at our institution at high resolution(1 mm slice thickness and sub-millimeter axial resolution). Thisdataset consisted of normal and hepatomegaly (enlarged liver)cases. The livers were manually segmented in the 27 CT data bythree research fellows supervised by an experienced radiologist.Additionally, 10 anonymized public cases (10 patients),

mainly pathological, with manual liver segmentations fromthe MICCAI liver segmentation challenge held in 2007 [22]were used for testing the automated segmentation of livers.The MICCAI cases were acquired on a variety of scanners, hadcontrast enhancement and no imaging artifacts. Images had1–5 mm slice thickness and 0.5–0.8 mm axial resolution. Theground truth data was available only to the organizers of thecompetition (http://www.sliver07.org).Four more anonymized public pathological cases with

manual segmentations of ten hepatic tumors from theMICCAI liver tumor segmentation challenge held in 2008[11] (http://lts08.bigr.nl/) were used to test the automatedsegmentation of liver tumors. Cases were obtained using threescanners and a contrast-enhanced imaging protocol with slicethickness of 1–1.5 mm and in-plane resolution of 0.6–0.9 mm.There was no ground truth available for the segmentation oflivers in these four cases.

A. Initial Liver Segmentation

All test CT images were automatically cropped at the firstslice containing the liver. For that purpose the lungs were seg-mented through histogram analysis and image parsing in thecranio-caudal direction identified the liver dome. Livers wereautomatically segmented from the 74 test CT cases using a tech-nique previously designed for the analysis of hepatic artifact-free CT data acquired at portal-venous enhancement and ap-plied to patient data with less severe liver diseases [34]. Thesegmentation technique was based on a probabilistic atlas of theliver constructed from training data. For the coarse estimation

of organs, an average model of the liver was registered to thepatient’s contrast-enhanced CT image. This estimation was im-proved by a geodesic active contour. Subsequently, the patientspecific intensity statistics inside the liver were estimated andused to discard tissue areas that did not satisfy the intensity con-straints. Finally, location corrections from the normalized prob-abilistic atlas were performed [34]. While the probabilistic anal-ysis ensured some level of compliance with the pathologies inthe test data, unsurprisingly, there were large segmentation er-rors on difficult clinical cases. Notably, after this preliminaryliver segmentation, 19 of the 50 clinical test cases had severeliver segmentation errors ( volume error) and the other 31livers exhibited small to moderate errors ( volume error).

B. Shape Analysis and Surface Parameterization

To detect shape ambiguities, a 3-D-analogue of a curvature-feature [37] was used as shape feature for comparing closedplanar curves [62]. Specifically, at a given point on a planarcurve, is the area of intersection of the interior of the curve anda “seed” (a sphere centered at ). of a curve can be usedfor both local (at every corresponding point on two matchedcurves) and global comparison of two curves, given an adequatesimultaneous parameterization of the two curves (Fig. 2)

(1)

is an indicator function on the interior of the sphericalseed centered at . is then the normalized volume of the inter-section of and the seed sphere of radius centered at a point. A compensation function accounted for the pixelation of dig-ital objects. The shape descriptor is rotation and scale invariantby design and robust to noise [37].To allow point-to-point comparisons across multiple sur-

faces, our method uses the structure of a general class of objectswe call “planar-convex.” We assume that livers fall under thiscategory. We define a planar-convex object in to be aclosed surface for which a set of parallel hyper-planes exists,such that every intersection of a plane in with resultsin a singular closed planar curve. We call each set of parallelhyper-planes which intersects with in this way “convexityplanes” [62]. Some 2-D examples are shown in Fig. 3.To find convexity planes, we could search over all sets of

parallel planes with normal-vectors lying on the top unit-hemi-sphere. An approximation to doing this is to search over a uni-formly spaced sampling on the top-half of the unit sphere. Sucha uniform sampling is provided by the vertices of a dodeca-hedron. We choose a dodecahedron with 32 vertices for easeof computation and sufficient sampling power. Thus, to matchtwo objects, we align their principal components and then orientabout the object’s largest principal component a set of sym-metric points comprising the vertices of a dodecahedron forsampling. Each intersection of the planes with the liver is thenanalyzed and the average number of connected components isfound. The minimum sum of average components across thecorresponding axes/planes of the two compared objects is thencomputed. This defines the set of matched convexity planes(as defined above) between the two compared objects. The


Fig. 2. An illustration of the shape descriptor on 2-D closed curves. The seed is a circle that intersects the objects (here a square and a larger circle). Given acorrect parameterization of the two closed curves, their point-to-point local difference can be assessed.

Fig. 3. Objects represented in the planar-convex space. Objects include thesimpler ‘V’ shape (left), a non-star shape domain such as the ‘S’ shape (middle),and the more irregular ‘ink blot’ shape (right). Convexity planes are coloredblue, while their intersections with the respective objects are shown in red.

number of convexity planes could be varied with the surfacesize, but it was kept constant to eight in our application.The surface of each convexity plane is uniformly sampled by

a user-defined number of partitions, with points at these par-titions being projected onto the object surface (Fig. 4). Fig. 4also shows an example of liver parameterization. These pro-jections or “parameterization points” have point-to-point cor-respondence between the compared objects/livers.

