Lumen segmentation and stenosis quantification of atherosclerotic carotid arteries inCTA utilizing a centerline intensity priorHui Tang, Theo van Walsum, Reinhard Hameeteman, Rahil Shahzad, Lucas J van Vliet, and Wiro J Niessen

Citation: Medical Physics 40, 051721 (2013); doi: 10.1118/1.4802751 View online: http://dx.doi.org/10.1118/1.4802751 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/40/5?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Model generation of coronary artery bifurcations from CTA and single plane angiography Med. Phys. 40, 013701 (2013); 10.1118/1.4769118 Dynamic cone beam CT angiography of carotid and cerebral arteries using canine model Med. Phys. 39, 543 (2012); 10.1118/1.3673068 Automatic segmentation of intracranial arteries and veins in four-dimensional cerebral CT perfusion scans Med. Phys. 37, 2956 (2010); 10.1118/1.3397813 Coronary centerline extraction from CT coronary angiography images using a minimum cost path approach Med. Phys. 36, 5568 (2009); 10.1118/1.3254077 An abdominal aortic aneurysm segmentation method: Level set with region and statistical information Med. Phys. 33, 1440 (2006); 10.1118/1.2193247

Lumen segmentation and stenosis quantification of atherosclerotic carotidarteries in CTA utilizing a centerline intensity prior

Hui Tanga)

Biomedical Imaging Group Rotterdam, Departments of Radiology and Medical Informatics, Erasmus MC,P.O. Box 2040, 3000 CA Rotterdam, The Netherlands and Quantitative Imaging Group, Department of ImagingScience and Technology, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ,Delft, The Netherlands

Theo van Walsum and Reinhard HameetemanBiomedical Imaging Group Rotterdam, Departments of Radiology and Medical Informatics, Erasmus MC,P.O. Box 2040, 3000 CA Rotterdam, The Netherlands

Rahil ShahzadBiomedical Imaging Group Rotterdam, Departments of Radiology and Medical Informatics, Erasmus MC,P.O. Box 2040, 3000 CA Rotterdam, The Netherlands and Quantitative Imaging Group, Department of ImagingScience and Technology, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ,Delft, The Netherlands

Lucas J van VlietQuantitative Imaging Group, Department of Imaging Science and Technology, Faculty of Applied Sciences,Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, The Netherlands

Wiro J NiessenBiomedical Imaging Group Rotterdam, Departments of Radiology and Medical Informatics, Erasmus MC,P.O. Box 2040, 3000 CA Rotterdam, The Netherlands and Quantitative Imaging Group, Department of ImagingScience and Technology, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ,Delft, The Netherlands

(Received 12 February 2013; revised 27 March 2013; accepted for publication 9 April 2013;published 30 April 2013)

Purpose: The degree of stenosis is an important biomarker in assessing the severity of cardiovasculardisease. The purpose of our work is to develop and evaluate a semiautomatic method for carotidlumen segmentation and subsequent carotid artery stenosis quantification in CTA images.Methods: The authors present a semiautomatic stenosis detection and quantification method follow-ing lumen segmentation. The lumen of the carotid arteries is segmented in three steps. First, center-lines of the internal and external carotid arteries are extracted with an iterative minimum cost pathapproach in which the costs are based on a measure of medialness and intensity similarity to lumen.Second, the lumen boundary is delineated using a level set procedure which is steered by gradientinformation, regional intensity information, and spatial information. Special effort is made in addingterms based on local centerline intensity prior so as to exclude all possible plaque tissues from thesegmentation. Third, side branches in the segmented lumen are removed by applying a shape con-straint to the envelope of the maximum inscribed spheres of the segmentation. From the segmentedlumen, the authors detect and quantify the cross-sectional area-based and cross-sectional diameter-based stenosis degrees according to the North American Symptomatic Carotid En-darterectomy Trialcriterion.Results: The method is trained and tested on a publicly available database from the cls2009 challenge.For the segmentation, the authors obtain a Dice similarity coefficient of 90.2% and a mean absolutesurface distance of 0.34 mm. For the stenosis quantification, the authors obtain an average error of15.7% for cross-sectional diameter-based stenosis and 19.2% for cross-sectional area-based stenosisquantification.Conclusions: With these results, the method ranks second in terms of carotid lumen segmentationaccuracy, and first in terms of carotid artery stenosis quantification. © 2013 American Association ofPhysicists in Medicine. [http://dx.doi.org/10.1118/1.4802751]

Key words: geodesic active contour, gradient magnitude, regional intensity, calcium, envelope of themaximum inscribed spheres

I. INTRODUCTION

The latest report from WHO shows that cardiovascular dis-eases are the leading causes of death and disability in the

world.1 Atherosclerosis, a disease of the vessel wall, is oneof the main causes of stroke and cardiac attack. The degree ofstenosis in the internal carotid arteries is an important factorin grading cardiovascular disease severity. It also determines

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the treatment plan for carotid atherosclerosis. In the past dig-ital subtraction angiography (DSA) was the diagnostic testto assess the severity of stenosis. The invasive nature of thisprocedure and the small, but clinically relevant complicationshas promoted the introduction of less invasive workup of pa-tient with ischemic stroke. Nowadays Doppler ultrasound isthe standard imaging modality followed by MRA or CTA as aconfirmatory test for the assessment of atherosclerotic carotidartery disease. CTA was found to be an accurate modality forthe detection of severe carotid artery disease, especially fordetection of occlusions.2 For diagnosis and treatment plan-ning, accurate stenosis quantification on CTA would be re-quired. We aim to develop a semiautomatic carotid lumen seg-mentation and stenosis grading method in CTA.

Previous work on stenosis detection and grading in CTA.There are three criteria for quantifying the carotid stenosisdegree, one established by the North American SymptomaticCarotid Endarterectomy Trial (NASCET),3 one established bythe European Carotid Surgery Trial (ECST),4 and the com-mon carotid (CC) method.5 In (semi)automatic quantification,the NASCET is commonly used,6, 7 in which the referencevessel diameter is defined at a location distal to the stenoticpart of the vessel. Stenosis can be quantified based on thecross-sectional area (CSA) or cross-sectional diameter (CSD).Scherl et al.7 first performed an internal carotid branch seg-mentation and then quantified the stenosis degree at manu-ally annotated positions. Similarly, Zuluaga et al.8 performedsegmentation before stenosis detection and grading. They lo-cated the stenosis at the centerline location where the CSA isminimal. Kelm et al.9 estimated the CSA curve for coronaryarteries by a regression model using features from a cylinderaround the extracted centerline points. We choose to performan accurate segmentation before stenosis quantification.

