# 3-D Vascular Skeleton Extraction and Decomposition

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 1, JANUARY 2014 139

3-D Vascular Skeleton Extraction and DecompositionAshirwad Chowriappa, Yong Seo, Sarthak Salunke, Maxim Mokin, Peter Kan, and Peter Scott

AbstractWe introduce a novel vascular skeleton extraction anddecomposition technique for computer-assisted diagnosis and anal-ysis. We start by addressing the problem of vascular decomposi-tion as a cluster optimization problem and present a methodologyfor weighted convex approximations. Decomposed vessel struc-tures are then grouped using the vessel skeleton, extracted usinga Laplace-based operator. The method is validated using preseg-mented sections of vasculature archived for 98 aneurysms in 112patients. We test first for vascular decomposition and next for ves-sel skeleton extraction. The proposed method produced promisingresults with an estimated 80.5% of the vessel sections correctly de-composed and 92.9% of the vessel sections having the correct num-ber of skeletal branches, identified by a clinical radiological expert.Next, the method was validated on longitudinal study data fromn = 4 subjects, where vascular skeleton extraction and decompo-sition was performed. Volumetric and surface area comparisonswere made between expert segmented sections and the proposedapproach on sections containing aneurysms. Results suggest thatthe method is able to detect changes in aneurysm volumes andsurface areas close to that segmented by an expert.

Index TermsAnalysis, decomposition, skeleton, vascular.

I. INTRODUCTION

SUBARACHNOID hemorrhage caused by the rupture of ananeurysm is one of the common causes of stroke. Each year,approximately 795 000 Americans experience a new or recur-rent stroke [1]. To perform pre- or poststroke assessment, someform of analysis of the vasculature has to be carried out [2], [3].In this paper, we focus on vascular decomposition and vesselskeleton extraction as a fundamental approach to understand thenature of complex vascular structures in computer-assisted di-agnosis (CAD) and analysis. The weighted approximate convexdecomposition (WACD) methodology for vessel decompositionwas first proposed in [4]. We extend this prior work and proposea twofold vessel segmentation approach. We first decomposethe vasculature into substructures. Next, the substructures aregrouped using the extracted vessel skeleton (see Fig. 1).

Manuscript received October 28, 2012; revised February 20, 2013 and April22, 2013; accepted April 27, 2013. Date of publication May 7, 2013; date ofcurrent version December 31, 2013.

A. Chowriappa and P. Scott are with the Department of Computer Scienceand Engineering, The State University of New York, Buffalo, NY 14214 USA(e-mail: ajc48@buffalo.edu; peter@buffalo.edu).

Y. Seo and S. Salunke are with the Department of Mechanical and AerospaceEngineering, The State University of New York, Buffalo, NY 14214 USA(e-mail: yongwons@buffalo.edu; ssalunke@buffalo.edu).

M. Mokin and P. Kan are with the Department of Neuroscience, BuffaloGeneral Hospital, Buffalo, NY 14214 USA (e-mail: maximmokin@gmail.com;peterkantzeman@yahoo.ca).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JBHI.2013.2261998

A. Previous Work on Decomposition and Skeleton Extraction

The literature shows several 2-D/3-D vascular segmentationand skeleton extraction methods [4][9]. For extended reviewson vessel segmentation algorithms, we refer the reader to the fol-lowing surveys [10][12]. Methods adapted from generic seg-mentation algorithms generally use a model-based approach,whereas others use the notion of vessel skeleton (centerline) forsegmentation.

On skeleton-based approaches, Ertan et al. [13] presented aunified coarse-to-fine approach for extracting the medial axisof the vascular tree. An innovative 3-D multibranch tubularstructure and centerline extraction method is proposed in [14].Although the classical minimal path techniques can only detecta single curve between two predefined initial points, this methodpropagates outward from only one initial seed point to detect 3-Dmultibranch tubular surfaces and centerlines simultaneously. In[15], vessel centerlines are obtained from a homotopic thinningof the vessels segmented using a level set method.

In contrast to skeleton-based methods, model-based tech-niques naturally capture the physics and geometry of vascu-lar structures (more generally, tube-like structures) that varyspatially. A geometric deformable model for segmenting tubu-lar structures is presented in [16]. The main advantage of thistechnique is its ability to segment twisted, convoluted, and oc-cluded structures without the need for user interaction. Christianet al. [17] present an approach for simultaneously separating andsegmenting multiple interwoven tubular tree structures. Alsoin [18], the authors discus a deformable model for detectingbifurcations and providing structural analysis.