C. Correction of Liver Segmentation

At each parameterization point we compute the shape fea-ture on both matched objects’ surfaces to allow the visualiza-tion of results. The dissimilarity between two matched shapes (atraining and a test shape) at is computed as the absolute differ-ence of their shape features at : a large value indicates highdissimilarity, while zero is the perfect match. The dissimilarityat is then averaged as the mean value between dissimilaritieswith all training shapes at . By using the average, we avoidsimilarity to a single shape in the reference database that maybe itself unusual. is the shape image obtained from extrap-olating the dissimilarity values on the surface of the test liver,normalized between 0 and 1.

Fig. 4. Parameterization points. Left—Uniformly spaced points are projectedonto the object in the convexity plane shown in different colors. Right—theparameterization points are highlighted as small cubes on the surface of a liverwith irregular shape, when 13 convexity planes were used. These points allowpoint-to-point correspondence between two shapes.

From the initial liver segmentation, the shape analysis onmatched surface points with training data identifies areas onthe surface of the liver that have ambiguous shape. To allowsome level of intra-patient variability, is thresholded at 0.5and component analysis used to assign individual labels to eachambiguous area. As livers were primarily undersegmented bythe initial method [34], seeds are placed at the centroid of theselabels and a fast marching level set [53] employed to “grow”the segmentation based on the sigmoid of the gradient of the CTimage. A geodesic active contour [8] refines the segmentation.Our formulation of the geodesic active contour includesas shape condition

(2)

where is the sigmoid of the gradient of image with param-eters and [25], is the speed parameterand the curvature. The stopping condition of the adapta-tion of the active contour is that or the volume changebetween iterations becomes insignificant.


D. Correction of Liver Segmentation

With the liver segmented, a graph-cut approach [4] is appliedto find hepatic tumors. In the basic form, graph cuts suffer fromthe shrinking bias problem, particularly for segmenting elon-gated and small structures, such as the blood vessels and certaintypes of tumors [30]. Graph-cuts were shown to improve thesegmentation of abdominal organs in [35] using training shapes,but tumors are highly variable between cases. However, tumorsare generally round.The graph cuts method for image segmentation operates

by finding a globally optimal cut through the graph based onthe input data. Let be a binaryvector with components that can be either objects of in-terest (tumors) denoted by or background (healthy liverparenchyma), where . Typical graphs performdata labeling (t-links), via log-likelihoods based solely on in-teractive histogram fitting, and penalize neighborhood changes(n-links) through likelihoods from the image gradients [4]. Inour application, seed points were generated automatically forthe tumors by finding adaptive thresholds in the data. Multipleintensity threshold values are tried and the number of remainingvoxels inside the liver is plotted against the threshold value.The resulting curve is then approximated by pairs of fitted linesas in [52] and the optimal threshold is the one that generates thepair of lines with the highest sum of correlation coefficients.Additionally, the object seed points were further constrainedto have non-zero Hessian-based shape response, as describedbelow. Background seeds were obtained from the inverted bi-nary image of the foreground seeds followed by morphologicalerosion.The cost function of the graph in our application can be

written as

(3)

with

and is the voxel intensity at , the probability ofto be object , a local neighborhood of , the Eu-clidean distance between two voxels and , and the standarddeviations of image noise [4].The new terms in the formulation are and .

is the regional term that penalizes voxels that do notfollow the difference in the enhancement distribution betweenthe tumor and healthy liver parenchyma models, as determinedfrom training. With our database, encourages darkerregions inside the liver to be labeled as tumors, as the healthy

liver is brighter than the cancerous tissue. This relation betweenthe healthy (background) and unhealthy (object) liver changesduring training for other types of liver cancers

(4)

where is the intensity value at given that is an objectand the intensity value at the background (B).

is a Hessian-based shape condition to emphasizerounder tumors at multiple scales . The eigenvalues of theHessian at point define unique shapeconstraints to optimize the segmentation of tumors and reducetumor false positives [48]. The following energy terms areincorporated in the graph-cut definition:

(5)

with ; and .The method does not intend to segment the hepatic vascula-

ture, as the enhancement in our cases is irregular. To accountfor the slight undersegmentation of tumors, a classic geodesicactive contour [8] was employed to refine their segmentationwith a speed propagation parameter of 5 and a curvature pa-rameter of 2.5. The total volume of tumors was computed foreach patient and normalized by the total liver volume to com-pute tumor burden and monitor cases with metastatic hepaticcancer. The tumor burden error is estimated as the absolute dif-ference between manually and automatically measured tumorburdens. To study the reproducibility of the estimation of tumorburden under image noise and patient position variation, artifi-cial Gaussian noise and body rotations in the axial plane wereinduced in one dataset and the tumor burden recorded and com-pared to the ground truth.