Previous work on lumen segmentation: Lesage et al.10 re-viewed most of the recent vessel lumen segmentation methodsfor contrast enhanced imaging modalities (MRA and CTA)and categorized them according to their vessel extractionschemes, vascular models and image features. Several extrac-tion schemes can be used for vessel segmentation, such asactive shape/appearance models,11, 12 graph cuts,13 and levelsets, including level sets using boundary information,14 us-ing global regional information15 and using variational lo-cal regional information.16–18 Vessels are usually modeled astubular structures.14, 19, 20 The tubular pattern is maintained byminimizing the minimal principal curvature in level sets14 orby restricting the distance to centerlines in graph cuts.21

Graph cuts21–23 and level sets7, 24–27 are the two main ex-traction schemes for carotid lumen segmentation in CTA. Ac-tive shape models are not often applied due to the bifurca-tion of carotid arteries. A common initialization of these twoschemes is the carotid artery centerline, which can be manualor (semi) automatically extracted.

Scherl et al.7 extended the Chan-Vese15 model by addingan intensity based regularization term to remove calcium fromthe segmentation. The regularization term is based on a globallumen intensity estimation, which may not be realistic due tononuniformity of the contrast agent. This method was evalu-ated on ten internal carotid branches. Krissian and García26

also used the level sets extraction scheme steered by gradi-ent magnitude information. Gülsün and Tek21 segmented thecarotid arteries using a graph cut approach.28 The novelty intheir work is that they normalized the edge weight by the dis-tance to centerlines to remove nonisolated topology causedby side branches or nearby veins. Manniesing et al.24 utilizedboth gradient magnitude and intensity information to steer alevel set evolution. Tang et al.29 combined gradient magni-tude information with a centerline intensity prior to segmentcarotid artery lumen while excluding calcium and soft plaquetissues. The aforementioned methods are all initialized by ansemiautomatically extracted centerline. Ukwatta et al.27 com-bined local intensity regional energy defined under a varia-tional framework, together with global intensity regional en-ergy, boundary energy, and energy that encourages the bound-ary to pass through anchor points to segment the lumen andouter vessel wall of carotid arteries in 3D ultrasound. Theirmethod was evaluated on 231 transverse 2D image slices from21 subjects.

Plaques, especially calcified plaques, pose challenges forlumen segmentation. Methods used for calcium exclusion canbe divided into three types: excluding as part of a prepro-cessing step,30, 31 in the segmentation step,7, 21 or as a post-processing step. Schaap et al.30 suppressed calcium using in-tensity based kernel regression. In this method, hyperintenseareas are labelled as outliers and those areas are assigned anintensity which are much lower than the normal lumen inten-sity. Manniesing and Niessen31 applied a mask to remove cal-cium and bone. Scherl et al.7 segmented calcium and lumensimultaneously using a modified Chan-Vese model in whichcalcium is removed by a intensity-based regularization term.Gülsün and Tek21 excluded calcium by setting the ascendinggradient from the centerline to zero. Cuisenaire32 removed thecalcium by applying a threshold to the segmented foreground.In all these methods, only Scherl et al.7 explicitly proposed away to remove the entire calcium and voxels around the cal-cium which has similar intensity to lumen but not lumen.

There has been some previous work on suppressing out-liers (side branches) from lumen segmentation. Schaap et al.22

removed outliers in a postprocessing step by performing a ro-bust kernel regression (both longitudinal and cross-sectional)on the distance of surface points to the centerline. The per-formance of the method was not evaluated on arteries withasymmetric stenoses. The second principal curvature is alsoa crucial feature in detecting side branches. Wijk et al.33 re-moved protrusions from the colon surface by minimizing thesecond principal curvature flow. Even though it is possibleto steer a level set evolution using curvature flow,34 in ourtask, this method is not suitable since the surface in the dis-tal branches have a curvature that is similar to that in theside branches. Thus the distal part of external/internal carotidartery will shrink with the same speed as the side branches.

In this paper, we present a semiautomatic stenosis detec-tion and stenosis grading method based on accurate lumensegmentation which requires minimal user interaction. Oursegmentation method excludes soft and hard tissues but alsovoxels around calcium by integrating a localized centerlineintensity prior into a level set evolution scheme to guarantee

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sub-voxel accuracy. The method consists of three stages. First,the centerlines of the internal and external branches are ex-tracted by a minimum cost path approach between user spec-ified seed points. The cost image is defined by a measureof medialness and lumen intensity similarity to lumen. Thecenterlines are refined25 to achieve an accuracy comparableto interobserver variability, especially in curved regions, withcost defined in an image after hyperintense suppression (sup-pressed using the initial centerlines). Second, we extend thegeodesic active contour14, 35 segmentation method by combin-ing it with regional intensity information and spatial infor-mation. In this way, both the plaques and the voxels aroundcalcium which have a similar intensity to lumen can be ex-cluded successfully from the segmented lumen. Third, we re-move side branches (mainly occurring in the distal part) byimposing a shape constraint to the envelope of maximum in-scribed spheres.

Compared to previous segmentation methods, our paperhas four main contributions. First, we add a local regional in-tensity term besides the geodesic active contour approach toexclude nearby background such as plaques from segmenta-tions. Second, we propose a spatial regularization term in thelevel set energy function to exclude voxels around calciumwhich have a similar intensity to that of the lumen. Third, weremove side branches in a post-processing step by imposinga shape constraint. Fourth, we evaluate the proposed methodextensively using data of 56 carotid arteries from a publiclyavailable dataset.

This paper is organized as follows: Section II describesthe method. Section III describes the data, the parameter opti-mization, and the results. We discuss the results and concludein Sec. IV.

II. SEGMENTATION AND QUANTIFICATIONMETHOD

Carotid arteries originate from the aorta and split inthe neck into the external and internal carotids. The pro-posed segmentation method requires three seed points: onein the internal, one in the external, and one in the com-mon carotid branches respectively. The internal and externalcenterline are extracted from the three seed points and usedfor initialization in the subsequent segmentation. We quan-tify stenosis based on the segmented lumen of carotid artery.Subsections II.A–II.D describe each step for the segmentationand stenosis grading.