B. Our Vascular Decomposition Approach

In this paper, we propose a hybrid approach that 1) first de-composes the vasculature into subcomponents. 2) Next, a group-ing of subcomponents is performed from the extracted vesselskeleton. Our approach uses convex decomposition, a topic thathas been significantly investigated [19], [20]. However, exactconvex decomposition is not well suited for complex shapessuch as vascular structures. An exact decomposition of a com-plex shape such as a vascular tree can lead to unacceptablylarge number of components which may not have meaningfulrelationships. To overcome this problem, we propose a WACDmethodology that is well suited for vessel decomposition illus-trated in Fig. 1. It can be seen that an approximate decomposi-tion [see Fig. 1(c)] produces a parsimonious representation ofthe vessel structure.

Our proposed vascular decomposition approach can be di-rectly performed on the surface mesh without the need for skele-ton extraction. However, when dealing with complex and highlytortuous structures seen in the vasculature, such decomposi-tion would produce subcomponents without correct anatomical

2168-2194 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

140 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 1, JANUARY 2014

Fig. 1. (a) Reconstructed surface mesh of a tortuous vessel tree, followed by (b) decomposition using the WACD strategy produces nine clusters for the vesseltree. Clusters are shown as different colored convex hulls of varying sizes. (c) Vessel skeleton is extracted and (d) decomposed clusters are grouped according toskeleton branches.

associations [since several decomposed components can belongto the same vessel branch, shown in Fig. 1(b)]. Using the vesselskeleton, we group the decomposed components into parsimo-nious descriptions with useful physiological significance [seeFig. 1(d)].

C. Our Vascular Skeleton Extraction Approach

We introduce a new vessel skeleton extraction technique thatis applied directly on the vascular mesh representation. Themethod that we propose is similar to that of Cao et al. [21].However, their approach only works on point cloud models anddoes not consider the mesh topology. In our approach, the vesseltwo-manifold surface is iteratively shrunk into an approximatezero-volume degenerate mesh that abstracts the given vesselskeleton topology [see Fig. 1(c)]. The contraction process issetup as an energy minimization problem involving a discreteLaplace operator [22], [23] that removes the vessel geometry de-tails along the normal directions. Appropriate weight functionsare chosen such that the surface mesh contracts into a minimalvolume skeletal representation. This skeleton representation ofthe vasculature is also important for diagnosing and treatingpathologies, and in follow-up study analysis.

The two main contributions of this paper are as follows: 1)We propose a novel Laplacian-based vessel skeleton extractionmethodology. 2) We extend our WACD approach [4] and use theproposed vessel skeleton methodology to perform vascular seg-mentation (aneurysm and bifurcation decomposition) in CADanalysis.

This paper is organized as follows. In Section II-A, we intro-duce surface mesh generation for clinical data. In Section II-B,we compute the dual graph and define curvature parameters thatdrive the decomposition cost function. Vessel skeleton extrac-tion using the Laplace smoothing is discussed in Section II-C.Finally, we present our results in Section III and conclude inSection IV.

II. MATERIALS AND METHODS

A. Data Preprocessing and Mesh Generation

The clinical dataset consisting of contrast enhanced CTA data(slick thickness: 1.25 mm, stored using DICOM standards) wasused for the mesh generation. Volumes of interest around iden-tified vascular structures are specified using maximum inten-sity projections (MIP). More specifically, the following vessel

sections are reconstructed: basilar artery (BA), anterior commu-nicant artery (ACoA), posterior communicant artery (PCoA),middle cerebral artery (MCA), internal carotid artery (ICA),and superior cerebelar artery (SCA). Prior to segmentation andreconstruction, an anisotropic diffusion filter is applied [24].This filter reduces the noise while preserving small vascularstructures enabling better segmentation, which is important inthe region of the brain. Next, we remove the skull bones, thesinuses and the skin, having similar intensity as the vessels, us-ing double thresholding (dt1 , dt2 , dt3 , dt4). A 3-D model of thevessel is obtained as an isosurface of intensity zero, resultingfrom the level set evolution, implemented utilizing ITK [25].For a detailed description, we refer the reader to [26]. In orderfor small vessels to be included, isosurface Iiso = 118 valueis used. Values for the level set threshold lt = 36, variancel2 = 0.3, and number of iteration it = 120 in ITK were chosen.The parameter settings that were used in double thresholdingwere dt1 = 183 (bone), dt2 = 318 (bone boundary), dt3 = 714(mean bone boundary), and dt4 = max(I) (maximum intensityof the dataset).