E. Tumor Features and Classification

For each tumor candidate a set of 157 features were auto-matically computed to characterize the detection. They includesize, enhancement, 3-D shape, 3-D texture and statistics of thesemeasures, as shown in Table I. Due to the large number of fea-tures used for classification, feature selection was used to retainthe optimal combination of features for the separation of truepositive (TP) from false positive (FP) detections. Since thesefeatures can be redundant and correlated, identifying the mostinformative and independent features is keypoint to the successof the classifier. Otherwise the discriminant information hiddenin these features may be contaminated or affected by noisy fea-tures when we calculate similarities between training sampleswhich in turn will lead to poor classification accuracy. To ad-dress this issue, we conducted experiments on feature selectionusing the minimum redundancy and maximum relevance fea-ture selection method (mRMR) [44]. mRMR is a state-of-the-artfeature selection method popular in biomedical data analysis. Itselects good features according to the maximal statistical depen-dency criterion based on mutual information and minimizes theredundancy among features simultaneously.


TABLE I157 AUTOMATED TUMOR FEATURES WERE COMPUTED FOR

THE TUMOR CANDIDATES

Support vector machines (SVM) are a set of kernel-based su-pervised learning methods used for classification and regres-sion. Kernel refers to a matrix that encodes the similarities be-tween samples (evaluated by a certain kernel function, whichis a weighting function in the integral equation used to calcu-late similarities between samples). SVM minimize the empir-ical classification error and maximize the geometric margin si-multaneously on a training set, which leads to a high general-ization ability on the test samples. Through feature selection,SVM optimize the similarity between samples to maximize themargin between the two classes of samples (TP and FP). Fortraining and testing purposes, a leave-one-patient-out strategywas employed.The receiver operating characteristic (ROC) curves for the

hepatic tumor detection were generated with and without fea-ture selection to record the effects of classification and featureselection on the reduction of false detections. The performances

TABLE IIVOLUME ERROR (VER) FOR LIVER SEGMENTATION FROM THE CLINICAL

TEST DATA (5 MM SLICE THICKNESS)

of the two classifiers (with and without feature selection) werecompared using ROCKIT [39]. ROCKIT uses maximum likeli-hood estimation to fit binormal ROC curves and calculates thestatistical differences between ROC with regard to the differ-ence in the areas under the curve (AUC).

III. RESULTS

The livers were shown to be planar-convex. In other words,for each organ there exists a set of parallel planes such that everyintersection of a plane and the organ is a closed planar curve.Planes were found uniquely for each pair of compared liversor shapes. The planar convexity attribute was valid for everycombination of livers paired between the training and testingset, and allowed to identify local shape discrepancies.The preliminary segmentation technique was less accurate

than previously reported [34] due to the presence of tumorsand artifacts in our data, and an inconsistent acquisition of con-trast-enhanced images. Quantitative results from applying ourmethod to the automated segmentation of the liver are shown inTable II before and after the segmentation correction. The useof liver-to-liver shape parameterization coupled with geodesicactive contours reduced the percentage of volume error signif-icantly for both cases of severe segmentation failure and casesin need of only minor/moderate adjustments.Our technique improved significantly the segmentation of

cases with large tumors and segmentation errors ,while avoiding the generation of errors in well-segmented livers(Table II). Additionally, a t-test was performed between theresults (volume errors) of liver segmentation on the clinical testset and the MICCAI set (shown in Table II); the p-value was0.07. Fig. 5 presents an example of segmentation from a casewith artifacts and without contrast-enhancement, a moderatelyinaccurate segmentation, and a severe segmentation failure withtheir corresponding shape images and final corrected outputs.More quantitative results were obtained on the segmentation

of livers from the MICCAI liver data. The volume overlaps be-tween manual and automated segmentations were(Jaccard Index) with volume error,average surface distance and root-mean-squaredistance. The average score obtained with the evaluation soft-ware offered by the organizers of the MICCAI liver competitionwas 76.2; for details please refer to [22].


Fig. 5. Examples of liver segmentation (overlaid in green on axial views of 3-D CT data) of a case without contrast enhancement and with motion artifacts (a),a moderately inaccurate segmentation (b), and a severe segmentation failure (c). Initial segmentations are shown in the top row and their corresponding shapeimages in the second row. Shape ambiguities are depicted in a cold (low) to hot (high) colormap. The corrected liver segmentations are shown in the third row andtheir corresponding shape images in the bottom row.

Fig. 6. The variation of the volume error (estimated over the 50 clinical cases)with the number of training liver shapes.