II.A. Centerline extraction

Centerlines are extracted in two steps. First, initial center-lines are extracted by a minimum cost path approach36 ap-proach between user-supplied seed points. We define the cost,which is used to compute the minimum cost path, as the in-verse of the product of a slice-based medialness term37 anda term indicating how similar a voxel is to the lumen inten-sity. The similarity term, which is close to one inside thelumen and close to zero in the background, is used to pre-vent centerline tracking through background. The initial cen-

FIG. 1. An illustration of hyper-intense suppression along a profile. (a) Theoriginal image showing the profile location and (b) the intensity profile of theoriginal image and the simulated profile after hyperintensity suppression.

terlines extracted by the minimum cost path approach havetwo drawbacks: (1) they take short cuts (following the innercurve) in curved regions and (2) they tend to shift towardscalcified regions. To address the first drawback, the extractedcenterline is then iteratively refined by repeating the minimumcost path approach in a curved multiplanar reformatted imagestack generated perpendicular to the centerline from the pre-vious iteration. More details of this approach are provided inRefs. 25 and 38. To address the second drawback, we suppresshyperintense regions as follows:

Ip(x) ={

I (x), if I (x) < Ic(x) + σc

Ic(x) − (I (x) − Ic(x)), otherwise, (1)

where Ip(x) is the intensity after hyperintense suppression,Ic(x) denotes the average centerline intensity, and σ c the stan-dard deviation of the intensity along the initial centerline. Anillustration of Eq. (1) is shown in Fig. 1. Intensity fluctua-tions that are only slightly higher than the estimated lumenintensity will only be marginally affected by the hyperinten-sity suppression. In Fig. 2, we show an example of the me-dialness measure applied to both the original image and thehyperintense-suppressed image. The green contour denotesthe manual segmentation and the green marker points to theposition with maximal medialness. The maximal medialnessin which calcium has been suppressed is located more towardsthe lumen center for images with hyper-intense suppression.

II.B. Lumen segmentation

A geodesic active contour35, 39 is commonly used to steera level set to the lumen border which is defined by a highgradient magnitude. However, for atherosclerotic vessels, thegradient magnitude is not sufficient to find the lumen border

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FIG. 2. Medialness computation with and without hyper-intense suppression. (a) Original image, (b) medialness of original image, (c) hyperintense suppressedimage, and (d) medialness of hyperintense suppressed image.

since calcified regions adjacent to the lumen yield an evenhigher value of the gradient magnitude. Figure 3(c) shows anexample of the gradient magnitude of a carotid artery in CTA.In this case, the gradient between lumen and soft plaque tis-sue is weaker than the gradient between calcification and softplaque tissue. If the level set is steered to the region with max-imal gradient, it will not segment the lumen appropriately, theresult will erroneously cover the plaque soft tissue region aswell, as shown in Figs. 3(b)–3(d).

To avoid this we include local lumen-intensity-based termsin the energy formulation. The foreground voxels should havean intensity as similar as possible to the lumen intensity andthe background voxels should have an intensity as dissimi-lar as possible to the lumen intensity. Combining this witha geodesic active contour gives the following energy to beminimized:

E(S) = γ

∫ ∫S

P (I (S(u, v)))|S′(u, v)|dudv

+α

∫ ∫ ∫�1

(1 − s(x))dxdydz

+β

∫ ∫ ∫�2

s(x)dxdydz. (2)

u and v are used for parameterizing the surface S,i.e., for points on the surface,39 we have S = (x(u, v),y(u, v), z(u, v)). �1 represents the region enclosed by sur-

face S(u, v), �2 represent the region not enclosed by sur-face S(u, v). From top to bottom in Eq. (2), the first term isa geodesic active contour which integrates gradient magni-tude information over the whole surface S(u, v) , the secondterm is used for minimizing the lumen intensity dissimilarityto the foreground, and the last term is used for minimizingthe lumen intensity similarity to the background. The param-eters α and β are used to weigh the boundary and regionalterms. The term P (I (S)) is inversely proportional to the gra-dient magnitude at scale σ g, 1

|Gσg ∗I |+η. η is a small positive

value to prevent dividing by zero. s(x) determines the similar-ity of a voxel to the lumen:

s(x) = e−(I (x)−Im(x))2/σ 2. (3)

Here Im(x) represents the local mean intensity of the lumen,which is obtained from a spherical region Sx centered at theclosest point on the extracted centerline. Let {xc} denote theset of points along the centerline, then Im(x) is defined by

Im(x) = I (argminxc(d(x, xc))),

subject to: |I (x) − Ic| < kσc, (4)

where I (x) is the average intensity over a region Sx centredaround x. Sx is empirically chosen to be a sphere with a ra-dius of 1 mm. Ic and σ c are the mean and standard deviationof the intensity along the centerline, d(x1, x2) is the Euclideandistance between x1 and x2, and k is a constant which controlsthe tolerance of the constraint. The constraint prevents outlier

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

FIG. 3. Example of: (a) original CTA of atherosclerotic carotid arteries, (b) original CTA overlaid by manual segmentation (red) and segmentation usingonly boundary information (yellow), (c) corresponding gradient magnitude of original CTA, and (d) gradient magnitude of original CTA overlaid by manualsegmentation and segmentation using only boundary information.

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FIG. 4. (a) Original image with the manual segmentation overlaid in red, (b) original image with a mask in blue indicating the voxels whose intensity is betweenthe maximum and minimum lumen intensity, (c) the segmentation using only gradient magnitude and regional intensity [by Tang et al. (Ref. 29)] shown in green,yellow is the overlap between manual segmentation and segmentation from the work in Ref. 29, and (d) zoomed-in version of image in (c).

intensities along the centerline to be used in determining theintensity term.

Due to partial volume effects, the intensity of voxels sur-rounding the calcium may be similar to the lumen intensity.Hence, in the cases where the calcium and the lumen are con-nected, the segmentation according to Eq. (2) will containthe voxels surrounding calcium. Figure 4(a) shows the origi-nal image with the manual segmentation overlaid in red andFig. 4(b) shows the voxels which are between the minimal lu-men intensity and maximal lumen intensity in blue. The vox-els around calcium also have intensities lying in the range ofthe lumen intensity. The segmentation thus contains the vox-els around calcium as it is also surrounded by a high gradientmagnitude, shown in Figs. 4(c) and 4(d).

In order to exclude the voxels around calcium from thesegmentation, we first label calcium voxels as follows:

C(x) ={

1, I (x) − Im(x) > Tc

0, otherwise, (5)

and each voxel at x has a label CN (x) to indicate whether itis surrounding a calcium spot or not.

CN (x) = C(x) ⊕ Nx, (6)

where Tc is experimentally selected. Nx is a cube of size5×5×5 voxels.

