a review on mr vascular image processing: skeleton versus nonskeleton approaches: part ii

338 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 6, NO. 4, DECEMBER 2002

A Review on MR Vascular Image Processing:Skeleton Versus Nonskeleton Approaches: Part II

Jasjit S. Suri, Senior Member, IEEE, Kecheng Liu, Laura Reden, and Swamy Laxminarayan, Senior Member, IEEE

Abstract—Vascular segmentation has recently been givenmuch attention. This review paper has two parts. Part I of thisreview focused on the physics of magnetic resonance angiography(MRA) and prefiltering techniques applied to MRA. Part II ofthis review presents the state-of-the-art overview, status, and newachievements in vessel segmentation algorithms from MRA. Thefirst part of this review paper is focused on the nonskeleton or di-rect-based techniques. Here, we present eight different techniquesalong with their mathematical foundations, algorithms and theirpros and cons. We will also focus on the skeleton or indirect-basedtechniques. We will discuss three different techniques along withtheir mathematical foundations, algorithms and their pros andcons. This paper also includes a clinical discussion on skeletonversus nonskeleton-based segmentation techniques. Finally, weshall conclude this paper with the possible challenges, the future,and a brief summary on vascular segmentation techniques.

Index Terms—Arteries, centerline, cross section, curvature,deformable models, direct, indirect, level sets, magnetic resonanceangiography (MRA), nonskeleton, partial differential equations,quantification, scale-space, segmentation, skeleton, stenosis,threshold, tracking, vasculature, veins, vessels.

I. INTRODUCTION

PART I of this review discussed the facts and figures due tochronic vascular diseases. We also presented five different

types of magnetic resonance angiography (MRA) coils usedwith a magnetic resonance imaging (MRI) system for data ac-quisition. A major portion of Part I was on the physics of MRAgeneration, where we talked about five different types of themost popular data acquisition techniques: time-of-flight (TOF),phase-contrast, contrast-enhanced, black-blood,-weighted,and -weighted, along with their pros and cons. We alsoexplored the different kinds of MR filtering algorithms, andwent into detail concerning the state-of-the-art scale-space MRfiltering. Interested readers can refer back to Part I for thesedetails. Here, in Part II, we will begin with presenting the mainmotivations for performing vascular segmentation along withthe major complications in segmentation of vasculature. Notethat for convenience of the readers, we have taken part of the

Manuscript received July 5, 2001; revised November 29, 2001 and December30, 2001.

J. S. Suri was with Philips Medical Systems, Inc., Cleveland, OH 44143 USA.He is now at 655 Dewitt Drive, Highland Heights, OH 44413 USA.

K. Liu and L. Reden are with the MR Clinical Research Science Division,Philips Medical Systems, Inc., Cleveland, OH 44143 USA.

S. Laxminarayan was with the Department of Biomedical Engineering andthe Department of Medical Informatics, New Jersey Institute of Technology,Newark, NJ 07102 USA. He is now with the Institute of Rural Health, IdahoState University, Pocatello, ID 83209 USA.

Digital Object Identifier 10.1109/TITB.2002.804136

discussion on motivations and complications from Part I of thisreview.

Researchers are aggressively attempting to segment the ves-sels (arteries and veins) from the human body using computervision, graphics, and image processing (CVGIP) techniques.Recently, there has been tremendous interest in using automatedsegmentation of vasculature from MRA data sets.

Having already discussed the motivations and difficultiesin vasculature segmentation in Part I, we will next discussthe taxonomy of the vasculature segmentation techniques (seeFig. 1). The vasculature segmentation techniques are furtherdivided into two types: indirect or skeleton-based and director nonskeleton-based. Skeleton-based techniques are thosewhich segment and reconstruct the vessels by computingfirst the skeleton of the vessels from the two-dimensional(2-D) slices. These are also called indirect methods, sincethe vessels are reconstructed by computing the vessel crosssections. Nonskeleton-based techniques are those that com-pute the vessels in three dimensions (3-D) directly. Herethe vessel reconstruction is done without estimating thevessel cross sections. Both of these broad techniques canbe computed by using one of two types, either with mul-tiscale or without multiscale.1 Skeleton or indirect-basedtechniques are classified into three broad classes: 1) skeletonwith vessel cross section estimation using edge-based tech-niques; 2) skeleton with vessel cross-section estimation usingparametric-based models; and 3) skeleton with vessel crosssection estimation using geometric-based models. Given theskeleton center line of the vessels, the difference betweenthese three classes is in the way the cross section of thevessels is estimated. Nonskeleton or direct-based techniquesare classified into eight different types: 1) threshold-based;2) fitting-based; 3) mathematical-morphology-based; 4) fuzzyconnectivity-based; 5) deformable model-based; 6) scale-spaceline filter-based; 7) waveform propagation-based; and 8) dif-ferential geometry-based. In threshold-based techniques, oneestimates the threshold to separate the vasculature from non-vasculature structures. The threshold estimation method couldbe manual, semiautomatic, or automated. The threshold-basedtechniques are divided into four types, depending upon themethod for computing the threshold: 4) maximum intensityprojection (MIP)/Local MIP; 2) manual; 3) expectation-max-imization (EM)-based (see Wilsonet al. [1], [2]); and4) threshold followed by shading. The fitting-based type usesthe method of fitting the cylindrical or elliptical models forvessels (see the work by Coatrieuxet al. (see [3]–[5]). Themain idea is to fit the piecewise cylinders to the vessels. The