The volume error was used to estimate the sensitivity of themethod to the number of training liver shapes. The error be-comes stable at approximately 14 training shapes, though notat the optimal value, which is reached when about 23 trainingshapes are employed, as shown in Fig. 6. Our method uses 27training cases to ensure that sufficient inter-patient variability iscaptured.The results of the detection and segmentation of hepatic tu-

mors are presented in Table III. All 79 tumors in the clinical

test set were correctly identified. False positives occurred gen-erally near the porta hepatis and coronary ligaments, where thereis lack of enhancement and high curvatures. There was no sig-nificant difference between the manual and automatic measure-ments of tumor burden ( from the Wilcoxon rank sumtest).Table III also presents quantitative results for the segmenta-

tion of the ten tumors in the MICCAI liver tumor dataset withsimilar results to those obtained on the clinical test set. TheTP, FP fraction and tumor burden could not be calculated forthis dataset, as there was no ground truth available for the totalnumber of tumors and the volumes of the livers. The errors inestimating tumor burden under variations in image noise andpatient position are presented in Table IV. The range of tumorburden errors is .Fig. 7 illustrates the manual and automatic segmentation of

hepatic tumors for two patients, each at two time points.Manual,automatic, and false positive segmentations are presented forcomparison. In Fig. 8, the change over time in liver volume ispresented for several patients. Fig. 9 shows quantitatively thechange in tumor burden in the five patients with multiple scansat different time points and manual measurement of the tumorburden.The SVM classifier was employed after extracting 157 fea-

tures for each true and false tumor candidate. Without feature


TABLE IIITRUE POSITIVES FRACTION (TPF) AND FALSE POSITIVES (FP)/CASE ARE REPORTED FOR THE DETECTION OF HEPATIC TUMORS

TABLE IVTUMOR BURDEN ERROR UNDER VARIATIONS IN IMAGE

NOISE AND PATIENT POSITION

Fig. 7. Examples of hepatic tumor segmentation: manual (blue), automated(yellow) and their overlaps in green overlaid on axial views of 3-D CT of twopatients (a) and (b), each at two time points (different CT scans of the samepatient). False positives from the automated segmentation are displayed in red.The two cases also illustrate the difference in the enhancement protocols withwell-enhanced portal and hepatic veins in (a), which are not visible in (b).

selection, the AUC of the classifier was 0.62. The maximumAUC of 0.85 was achieved for a combination of eight tumorcandidate features. The eight selected features were a combina-tion of intensity, shape and texture inside and outside the tumorcandidates. Namely, the eight selected tumor features were: themedian intensity, roundness, mean , mean , and minimumvalue of the Haralick correlation. Additionally, the followingfeatures computed around the edge of the tumor were retainedfor classification: the median of the energy, and kurtosis andvariance of the inverse difference moment.The SVM classifier with eight features achieved a sensitivity

of 100% TP at 2.3 FP/case (or 94% TP at 1.6 FP/case). Therewas a significant difference between the SVM

Fig. 8. Examples of change over time in liver volume for three cases fromthe clinical data with small (case1—red), moderate (case 2—green), and large(case 3—blue) metastatic liver tumors. Manual and automated estimationsare presented for comparison. Image data for cases 1 and 3 are shown inFig. 7(a) and (b), respectively.

Fig. 9. The change in tumor burden in five patients with two (cases 2, 3, and 5)and three (cases 1 and 4) scans obtained at different time points. The automatedmeasures are compared with the manual estimates of tumor burden at each timepoint.

classifiers with and without feature selection. Feature selectionresulted in 24% sensitivity increase at 1.6 FP/case, as shown inthe free-response ROC curves in Fig. 10.

IV. DISCUSSION

Use the focus of this manuscript is on the computer-assistedanalysis of diseased livers from noisy data with highly variablepathology, as existing techniques often fail when the liver is ab-normal and imaging conditions are not ideal. CT data were ac-quired from a cohort of patients withmetastatic liver cancer withhighly variable contrast enhancement. Imaging and movementartifacts were also present in the database. It can be noted both


Fig. 10. The top figure shows the variation of AUCwith the number of featuresused in the SVM classification. The maximum AUC was achieved using eightfeatures. The bottom figure shows comparative free-response ROC curves usingeight (SVM 8) and all 157 (SVM 157) features for classification. The differencebetween the two classifiers was significant .

visually from Figs. 5 and 7 and from the results in Table II thatthe livers in our clinical test set originate from patients with verycomplex diseases and images difficult to process.First, we introduce a technique for shape parameterization

with promising results for point-to-point matching of abdominalorgans with complex anatomy. The parameterization, combinedwith an invariant shape feature allows comparing local shapeacross abdominal organs, such as the liver. While the shape pa-rameterization is intuitively robust, it is difficult to judge the ac-curacy of point correspondences, which is dependent on the typeof data and application. We hope to have achieved a simpler andmore intuitive way to represent abdominal organs. The level setrepresentation in [43] could be an alternative and it was shownto work with a variety of shapes. Besides the relative simplicityof our parameterization, we avoid using nonlinear registration inthe absence of anatomical landmarks to control it. Importantly,the proposed shape parameterization scheme allows the identi-fication of local shape incongruities between one object and ashape training set to guide the segmentation of difficult or usualdata.Our confidence in claiming that planar convexity occurs gen-

erally with organ-surfaces is based on the results of our testscomparing local shape of 101 livers and our intuition based onexperience with radiological data outside of this project. In ourliver database, the assumption of planar-convexity was valid in100% of cases. Perhaps offering some examples of curves/sur-faces that are not planar-convex, such as curves/surfaces witha hole or large-scale concave indentation, can provide some