To exclude the voxels around calcium from the segmenta-tion, the energy function is modified to penalize the inclusionof voxels that are surrounding the calcium.

E(S) = γ

∫∫S

P (I (S(u, v)))|S′(u, v)|dudv

+α

∫∫∫�1

(1 − s(x))dxdydz

+β

∫∫∫�2

s(x)dxdydz

+ δ

∫∫∫�1

CN (x)dxdydz. (7)

Replacing S(u, v) by a level set function φ(x), which isnegative inside surface S(u, v) and positive outside S(u, v)(Ref. 40) in Eq. (7), and replacing region �2 by the Heavisidefunction Hε(φ(x)), region �1 by 1 − Hε(φ(x)), we get

E(φ) = γ

∫∫∫(H ′

ε(φ(x)P (I (φ(x))|∇φ(x)|

+α(1 − Hε(φ(x))(1 − s(x))|∇φ(x)|+βHε(φ(x))s(x)|∇φ(x)|+ δ (1 − Hε(φ(x))CN (x))|∇φ(x)|)dxdydz, (8)

in which Hε(φ(x)) is a regularized version of the Heavisidefunction and H ′

ε(φ(x)) is its derivative, similar to the approachby Chan and Vese.15

Minimizing Eq. (8) by gradient descent yields

φt = H ′ε(φ(x)){γcκP (I (φ(x)))|∇φ|

+ γa∇P (I (φ(x))) · ∇φ

−α(1 − s(x))|∇φ|+βs(x)|∇φ|− δCN (x)|∇φ|}. (9)

For tubular structure segmentation, κ is changed to be theminimum principal curvature.14

There are five terms in Eq. (9), from top to bottom theseare the curvature term for maintaining the tubular structure ofthe vessel, the advection term for finding the lumen borderin healthy regions, the foreground regional term for maintain-ing intensity similarity inside the vessel, the background re-gional term for maintaining intensity dissimilarity in the back-ground, and the spatial term for excluding the voxels aroundcalcium. The advection term is bilateral and depends on thecurrent position of the contour with regard to the gradientpotential valley. The sign in front of each remaining termindicates the direction of each term during evolution, nega-tive means shrinking while positive means expanding. In our

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FIG. 5. (a) Semiautomatic segmentation color coded by the distance to the manual segmentation, red indicates that the distance to manual segmentation isover 0.5 mm, (b) initial segmentation with side branch in green and the envelope of the maximum inscribed spheres in white, (c) original cross section, and (d)original cross section with superimposed manual segmentation (red), and semiautomatic segmentation in green, and overlap in yellow.

implementation, the curvature term and advection term areweighted separately by γ c and γ a.

II.C. Side branch removal

Side branches may occur in the distal region of the exter-nal and internal branches. The segmentation obtained fromEq. (7) contains part of the side branches, and that willcause inaccuracies in the stenosis quantification when the seg-ment containing side branches is included in the referenceCSA/CSD calculation. Figure 5(a) shows an example withside branches. Along the centerline, we extract the curvedmultiplanar reformatting (CMPR) image. The surface inFig. 5(a) is colored in those regions where the surface distancebetween the manual segmentation and the semiautomatic seg-mentation is over 0.5 mm. The image at the level of the sidebranch is shown in Fig. 5(c), and the corresponding segmen-tations are shown in red in Fig. 5(d) (manual: green, semiau-tomatic: red, overlap: yellow).

We propose to remove the side branches in a three-stepprocedure. First, from the initial segmentation, we com-pute the internal and external carotid artery centerlines us-ing a publicly available package Vessel Modeling Tool Kit(VMTK, www.vmtk.org).41 Now the centerlines are alsocomputed using a minimum cost path approach with thecost defined to be the inverse of the maximum inscribedsphere’s radius. Second, an envelope of the maximum in-scribed spheres of the initial segmentation is generated usingthe same package. The side branches are distant to the en-velope, shown in Fig. 5(b). However, this is not sufficient toidentify side branches, as in the stenotic areas, especially incases of asymmetric stenosis, the initial segmentation is alsopartially distant to the envelope, c.f., in Figs. 6(a) and 6(b).Third, to detect the location of side branches we compute thelong axis through cross sections of the segmentation alongthe centerline. The long axis is defined to be the longest axisthat divides the cross-sectional area in two equal parts. Subse-quently, this long axis is smoothed along the centerline usinga Gaussian kernel with a scale of 10 mm. The side branchcandidate locations are the locations where the original longaxis is larger than the smoothed long axis and at the same

time the distance to the maximum sphere envelope exceeds athreshold. An example of a side branch candidate detectionis shown in Figs. 7(a) and 7(b). The green curve is the longaxis before smoothing and the red curve is the long axis aftersmoothing. From Fig. 7(a), two regions have a long axis priorto smoothing that is larger than the smoothed axis. The regionon the left is the carotid bifurcation region but in that regionthe segmentation is not distal to the envelope of the maxi-mum inscribed spheres. In that region, the maximum distancebetween the envelope of maximum inscribed spheres and thecontour in a cross-sectional plans along the centerline is small(shown in blue). Thus only the region on the right will be seenas a side branch. From Fig. 7(b), an asymmetric stenosis willhave a large distance to the envelope of maximum inscribedspheres but the long axis is not larger than the smoothedlong axis. Only the region that has both a larger long axiscompared to smoothed long axis and a large distance to theenvelope of maximum inscribed spheres will be considered asa side branch. In this work, a distance between the envelopeof maximum inscribed surface and the semiautomatic seg-mentation will be considered as an indication of side branch

FIG. 6. (a) Manual segmentation in green and initial segmentation with sidebranch in transparent green and (b) initial segmentation with side branch ingreen and envelope in red, and overlap in yellow.

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FIG. 7. An example of side branch detection. Long axis (green), highlysmoothed long axis (red), and the maximum distance between the contours incross-sectional planes and the envelope of maximum inscribed spheres alongthe external centerline. (a) Carotid artery with side branch and (b) carotidartery without side branch but a stenosis.

if it is over 1 mm, shown in the dash blue line in Figs. 7(a)and 7(b).

II.D. Stenosis detection and grading

We quantify the stenosis using the NASCET criterion.3

The area/diameter of the stenotic segment is divided by thearea/diameter of a normal, distal segment of the internalcarotid artery (also called reference segment, where the vesselwalls are running parallel) and subtracted from one. Althoughthere may be multiple stenoses in one internal carotid artery,in this work, we select the most severe stenosis.