B. Vascular Decomposition

In this section, we summarize our WACD methodology [4].From the computed vessel surface representation, convex de-composition is employed to partition the mesh into a minimalset of convex subsurfaces,S = {s1 , s2 , ..sn}. The two-manifoldsurface S is defined in R3 as V = {v1 , v2 , v3 , .., vi}, T ={t1 , t2 , t3 , .., tj}, and E = {e1 , e2 , e3 , . . . , ek} (where V is thevertex set, T is the set of triangles, and E is the edge set). Wedefine the dual graph D associated with the surface mesh S.Edge weights for D are computed from shape indices to favorcertain features over others. In mesh decimation, vertices of Dare iteratively clustered by applying a decimation operator thatminimizes a weighted cost function.

1) Computing Shape Index and Edge Weights: The curva-ture of a point on the surface can be defined by its maximumand minimum curvatures (k1 , k2). Using these curvature mea-sures, we determine whether the given point lies on a concave,convex, ridge, or saddle region (see Fig. 2). Saddle regions arecharacterized by being concave on one plane and convex fromanother (e.g., horse saddle) and most frequently correspond tosurfaces at vessel bifurcations. Ridges on the other hand can befound on aneurysm heads and ostiums (neck). For each nodein the graph D, we define a set of rings around the node as

CHOWRIAPPA et al.: 3-D VASCULAR SKELETON EXTRACTION AND DECOMPOSITION 141

Fig. 2. Primitive shape types for corresponding surface characteristics of ananeurysm sac.

Fig. 3. Decomposition using WACD on sections of vasculature, (a) and (b)shows decomposition of vessel tree with bifurcations, (c)(f) shows decompo-sition used to separate vessel sections fused with sections of cranium.

follows: the ith ring around node vj is defined as the set ofvertices v V for which there exists a shortest path from vjto v containing i edges. The Lring neighborhood of node vjis defined as the set of rings i < L about node vj . To capturethe shape of the Lring neighborhood (in our implementationa three-ring neighborhood), we use the shape index introducedby Cees et al. [27], where the shape index SI derived from theprincipal curvatures is given as

SI =12 1

arctan

kmin + kmaxkmin kmax

. (1)

The values of SI varies in the closed interval [0.0, 1.0] andevery distinct surface shape (see Table I) corresponds to a uniquevalue of SI (except for planar surfaces, which will be mappedto the value 0.5, together with saddle shapes).

Edge weights are then computed from the SI ranges as fol-lows. Two neighboring vertices connected by an edge in thedual graph D are assigned an edge weight determined by the

TABLE ISHAPE TYPES FOR SI RANGE

following criteria:

=

1 , 0 < SI 0.5 (umbilicpoints)2 , 0.5 < SI 0.75 (hyperbolicpoints)3 , 0.75 < SI 1.0.

(2)

One advantage of using shape indices as edge weights is thattransition from one shape type to another is continuous; hence,they can be used to describe subtle vessel shape variations.

2) Mesh Decimation: Following the assignment of the edgeweights to the dual graph D, convex decomposition is initi-ated by iteratively applying a half-edge collapse operation onneighboring vertices. A half-edge collapse operator, defined ashcol(u, v), when applied to two vertices (u, v) connected by anedge in 50 < < 250 merges v with u and all incident edgeson v are connected to u. The decimation process using the half-edge collapse operator is governed by a cost function that isweighted on and minimizes for concavity. The cost associatedwith hcol(u, v) is given by

C(u, v) = AR(u, v) + Con(S(u, v))

N(3)

where Con is the concavity of surface S(u, v) and N is thenormalization factor which is set as the diagonal of the boundingbox of S(u, v). The parameters and control contributions ofthe aspect ratio AR and concavity Con(S(u, v)). We set = 2to favor the generation of compact disks in which case the costis unity. The aspect ratio AR of the surface S(u, v) is definedby

AR(u, v) =(S(u, v))2

2 (S(u, v)) (4)

where is the perimeter and is the area of the surface S(u, v).After each edge collapse operation, is locally recomputed forsurface S(u, v) and the new edge weight new obtained from(5) is used in the update of D:

new =(1

)

. (5)

An influence parameter is used in order to minimize theinfluence of newly formed surface features caused by the deci-mation in successive iterations of hcol.

3) Mesh Partitioning: With each iteration of the hcol op-erator, the lowest mesh simplification cost is applied to a newpartition (n) = {n1 , n2 , n3 , n4 , . . . , nP (n)} minimizing Cthe cost function.

C(u, v) k {1, . . . , P (n)} , nk = pnk H(pnk ) (6)

142 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 1, JANUARY 2014

Fig. 4. Contraction of v...

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