1We will deal with the multiscale concept later but for now, think of multiscaleas a technique which can adjust the detection process of varying thickness byadjusting its scale.

1089-7771/02$17.00 © 2002 IEEE

SURI et al.: A REVIEW ON MR VASCULAR IMAGE PROCESSING: PART II 339

Fig. 1. Vasculature segmentation techniques.

fitting-based method is of three types: 1) moment-based;2) spline-based; and 3) cylindrical plus scale-space-based. Themoment-based method uses 3-D moment rules for computationof orientations of the vasculature model. The spline-basedmethod fits the spline with a certain degree of basis-functions.The cylindrical scale-space-based method uses the cylindricalmodel to start with and then uses the scale-space for detection.The mathematical morphology-based technique uses thenonlinear mathematical operators along with connectivity forvascular segmentation (see the work by Masutaniet al. [6]and Cline [7]). The fuzzy connectivity-based technique usesthe the fuzzy method for segmenting the vessels from the 3-DMRA volume (see [8]–[14]). The deformable-based techniqueis divided into two types: 1) parametric and 2) geometricdeformable models for segmenting the vessels from the MRAvolume (see [15] and [16], based on [17]). The scale-space3-D line filter method uses 3-D Hessian computation inscale-space for 3-D vascular segmentation (see [18]–[21]). Thewave propagation-based method (see [22]) uses the conceptof the propagation of the zero-level set contours in the levelset framework. Differential geometry-based techniques usethe first and second order surfaces for estimating ridges anddirections (see [23]–[28]). Differential geometry is divided intotwo types, with and without Gaussian-based techniques whichuse partial derivatives of the image volumes for computing thedirections of the vessel.

Having discussed the importance, motivations, difficulties inPart I, the taxonomy in Part II of the vasculature segmentation,we will now define the goals of this paper: 1) To learn aboutthe fast expanding classification of vascular segmentation

techniques and their links between these core classes. Further,to establish the relationships between low-level computervision and fast differential geometric techniques for a varietyof vasculature applications. 2) To survey the state-of-the-art lit-erature in: i) region-based 2-D and 3-D vascular segmentation;ii) boundary/surface-based 2-D and 3-D vascular segmentation;and iii) the fusion of boundary/surface-based with region-basedfor 2-D and 3-D MRA vascular segmentation techniques. Thiswill also involve discussing the pros and cons of the vascularsegmentation techniques (especially from INRIA,2 ISI-UU,3

IMDM, 4 MIT,5 NIH,6 PMS,7 UI,8 UNC,9 OU,10 and UPenn)11

and the salient features. Special emphasis will be given on thesuccess of scale-space vision and how the fusion of regionalforces is incorporated into the topology driven snakes/surfacesin the level-set framework using partial differential equations(PDEs). 3) To discuss the validation of vascular segmentationtechniques, challenges in vasculature segmentation and the

2Institut National de Recherche en Informatique et Automatique, Sophia-An-tipolis, France.

3Image Science Institute, Utrecht University, Utrecht, The Netherlands.4Institute of Math. and Computer Science in Medicine, University Hospital

Eppendorf, Hamburg, Germany.5Massachusetts Institute of Technology, Cambridge, MA, USA.6National Institutes of Health, Bethesda, MD, USA.7Philips Medical Systems, Inc., Cleveland, OH, USA.8University of Iowa, Ames, IA, USA.9University of North Carolina, Chapel Hill, NC, USA.10Osaka University, Osaka, Japan.11University of Pennsylvania, Philadelphia, PA, USA.


Fig. 2. Orthogonal projections using the MIP algorithm for bright blood arterial images. (Left) Transverse. (Middle) Coronal. (Right): Sagittal. Imaging parametersused: Volume TOF technique,T = 6:7ms,T = 27ms,FoV = 20 cm, Matrix size= 384�512,Thick = 1mm,Gap = 0mm,NSA = 1, Flip Angle= 35(Courtesy of Philips Medical Systems, Inc., Cleveland, OH).