From the segmentation, we extract the internal centerlineusing VMTK. Along the centerline, we calculate the area anddiameter of the cross-sectional plane, i.e., CSA and CSD. Thediameter is defined as the length of the shortest axis that splitsthe cross-sectional area in two equal parts. An example of theshort axis calculation is shown in Fig. 8. We then smooth theCSA/CSD curve by a Gaussian filter with a scale of 1 mmto suppress noise. The stenotic segment is the position wherethe smoothed CSA/CSD is minimal. The reference segment isthe segment which is 2 to 3 cm distal to the stenotic segment.

FIG. 8. An example of short axis (diameter).

The reference CSA/CSD is then the average value in the ref-erence segment region. An example of the CSA as a functionof centerline position in depicted in Fig. 9.

0 1.0 2.0 3.0 4.0

(a)

(b)

5.0 6.0 7.0 8.010

20

30

40

50

60

70

80

Distance along centerline w.r.t common start point (cm)

CS

A (

mm

)

2 cm 1 cm

Reference CSA

Minimum CSA

FIG. 9. An illustration of the stenosis grading. Internal CSA is to the rightof common CSA. (a) A color-coded 3D surface based on the CSA curve and(b) corresponding CSA curve.

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III. EXPERIMENTS

III.A. Data and implementation

The proposed method was trained on 15 datasets and eval-uated on 41 datasets of the “Carotid Lumen Segmentationand Stenosis Grading Challenge.”42 We implemented the pro-posed segmentation method in ITK (www.itk.org), ignoringH ′

ε(φ(x)) because of the narrow-band implementation (|φ(x)|< 3).43 Narrow-band methods update only the level set evolu-tion around the neighborhood of zero level set instead of thewhole image. We implemented the stenosis quantification inVTK (www.vtk.org) and VMTK (www.vmtk.org). The cen-terline extraction takes on average 10 min; the level set evo-lution takes on average 15 min; the side branch removal takesaround 20 min; the stenosis quantification takes on average5 s. All timings were done using a linux workstation with16 processors (AMD 6172) with 12 cores each. And eachprocessor has a clock frequency of 2.1 GHz and RAMmemory of 256 GB. None of the processing used parallelimplementations.

III.B. Parameter optimization

The parameters that were fixed in this method are listed inTable I. We optimized the segmentation method by tuning thefour remaining parameters: the curvature weight γ c, the ad-vection weight γ a, the foreground regional weight α, and thethreshold Tc that is used in determining calcium and voxelssurrounding calcium. We optimize the four aforementionedparameters for three different metrics: the Dice similarity co-

TABLE I. List of level set segmentation parameters (not optimized intraining).

Parameters Value

Minimum root mean square error 0.0001Number of iterations 1000Initial tube radius (mm) 2Gaussian gradient scale σ g (mm) 1β 1δ 1σ in Eq. (3) (HU) 90k in Eq. (4) 0.5Nx size 5×5×5

efficient (DSC) of the lumen segmentation,44 the CSA-basedstenosis error (SEa) and the CSD-based stenosis error (SEd).The curvature weight γ c is varied from 1e-5 to 1e1 logarith-mically in six steps, and we include a curvature weight of 0.The advection weight γ a is varied from five to 25 with a stepsize of five, the regional weight α is varied from 0 to 0.09with a step size of 0.03, and the threshold Tc is varied from 60to 150 HU with a step size of 15 HU. This optimization pro-cedure examined 840 different combinations of the four pa-rameters. The optimal parameter combination that maximizesthe DSC was γ c = 1, γ a = 20, α = 0, and Tc = 120 HU.Figure 10 shows the result of the training step with regard totwo out of four parameters while fixing the remaining twoto their optimal values. Figures 10(c) and 10(d) show thatthe curvature weight γ c hardly influences the DSC between 0

FIG. 10. Lumen segmentation accuracy expressed in DSC for various combinations of parameters on the training set. From top left to bottom right, segmentationaccuracy (a) as a function of Tc and α at γ c = 1 and γ a = 20, (b) as a function of γ c and γ a at Tc = 120 HU and α = 0, (c) as a function of γ c and α atTc = 120 HU and γ a = 20, (d) as a function of γ a and Tc at α = 0 and γ c = 1, (e) as a function of α and γ a at γ c = 1 and Tc = 120 HU, and (f) as a functionof γ c and Tc at γ a = 20 and α = 0.

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FIG. 11. Cross-sectional area-based stenosis quantification for various combinations of parameters on the training set. From top left to bottom right, SEa (a) asa function of Tc and α at γ a = 5 and (b) as a function of γ a and Tc at α = 0.15, (c) as a function of α and γ a at Tc = 225 HU.

and 1. As a result we fixed the curvature weight to 1 and min-imize the SEa and SEb for different combinations of γ a, α,and Tc. In this stage, the three parameters have larger rangescompared to that used in maximizing DSC to make sure thatthe optimal value is not in the border of the parameter range.γ a ranges from 5 to 40 with a step size of five, α ranges from0 to 0.21 with a step size of 0.03, and Tc ranges from 60 HUto 300 HU with a step size of 15 HU. Figures 11 and 12 showthe result of the stenosis quantification error as a function oftwo out of three parameters when the third one is kept at itsoptimal value.

Table II lists the optimal parameters for three different op-timization metrics and the performance according to all threemetrics.

III.C. Segmentation results

On 41 carotid arteries of the testing set, the proposedmethod successfully segmented 38 carotid arteries. Threecases failed due to erroneously extracted centerlines. Table IIIlists our segmentation accuracy. The average DSC obtainedwith the parameters trained by maximizing DSC is 89.3%,and the average mean surface distance (MSD) is 0.38 mm.The average DSC obtained w parameters trained by minimiz-ing SEa is 90.2%, and the average MSD is 0.34 mm. The av-erage DSC obtained with the parameters trained by minimiz-ing SEd is 88.9%, and the MSD is 0.43 mm. We performed a

TABLE II. Summary of optimal parameters for three metrics: DSC, SEa,SEd.

Optimal DSC SEa SEd

Metrics value (%) γ c γ a α Tc (HU) (%) (%) (%)

DSC 91.5 1 20 0 120 91.5 19.7 12.7SEa 17.1 1 5 0.15 225 91.0 17.1 13.31SEd 11.3 1 5 0.03 180 90.4 18.8 11.3

TABLE III. Averages lumen segmentation performance.