helpful clarification. Finding a set of convexity planes for thesurface is equally essential for the parameterization. The planarconvexity assumption is used to find a uniformly spaced set ofpoints on the surface of the liver. Thus, a set of convexity planeshelps to cover the surface fully with the sampling of points. Ad-ditionally, this uniform sampling allows dimensionality reduc-tion for shape analysis, which is time-consuming.Once shape differences are identified, the preliminary seg-

mentation of the liver, which was obtained using probabilisticatlases and level sets, is corrected through active contours gov-erned by image and shape information. Comparative results be-fore and after shape correction show significant improvements

on the accuracy of liver segmentation in even themost difficult cancerous cases. Cases with severe segmentationerrors had their volume error improved from 28.9% to 6.6%,while cases with tumors went from 17.0% to 5.2% volume error.The tumor detection and segmentation is achieved using

graphs constrained by shape and enhancement models. Thisallows to segment tumors of variable sizes with a reducednumber of false positives. The method does not specificallyaddress the heterogeneity of some liver tumors. The combina-tion of enhancement and shape constraints in the segmentationof tumors is generally robust to heterogeneous patterns, asillustrated by results, but may struggle with unusual cases.Additionally, we propose an extensive set of appearance, shapeand texture features (see Table I) to be computed for each tumorcandidate (inside and outside the tumor) and demonstrate thatthe number of false detections is reduced significantly throughfeature selection and classification using support vector ma-chines. Interestingly, the selected tumor features describe theintensity/enhancement, shape/roundness and the linear depen-dence of voxels inside the tumor, while the features computedon the tissue around the edge of the tumor represent measuresof the uniformity and local homogeneity of the normal liverparenchyma. For both segmentation and classification, infor-mation is used from a single enhancement phase, preferably theportal venous phase.All tumors were correctly detected at 2.3 false positives/case.

The segmentation of tumors resulted in 74% volume overlapbetween manual and automatic segmentations and 1.6 mmaverage surface distance and allowed to compute the livertumor burden, which was estimated with an error of 0.9%(the difference between manually and automatically measuredtumor burdens). The results of our method on the MICCAI livertumor data [11] are comparable to those achieved by the bestautomated method presented at the competition [55]. Namely,the overlap error, volume error and average surface distancewere 27.4%, 13.9%, and 1.3 mm for our method comparedto 28.9%, 18.2%, and 1.8 mm in [55]. The MICCAI livertumor competition data represented a range of pathologies withvariable enhancement, including hepato-cellular carcinoma,hemangioma and metastases. The clinical test set consisted ofmetastatic prostate cancers. These tumors tend to enhance less,though heterogeneously, than the healthy liver parenchyma.A similar comparison was performed with the results of the

MICCAI liver segmentation competition [22]. The MICCAIliver competition used mainly pathological cases, including pri-mary tumors, metastases and cysts, but the types of pathologieswere not available for consultation. Our results on the MICCAI


liver data are comparable to those achieved by the best two auto-mated liver segmentation method presented at the competition[28], [63]. Namely, the overlap error, volume error, averagesurface distance, root-mean-square distance and score were6.3%, 2.2%, 1.0 mm, 1.9 mm and 76.2 for our method comparedto 6.0%, , 0.9 mm, 1.8 mm and 77.3 for the technique in[28], and 6.4%, 1.0%, 1.0mm, 2.0mmand 76.8 for the algorithmin [63]. More details can be found at http://www.sliver07.org.As reviewed at the beginning of the manuscript, different

methods in the literature model the image information tosegment the liver and tumors. In particular, statistical shapemodels were successful to segment the liver [28] and ma-chine learning methods were effective to analyze tumors [55].Our approach combines anatomical (shape) and physiolog-ical (appearance/enhancement) modeling for both liver andtumor analysis. Additionally, probabilistic location informationis used to segment the liver and an extensive set of tumorand healthy parenchyma features are employed via machinelearning techniques for tumor analysis.In our approach, level sets were used to correct segmentations

given detected objects, while the initializations were performedby probabilistic atlases and graph-cuts for the liver and tumorsrespectively. Hence, discrete approaches were used for an initialestimation of the object of interest and the segmentation wasrefined by continuous formulations. In this scenario, histogramfitting and enhancement and location constraints were employedto both detect the objects and initiate their segmentation. Pleasenote that the level sets in our approach were designed to growthe segmented object from their initial segmentation and correctwhere the intensity model was insufficiently supple.The running time for one case was between 50–60 min,

including about 30–35 min for the initial liver segmentation,20–25 min for liver segmentation correction and a couple ofadditional minutes for tumor analysis. The most expensivecomputation part of the algorithm was the registration.The low rate of false positives in the detection of hepatic tu-

mors and the very small error in the tumor burden by the pro-posed technique suggest the high clinical utility of the com-puter-assisted tool for liver analysis. False positives are gen-erally small, easily identifiable by radiologists and do not addsubstantially to the tumor burden, which is performed at eachtime-point independently when a patient has multiple CT scans.Another potential application of the method would be tumorgrading, a highly important area in radiology and diagnosis anda subject of future work.The method proposed in this paper is designed for general

liver image analysis, but due to the availability of data, wasapplied to metastatic liver cancer. Future developments of thetechnique aim to constitute a computer-aided system for thefully automated integrated analysis of the liver. Importantly, thisstudy brings together the automated segmentation of the liverwith the detection, segmentation and classification of hepatictumors from typical clinical radiological data with variability inimaging acquisition parameters.