Team Total success Dice (%) MSD (mm) Max (mm)

Reference 41 100.0 0.01 0.06Observer A 41 95.1 0.10 0.65Observer B 41 94.6 0.11 0.83Observer C 41 94.4 0.12 0.91Gülsün (Ref. 21) 41 91.8 0.18 1.52OursAtMinSEa 41 90.2 0.34 3.45OursAtMaxDSC 41 89.3 0.38 3.51Krissian (Ref. 26) 41 87.3 0.54 4.42Hui Tang (Ref. 29) 41 88.9 0.38 3.88OursAtMinSEd 41 88.9 0.43 4.09

FIG. 12. Cross-sectional diameter-based stenosis quantification for various combinations of parameters on the training set. From top left to bottom right, SEd

(a) as a function of Tc and α at γ a = 5, (b) as a function of γ a and Tc at α = 0.03, and (c) as a function of α and γ a at Tc = 180 HU.

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TABLE IV. Paired t-test of segmentation performance between Tang et al.(Ref. 29) (SegHT), segmentation with the parameters trained by maximizingDSC (SegMaxDSC), segmentation with the parameters trained by minimiz-ing SEa (SegMinSEa), segmentation with the parameters trained by minimiz-ing SEd (SegMinSEd), confidence interval = 95%.

p value SegHT SegMaxDSC SegSEa SegSEd

SegHT . . . 0.449 0.006 0.925SegMaxDSC . . . . . . 0.014 0.329SegMinSEa . . . . . . . . . 0.000SegMinSEc . . . . . . . . . . . .

paired t-test to check for statistical significance of the afore-mentioned difference, also with our previous work.29 Sincefor the challenge data, individual stenosis grades are not avail-able to the participants, we could only perform this analysisfor the segmentation results. The results of the paired t-testare listed in Table IV. The segmentation obtained with theparameters trained by minimizing SEa performs statisticallysignificantly better than the three other segmentation results.In the challenge website, it is possible to compare each testingresult with the published methods. We compared the best seg-mentation that we obtained (SegMinSEa) to the three methodthat ranked first (Gülsün and Tek21), second (Krissian andGarcía26) and third (Tang et al.29). SegMinSEa ranks secondin the segmentation challenge.

FIG. 13. Example of the side branch removal.

After applying the side branch removal step, the sidebranches are successfully removed, shown in Figs. 13(a) and13(b). Example results of the proposed segmentation methodobtained at parameters trained to maximize DSC are shownin Figs. 14(a) to 14(f). In all cases, the plaque tissue is notincluded in the segmented lumen. With the CN term in the

FIG. 14. Segmentation example for an atherosclerotic vessel with optimized parameters obtained at max DSC (Tc = 120 HU and α = 0 at γ c = 1 andγ a = 20), manual (green), semiautomatic method (red), overlap (yellow). (a)–(c) Semiautomatic segmentation without the term for excluding voxels aroundcalcium. (d)–(f) Semiautomatic segmentation with the term for excluding voxels around calcium.

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TABLE V. Averages stenosis.

Team name Total success SEa (%) SEd (%)

Reference 41 0.0 0.0Observer A 41 3.4 2.9Observer B 41 5.4 4.3Observer C 41 5.7 5.0MinAreaStenosis 41 19.2 15.7MaxDSCStenosis 41 22.8 16.8MARACAS (Ref. 8) 41 17.0 16.9MinDiamStenosis 41 24 18.7

energy function of Eq. (8), the voxels around calcium are alsoexcluded from the segmentation.

III.D. Stenosis quantification results

We tested three sets of parameters for the stenosis quan-tification trained using the three metrics: DSC, SEa, and SEd.The results are listed in Table V. Before our submission, theMARACAS method performed the best in the stenosis chal-lenge among the three previously submitted stenosis quan-tification results. As a result, this table only compares ourtesting results with the MARACAS method. We comparedthe best quantification that we obtained (MinAreaStenosis) tothe method that ranked first (MARACAS8). MinAreaStenosisranks first in the stenosis quantification challenge.

III.E. Reproducibility with respect to user interaction

We also investigated the reproducibility of the method inview of the minimal user action (selecting three seed points)required. We automatically apply a random 3D translation tothe original seed points to simulate the inter-observer vari-ability of seed points clicking. The translation is uniformlydistributed between the range of [−r/4, r/4], where r is thenormal radius of the common, internal, and external originalseeds. In our experiment, r is 4.0 mm in the common, 2.0 mmin the internal, and 1.5 mm in the external carotid artery.

We performed centerline extraction, segmentation andstenosis quantification with the repositioned seeds on 15 train-ing data sets. Reproducibility with respect to seed point posi-tion was assessed by comparing the DSC and stenosis quan-tification error obtained with the original seed points and theautomatically shifted seed points. The results are shown inTable VI.

TABLE VI. Comparison of the segmentation and quantification results ob-tained with the original seeds and automatically shifted seeds (paired t-testconfidence interval = 95%).

DSC (%) SEa (%) SEd (%)

Original seeds 91.5 17.1 11.3Translated seeds 91.4 17.2 12.1Mean absolute difference 0.7 4.9 2.7p value 0.67 0.98 0.48

The DSC was calculated while using the parameters ob-tained by maximizing the DSC on the training set, the SEa

(SEd) was calculated while using the parameters obtained byminimizing SEa (SEd) on the training set. The parameters areprovided in Table II.

The paired t-test shows that, for the segmentation resultsand the quantification results, there is no significant differ-ence between the ones obtained with the original seed pointsand with the translated seed points, which indicates that ourmethod is robust with respect to seed point position selectionas long as the seed points are within the range of [−r/4, r/4]apart from the original seed points.

IV. DISCUSSION AND CONCLUSION

We developed and quantitatively validated a semiauto-matic level set based method for carotid artery segmentationand subsequent stenosis quantification.

The segmentation method was trained on 15 carotid arter-ies. In the training stage, three different metrics were opti-mized: the Dice similarity coefficient of the segmented lumen,and stenosis degree, either measured based on cross-sectionaldiameters or cross-sectional areas.

When optimizing parameters using the Dice similarity co-efficient as metric, it was found that the optimal value of theforeground regional weight is zero. The foreground regionalterm provides a shrinking force during the level set evolution.Probably, since our segmentation is initialized by a centerlineinside the carotid arteries, a shrinking force is not required.The optimal threshold to define the calcium is 120 HU, whichindicates that on average calcified objects are at least 120 HUhigher than the nearby lumen intensity.