REFERENCES[1] American Cancer Society, Cancer Facts and Figures 2011. Atlanta,

GA: Am. Cancer Soc., 2011.[2] D. H. Ballard and C. M. Brown, Computer Vision. Englewood Cliffs,

NJ: Prentice-Hall, 1981.

[3] A. Beck and V. Aurich, “HepaTux—A semiautomatic liver segmenta-tion system,” inMICCAI Workshop on 3-D Segmentation in the Clinic:A Grand Challenge, 2007.

[4] Y. Boykov and V. Kolmogorov, “An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision,” IEEETrans. Pattern Anal. Mach. Intell., vol. 26, no. 9, pp. 1124–1137, Sep.2004.

[5] D. C. Broering, M. Sterneck, and X. Rogiers, “Living donor liver trans-plantation,” J. Hepatol., vol. 38, pp. S119–S135, 2003.

[6] C. Brechbuhler, G. Gerig, and O. Kubler, “Parameterization of closedsurfaces for 3-D shape descriptor,” Comput. Vis. Image Understand.,vol. 61, no. 2, pp. 154–170, 1995.

[7] P. Campadelli, E. Casiraghi, and A. Esposito, “Liver segmentationfrom computed tomography scans: A survey and a new algorithm,”Artif. Intell. Med., vol. 45, pp. 185–196, 2009.

[8] V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,”Int. J. Comput. Vis., vol. 22, no. 1, pp. 61–97, 1997.

[9] C. Coghlin and G. I. Murray, “Current and emerging concepts in tu-mour metastasis,” J. Pathol., vol. 222, no. 1, pp. 1–15, 2010.

[10] B. M. Dawant et al., “Semi-automatic segmentation of the liver and itsevaluation on the MICCAI 2007 grand challenge data set,” inMICCAIWorkshop 3-D Segmentation in the Clinic: A Grand Challenge, 2007.

[11] X. Deng and G. Du, “Editorial: 3-D segmentation in the clinic: A grandchallenge II—Liver tumor segmentation,” inMICCAIWorkshop, 2008.

[12] E. A. Eisenhauer et al., “New response evaluation criteria in solid tu-mours: Revised RECIST guideline (version 1.1),” Eur. J. Cancer, vol.45, pp. 228–247, 2009.

[13] J. Ellert and L. Kreel, “The role of computed tomography in the initialstaging and subsequent management of the lymphomas,” J. Comput.Assist. Tomogr., vol. 4, no. 3, pp. 368–391, 1980.

[14] M. S. Floater and K. Hormann, Surface Parameterization: A Tutorialand Survey [Advances in Multiresolution for Geometric Modelling].New York: Springer, 2005, pp. 157–186.

[15] M. Freiman, O. Cooper, D. Lischinski, and L. Joskowicz, “Liver tu-mors segmentation from CTA images using voxels classification andaffinity constraint propagation,” Int. J. Comput. Assist. Radiol. Surg.,vol. 6, no. 2, pp. 247–255, 2011.

[16] G. Gerig and M. Styner, “Shape versus size: Improved understandingof the morphology of brain structures,”Medical Image Computing andComputer Assisted Intervention, vol. 2208, LNCS, pp. 24–32, 2001.

[17] P. Gobbi et al., “The clinical value of tumor burden at diagnosis inHodgkin Lymphoma,” Cancer, vol. 101, no. 8, pp. 1824–1834, 2004.

[18] C. F. Gonsalves et al., “Radioembolization as salvage therapy for he-patic metastasis of uveal melanoma: A single-institution experience,”Am. J. Roentgenol., vol. 196, no. 2, pp. 468–473, 2011.

[19] R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features forimage classification,” IEEE Trans. Syst., Man Cybern., vol. 3, no. 6,pp. 610–621, Nov. 1973.

[20] Y. Häme and M. Pollari, “Semi-automatic liver tumor segmentationwith hidden Markov measure field model and non-parametric distribu-tion estimation,” Med. Image Anal., 2011, to be published.

[21] T. Heimann and H. P. Meinzer, “Statistical shape models for 3-D med-ical image segmentation: A review,” Med. Image Anal., vol. 13, no. 4,pp. 543–563, 2009.

[22] T. Heimann et al., “Comparison and evaluation of methods for liversegmentation from CT datasets,” IEEE Trans. Med. Imag., vol. 28, no.8, pp. 1251–1265, Aug. 2009.