The method with optimized parameters was evaluated on41 carotid arteries. The Dice similarity coefficient obtainedwith the parameters optimized by training on minimizing thecross-sectional area-based stenosis is slightly higher than thatobtained at parameters trained maximizing the Dice simi-larity coefficient. Whereas the difference is small, it is sta-tistically significant (p = 0.006). The stenosis error on thetesting set is the smallest for the optimal parameter values ob-tained by minimizing cross-sectional area-based stenosis. Thetest results obtained by training on minimizing cross-sectionaldiameter-based stenosis are worse than when training usingthe other metrics. Also, the optimization landscapes for theparameter optimization for the cross-sectional diameter-basedstenosis were not as smooth as those for the other metrics.This demonstrates that optimizing using a more stable surro-gate metric, such as Dice similarity coefficient or area-basedstenosis give better results in our quantitative results. Further-more, the better performance also for Dice using the optimalparameters from the training on area-based stenoses suggeststhat it may be good to use a training set size larger than theone provided by the challenge.

Compared to the other carotid segmentation and quan-tification methods submitted to the same challenge, we ob-tained a slightly lower Dice similarity coefficient compared toGülsün and Tek21 who ranked first. Compared to our own pre-vious work29 which does not address voxels around calcium

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and a removal of side branches, the proposed method im-proved the average Dice similarity coefficient from 88.9% to90.2%. In other words, it reduced the mis-segmentation from11.1% to 9.8%. However, the impact in individual datasetscan be considerably larger, since calcified objects and sidebranches do not occur in all datasets.

Overall, our proposed method ranks first in the carotidartery challenge with respect to carotid artery stenosis quan-tification, slightly higher than the MARACAS algorithm inthe current challenge ranking system. The challenge setup,however, did not allow us to test whether the difference be-tween methods is significant.

In our evaluation, we found that our method may detectstenoses in vessels with slightly varying diameter, which areconsidered to be healthy. Since this results only in a minorstenosis, which is not clinically relevant, this does not pose anissue when using the method in practice.

In the future, we intend to use our approach for the steno-sis grading in clinical studies, e.g., by investigating the rela-tion of stenosis grade with clinical events. Additionally, ourapproach could be used in clinical practice by presenting thesegmentation results and also the minimal area curves, allow-ing the physician to manually select the minimal area locationand the reference segment.

In conclusion, we proposed an automated carotid lumensegmentation and stenosis quantification method which isable to exclude plaque tissues, voxels around calcified objectsand side branches from the segmentation, and evaluated thismethod in the context of a public challenge. We show thatdifferent parameter settings are optimal for carotid lumen seg-mentation than for carotid artery stenosis quantification. Withrespect to lumen segmentation accuracy our method rankssecond in the carotid artery challenge, and with respect tocarotid artery stenosis quantification it is the best performingmethod that has submitted results.

a)Author to whom correspondence should be addressed. Electronic mail:tanghui.seu@gmail.com

1S. Mendis, P. Puska, and B. Norrving, “Global atlas on cardiovascular dis-ease prevention and control,” WHO Report ISBN: 978 92 4 156437 3,2011.

2M. J. Koelemay, P. J. Nederkoorn, J. B. Reitsma, and C. B. Majoie, “Sys-tematic review of computed tomographic angiography for assessment ofcarotid artery disease,” Stroke 35, 2306–2312 (2004).

3H. J. Barnett et al., “Benefit of carotid endarterectomy in patients withsymptomatic moderate or severe stenosis,” N. Engl. J. Med. 339(20), 1415–1425 (1998).

4C. Warlow, “MRC European carotid surgery trial: Interim results for symp-tomatic patients with severe ( 70-99%) stenosis or with mild (0-29%)carotid stenosis,” Lancet 337, 1235–1243 (1991).

5M. Walker et al., “Endarterectomy for asymptomatic carotid artery steno-sis,” J. Am. Med. Assoc. 273(18), 1421–1428 (1995).

6K. Hameeteman et al., “Evaluation framework for carotid bifurcation lu-men segmentation and stenosis grading,” Med. Image Anal. 15, 477–488(2011).

7H. Scherl, J. Hornegger, M. Prümmer, and M. Lell, “Semi-automatic level-set based segmentation and stenosis quantification of the internal carotidartery in 3D CTA data sets,” Med. Image Anal. 11, 21–34 (2007).

8M. A. Zuluaga et al., “Adaptations of MARACAS algorithm to the seg-mentation of the carotid bifurcation and stenosis quantification in CTA im-ages,” in Proceedings of Carotid Lumen Segmentation and Stenosis Grad-ing Challenge, London, UK, 2009.

9B. M. Kelm, S. Mittal, Y. Zheng, A. Tsymbal, D. Bernhardt, F. Vega-Higuera, S. K. Zhou, P. Meer, and D. Comaniciu, “Detection, grading andclassification of coronary stenoses in computed tomography angiography,”in Proceedings of Medical Image Computing and Computer-Assisted In-tervention, Toronto, Canada (Springer-Verlag, Springer, Berlin Heidelberg,2011), Vol. 6893, pp. 25–32.

10D. Lesage, E. D. Angelini, I. Bloch, and G. Funka-Lea, “A review of3D vessel lumen segmentation techniques: Models, features and extractionschemes,” Med. Image Anal. 13(6), 819–845 (2009).

11T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, “Active shapemodels-their training and application,” Comput. Vis. Image Underst. 61,38–59 (1995).

12M. de Bruijne, B. van Bemmel, C. M. Ginneken, M. Viergever, andW. Niessen, “Adapting active shape models for 3D segmentation of tubularstructures in medical images,” Inf. Process. Med. Imaging 2732, 136–147(2003).

13Y. Boykov and G. Funka-Lea, “Graph cuts and efficient N-D image seg-mentation,” Int. J. Comput. Vis. 70, 109–131 (2006).

14L. M. Lorigo, O. D. Faugeras, W. E. L. Grimson, R. Keriven, R. Kikinis,A. Nabavi, and C. F. Westin, “Curves: Curve evolution for vessel segmen-tation,” Med. Image Anal. 5, 195–206 (2001).

15T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans.Image Process. 10(2), 266–277 (2001).

16C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore,“A level set method for image segmentation in the presence of intensityinhomogeneities with application to MRI,” IEEE Trans. Image Process.20(7), 2007–2016 (2011).

17C. Li, C.-Y. Kao, J. C. Gore, and Z. Ding, “Minimization of region-scalablefitting energy for image segmentation,” IEEE Trans. Image Process. 17,1940–1949 (2008).