[23] B. Hopenfeld, H. Ashikaga, and E. R. McVeigh, “Geodesic basedregistration of sensor data and anatomical surface image data,” Ann.Biomed. Eng., vol. 35, no. 10, pp. 1771–1781, 2007.

[24] K. D. Hopper, K. Singapuri, and A. Finkel, “Body CT and oncologicimaging,” Radiology, vol. 215, pp. 27–40, 2000.

[25] H. Huang et al., “Surface alignment of 3-D spherical harmonic models:Application to cardiac MRI analysis,” MICCAI, vol. 3749, LNCS, pp.67–74, 2005.

[26] L. Ibanez, W. Schroeder, L. Ng, and J. Cates, The ITK Software GuideSecond Edition 2005 [Online]. Available: http://www.itk.org

[27] S. Jagannath et al., “Tumor burden assessment and its implication fora prognostic model in advanced diffuse large-cell lymphoma,” J. Clin.Oncol., vol. 4, no. 6, pp. 859–865, 1986.

[28] D. Kainmuller, T. Lange, and H. Lamecker, “Shape constrained auto-matic segmentation of the liver based on a heuristic intensity model,” inMICCAI Workshop on 3-D Segmentation in the Clinic: A Grand Chal-lenge, 2007.

[29] S. Kawasaki et al., “Preoperative measurement of segmental livervolume of donors for living related liver transplantation,” Hepatology,vol. 18, no. 5, pp. 1115–1120, 1993.


[30] V. Kolmogorov and Y. Boykov, “What metrics can be approximatedby geo-cuts, or global optimization of length/area and flux,” in IEEEInt. Conf. Comput. Vis., 2005, pp. 564–571.

[31] H. Lamecker, T. Lange, and M. Seebass, “A statistical shape model forthe liver,” MICCAI, vol. 2489, LNCS, pp. 412–427, 2002.

[32] R. L. Lewis, Liver and Biliary Tract Tumors, L. Goldman and D.Ausiello, Eds., 23rd ed. Philadelphia, PA: Saunders Elsevier, 2007,ch. 206.

[33] H. Ling et al., “Hierarchical, learning-based automatic liver segmenta-tion,” in 26th IEEE Conf. Comput. Vis. Pattern Recognit., Anchorage,AK, 2008.

[34] M. G. Linguraru et al., “Atlas-based automated segmentation of spleenand liver using adaptive enhancement estimation,”Med. Phys., vol. 37,no. 2, pp. 771–783, 2010.

[35] M. G. Linguraru et al., “Multi-organ segmentation from multi-phaseabdominal CT via 4D graphs using enhancement, shape and locationoptimization,” in MICCAI 2010, New York, 2010, vol. 6363, LNCS,pp. 89–96.

[36] J. Liu, W. Gao, S. Huang, and W. L. Nowinski, “A model-based, semi-global segmentation approach for automatic 3-D point landmark local-ization in neuroimages,” IEEE Trans. Med. Imag., vol. 27, no. 8, pp.1034–1044, Aug. 2008.

[37] S. Manay et al., “Integral invariants for shape matching,” IEEE Trans.Pattern Anal. Mach. Intell., vol. 28, no. 10, pp. 1602–1620, Oct. 2006.

[38] L.Massoptier and S. Casciaro, “A new fully automatic and robust algo-rithm for fast segmentation of liver tissue and tumors from CT scans,”Eur. Radiol., vol. 18, no. 8, pp. 1658–1665, 2008.

[39] C. E. Metz, B. A. Herman, and C. A. Roe, “Statistical comparisonof two ROC curve estimates obtained from partially-paired datasets,”Med. Decision Making, vol. 18, pp. 110–121, 1998.

[40] J. Moltz, L. Bornemann, V. Dicken, and H. Peitgen, “Segmentationof liver metastases in CT scans by adaptive thresholding and morpho-logical processing,” inMICCAI Workshop on 3-D Segmentation in theClinic: A Grand Challenge II, 2008.

[41] M. A. Muller, B. Marincek, and I. Frauenfelder, “State of the art 3-Dimaging of abdominal organs,” JBR-BTR, vol. 90, pp. 467–474, 2007.

[42] T. Okada et al., “Automated segmentation of the liver from 3-D CTimages using probabilistic atlas andmultilevel statistical shapemodel,”Acad. Radiol., vol. 15, no. 11, pp. 1390–1403, 2008.

[43] N. Paragios, M. Rousson, and V. Ramesh, “Distance functions fornon-rigid registration,” Comput. Vis. Image Understand., pp. 142–165,2003.

[44] H. C. Peng, F. H. Long, and C. Ding, “Feature selection based onmutual information: Criteria of max-dependency, max-relevance, andmin-redundancy,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no.8, pp. 1226–1238, Aug. 2005.

[45] A. Peterhans et al., “A navigation system for open liver surgery:Design, workflow and first clinical applications,” Int. J. Med. Robot.Comput. Assist. Surg., 2010.

[46] S. R. Prasad et al., “CT tumor measurement for therapeutic responseassessment: Comparison of unidimensional, bidimensional, and volu-metric techniques—Initial Observations1,” Radiology, vol. 225, no. 2,pp. 416–419, 2002.

[47] L. Rusko et al., “Fully automatic liver segmentation for contrast-en-hanced CT images,” inMICCAI Workshop on 3-D Segmentation in theClinic: A Grand Challenge, 2007.

[48] Y. Sato et al., 3-D Multi-Scale Line Filter for Segmentation and Vi-sualization of Curvilinear Structures in Medical Images, ser. LectureNotes in Computer Science. New York: Springer, 1997, vol. 1205,pp. 213–222.

[49] G. Schmidt et al., “Cognition network technology for a fully automated3-D segmentation of the liver,” inMICCAI Workshop on 3-D Segmen-tation in the Clinic: A Grand Challenge, 2007.

[50] G. Schmidt, G. Binnig, M. Kietzmann, and J. Kim, “Cognition networktechnology for a fully automated 3-D segmentation of liver tumors,”in MICCAI Workshop on 3-D Segmentation in the Clinic: A GrandChallenge II, 2008.

[51] D. Seghers et al., “Model-based segmentation using graph representa-tions,” in Med. Image Comput. Comput. Assist. Interv. Int. Conf. Med.Image Comput. Comput. Assist. Interv, 2008, vol. 11, pp. 393–400.

[52] D. Selle, B. Preim, A. Schenk, and H. O. Peitgen, “Analysis of vas-culature for liver surgical planning,” IEEE Trans. Med. Imag., vol. 22,no. 11, pp. 1344–1357, Nov. 2002.

[53] J. A. Sethian, Level Set Methods and Fast Marching Methods. Cam-bridge, U.K.: Cambridge Univ. Press, 1999.

[54] N. Shevchenko et al., “MiMed liver: A planning system for liversurgery,” IEEE Annu. Conf. Eng. Med. Biol. Soc., pp. 1882–1885,2010.

[55] A. Shimizu et al., “Ensemble segmentation using AdaBoost with ap-plication to liver lesion extraction from a CT volume,” in MICCAIWorkshop on 3-D Segmentation in the Clinic: A Grand Challenge II,2008.

[56] D. Smeets, B. Stijnen, D. Loeckx, B. Dobbelaer, and P. Suetens, “Seg-mentation of liver metastases using a level set method with spiral-scan-ning technique and supervised fuzzy pixel classification,” in MICCAIWorkshop on 3-D Segmentation in the Clinic: A Grand Challenge II,2008.

[57] L. Soler et al., “Fully automatic anatomical, pathological, and func-tional segmentation fromCT scans for hepatic surgery,”Comput. AidedSurg., vol. 6, no. 3, pp. 131–142, 2001.

[58] P. Soyer et al., “Hepatic metastases from colorectal cancer: Influence ofhepatic volumetric analysis on surgical decision making,” Radiology,vol. 184, no. 3, pp. 695–697, 1992.

[59] J. Stawiaski, E. Decenciere, and F. Bidault, “Interactive liver tumorsegmentation using graph-cuts and watershed,” in MICCAI Workshopon 3-D Segmentation in the Clinic: A Grand Challenge II, 2008.

[60] M. Styner, A. J. Lieberman, D. Pantazis, and G. Gerig, “Boundaryand medial shape analysis of the hippocampus in schizophrenia,”Med.Imag. Anal., vol. 8, no. 3, pp. 97–203, 2004.

[61] Y. Tsushima and K. Endo, “Spleen enlargement in patients with non-alcoholic fatty liver: Correlation between degree of fatty infiltration inliver and size of spleen,” Dig. Dis. Sci., vol. 45, no. 1, pp. 196–200,2000.

[62] J. Watt, M. G. Linguraru, and R. M. Summers, “Affine invariant shapeparameterization to assess local 3-D shape in abdominal organs,” SPIEMed. Imag., pp. 79650-1–79650-8, 2011.

[63] A. Wimmer, G. Soza, and J. Hornegger, “A generic probabilistic activeshape model for organ segmentation,” Med. Image Comput. Comput.Assist. Intervent., vol. 12, no. 2, pp. 26–33, 2009.

[64] J. W. Xu and K. Suzuki, “Computer-aided detection of hepatocellularcarcinoma in hepatic CC: False positive reduction with feature selec-tion,” in IEEE Int. Symp. Biomed. Imag., 2011, pp. 1097–1100.

[65] Z. Xue, D. Shen, and C. Davatzikos, “Determining correspondencein 3-D MR brain images using attribute vectors as morphologicalsignatures of voxels,” IEEE Trans. Med. Imag., vol. 23, no. 10, pp.1276–1291, Oct. 2004.

[66] J. Zhou et al., “Semi-automatic segmentation of 3-D liver tumors fromCT scans using voxel classification and propagational learning,” inMICCAI Workshop on 3-D Segmentat. Clinic: A Grand Challenge II,2008.

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