18S. Lankton and A. Tannenbaum, “Localizing region-based active con-tours,” IEEE Trans. Image Process. 17, 2029–2039 (2008).

19A. F. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever, “Mul-tiscale vessel enhancement filtering,” in Proceedings of Medical ImageComputing and Computer-Asisted Intervention, Cambridge MA (Springer,Berlin Heidelberg, 1998), Vol 1496, pp. 130–137.

20Y. Sato, S. Nakajima, N. Shiraga, H. Atsumi, S. Yoshida, T. Koller,G. Gerig, and R. Kikinis, “Three-dimensional multi-scale line filter for seg-mentation and visualization of curvilinear structures in medical images,”Med. Image Anal. 2(2), 143–168 (1998).

21M. A. Gülsün and H. Tek, “Segmentation of carotid arteries by graph-cutsusing centerline models,” in Proceedings of Carotid Lumen Segmentationand Stenosis Grading Challenge, London, UK, 2009.

22M. Schaap, L. Neefjes, C. Metz, A. van der Giessen, A. Weustink, N.Mollet, J. Wentzel, T. van Walsum, and W. Niessen, “Coronary lumensegmentation using graph cuts and robust kernel regression,” Inf. Process.Med. Imaging 5636, 528–539 (2009).

23H. Homann, G. Vesom, and J. Noble, “Vasculature segmentation of CTliver images using graph cuts and graph-based analysis,” in Proceedingsof IEEE International Symposium on Biomedical Imaging, Paris, France(IEEE, 2008), pp. 53–56.

24R. Manniesing, M. Schaap, S. Rozie, K. Hameeteman, D. Vukadinovic,A. van der Lugt, and W. Niessen, “Robust CTA lumen segmentation ofthe atherosclerotic carotid artery bifurcation in a large patient population,”Med. Image Anal. 14(6), 759–769 (2010).

25H. Tang, T. van Walsum, R. S. van Onkelen, K. Hameeteman, S. Klein,M. Schaap, Q. J. B. Bouwhuijsen, J. Witteman, A. van der Lugt, L. J. vanVliet, and W. Niessen, “Semiautomatic carotid lumen segmentation forquantification of lumen geometry in multispectral MRI,” Med. Image Anal.16(6), 1202–1215 (2012).

26K. Krissian and S. A. García, “A minimal cost path and level set evolutionapproach for carotid bifurcation segmentation,” in Proceedings of MIC-CAI 2008 Workshop on Carotid Lumen Segmentation and Stenosis GradingChallenge, London, UK, 2009.

27E. Ukwatta, J. Awad, A. Ward, D. Buchanan, J. Samarabandu, G. Parraga,and A. Fenster, “Three-dimensional ultrasound of carotid atherosclerosis:Semiautomated segmentation using a level set-based method,” Med. Phys.38, 2479 (2011).

28Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimiza-tion via graph cuts,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1222–1239(2001).

29H. Tang, T. van Walsum, K. Hameeteman, M. Schaap, A. van der Lugt,L. J. van Vliet, and W. Niessen, “Lumen segmentation of atherosclerotic

Medical Physics, Vol. 40, No. 5, May 2013

051721-13 Tang et al.: Carotid lumen segmentation and stenosis quantification in CTA 051721-13

carotid arteries in CTA,” in Proceedings of IEEE International Sym-posium on Biomedical Imaging, Barcelona, Spain (IEEE, 2012),pp. 274–277.

30M. Schaap, T. van Walsum, L. Neefjes, C. Metz, E. Capuano, M. deBruijne, and W. Niessen, “Robust shape regression for supervised vesselsegmentation and its application to coronary segmentation in CTA,” IEEETrans. Med. Imaging 30(11), 1974–1986 (2011).

31R. Manniesing and W. Niessen, “Shape constrained vessel centerline ex-traction by integrating surface evolution and topology analysis,” in Pro-ceedings of IEEE International Symposium on Biomedical Imaging, Ar-lington, VA (IEEE, 2006), pp. 165–168.

32O. Cuisenaire, “Fully automated segmentation of carotid and vertebral ar-teries from CTA,” in Proceedings of Carotid Lumen Segmentation andStenosis Grading Challenge, London, UK, 2009.

33C. van Wijk, V. van Ravesteijn, F. Vos, and L. van Vliet, “Detec-tion and segmentation of colonic polyps on implicit isosurfaces by sec-ond principal curvature flow,” IEEE Trans. Med. Imaging 29, 688–698(2010).

34R. Malladi and J. A. Sethlan, “Image processing via level set curvatureflow,” Appl. Math. 92, 7046–7050 (1995).

35V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,” Int. J.Comput. Vis. 22(1), 61–79 (1997).

36E. W. Dijkstra, “A note on two problems in connexion with graphs,”Numer. Math. 1(1), 269–271 (1959).

37M. A. Gülsün and H. Tek, “Robust vessel tree modeling,” in Proceedings ofMedical Image Computing and Computer-Assisted Intervention, New York(Springer, Berlin Heidelberg, 2008), Vol. 5241, pp. 602–611.

38R. van Heekeren, F. Faas, and L. van Vliet, “Finding the minimum-costpath without cutting corners,” Image Anal. 4522, 263–272 (2007).

39V. Caselles, R. Kimmel, G. Sapiro, and C. Sbert, “Minimal surfaces: Ageometric three dimensional segmentation approach,” Numer. Math. 77,423–451 (1997).

40S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependentspeed: Algorithms based on hamilton-jacobi formulations,” J. Comput.Phys. 79, 12–49 (1988).

41L. Antiga and D. A. Steinman, “Robust and objective decomposition andmapping of bifurcating vessels,” IEEE Trans. Med. Imaging 23(6), 704–713 (2004).

42K. Hameeteman, M. Freiman, M. Zuluaga, L. Joskowicz, S. Rozie, M. vanGils, L. van den Borne, J. Sosna, P. Berman, N. Cohen, P. Douek,I. Sánchez, M. Aissat, A. van der Lugt, G. P. Krestin, W. Niessen, andT. van Walsum, “3D segmentation in the clinic: A grand challenge III,” inProceedings of MICCAI 2009 Workshop on Carotid Lumen Segmentationand Stenosis Grading Challenge, London, UK, 2009.

43R. T. Whitaker, “A level-set approach to 3D reconstruction from rangedata,” Int. J. Comput. Vis. 29, 203–231 (1998).

44L. R. Dice, “Measures of the amount of ecologic association betweenspecies,” Ecology 26(3), 297–302 (1945).

Medical Physics, Vol. 40, No. 5, May 2013