Fig. 3. Manual segmentation results. (Left) Sample slice of a bright blood volume MRA TOF SLiding INterleaved Ky (SLINKY) image using manualthresholding. (Right): Results of stacking of all the slices after manual segmentation on a slice-by-slice basis of the MRA images. Imaging parameters used:Volume TOF technique,T = 6:7 ms,T = 27 ms,FoV = 20 cm,NSA = 1, Flip Angle= 35,Thick = 1 mm,Gap = 0 mm, Matrix size= 384� 512(Courtesy of Philips Medical Systems, Inc., Cleveland, OH).

future of vasculature segmentation. 4) To provide a comprehen-sive reference for readers pursuing advanced vessel-imagingresearch covering the latest state-of-the-art literature andtechniques, which solves the complex problem of 2-D and3-D vasculature segmentation. Note that we will not discussthe work of segmentation used in endoscopy, even though thisbranch is seeming to emerge rapidly, because it is out of thescope of this paper.

Having discussed the taxonomy of the vasculature seg-mentation techniques, we will next discuss the segmentationtechniques for extracting of vessels in 2-D and 3-D usingMRA. Section II presents the nonskeleton-based techniquesand Section III will discuss the skeleton-based techniques.Finally, Part II of this review concludes with the challenges, alook at the future, and a summary in Section IV.

II. NONSKELETON (DIRECT) VASCULAR

SEGMENTATION TECHNIQUES

Segmentation in medical imaging modalities has been in ex-istence for more than 40 years, but computer-assisted segmen-tation only began in the last 20 years. Good survey papers onsegmentation have been written. Interested readers are referredto the latest book and survey papers by Suriet al. [29], [30],[32], [33] and Valevet al. [34]). These papers cite more thanten good survey papers in the area of medical imaging. Thesewell-researched surveys are worthwhile, however, they do notdirectly pertain to this review, therefore, they will not be furtherdiscussed. Segmentation in angiography has been active since

1985, when digital subtraction angiography (DSA) began (seeet al. [35] and postprocessing of MRA [36] and [37]).

The layout of this section is as follows: First, Section II-Apresents the thresholding-based techniques. The fitting-basedtechniques are presented in Section II-B. Techniques based onscale-space fuzzy connectedness for vasculature segmentationare presented in Section II-C. Vasculature segmentation usinggeometric deformable models is presented in Section II-D. Seg-mentation techniques using mathematical morphology are pre-sented in Section II-E. The multiscale technique for vasculaturesegmentation will be presented in Section II-F. The wave propa-gation-based technique is presented in Section II-G. Finally, thesection concludes with the partial differential-based techniquesin Section II-H. Note that we will not discuss multiscale tech-niques, as that has been discussed in Part I of this review.

A. Threshold-Based Segmentation Techniques:Manual and Automatic

Threshold-based techniques for vasculature segmentation arethose using manual semiautomatic, and automatic thresholdingmethods. This section has the following parts: In Section II-A1,we briefly present the maximum intensity projection (MIP),local MIP, and manual thresholding. Section II-A2 presentsthe thresholding method along with the shading techniques forvessel display. Automatic thresholding based on expectationmaximization (EM) is discussed in Section II-A3.

1) MIP, Local MIP, and Manual Thresholding:The MIPwas generated by selecting the maximum value along an opticalray that corresponds to each pixel of the 2-D MIP image. The


Fig. 4. Comparison of MIP versus local MIP of CT renal volume. (Left) MIP algorithm. (Middle-2) Local MIP (LMIP) algorithm. Comparison of surface shadingversus volume shading of the CT renal volume. (Middle-2) Volume rendering using Visual Tool Kit (VTK). (Right) Surface rendering using surface shaded display(SSD) algorithm (Courtesy of Prof. Sato, Osaka University, Osaka, Japan).

MIP results in three orthogonal planes are shown in Fig. 2. Thedisplay shows reasonably good presentation of the densitom-etry of vessels (see Fig. 3). Note that the corresponding imagesand MIPs can also be displayed for the venous flow. For detailson MIP, see [38]–[42].

Pros and Cons of MIP: The majoradvantagesof MIP include:1) easy design; 2) a fast way for visualization of angiographydata; and 3) MIP can be obtained irrespective of any directionof transverse, i.e., anterior to posterior or posterior to anterior.The majordisadvantagesof MIP are that, it loses the 3-D infor-mation, and it is not helpful for finding stenosis.

LMIP was recently developed by Satoet al. [40] whichshowed improvements over MIP. The basic principle was tocreate an image by tracing an optical ray traversing 3-D datafrom the view points in the viewing direction. Next, selectthe first local maximum value encountered that is larger thanthe preselected threshold value (see Fig. 4, showing the renalsystem). For details, see Satoet al. [40].

Pros and Cons of LMIP: The majoradvantagesof LMIP in-cluded the simplicity of the design and better performance com-pared to classical MIP. The major disadvantages of LMIP in-clude: 1) sensitivity to direction; 2) user selective threshold wasutilized for LMIP generation; and 3) 3-D information was notproduced. One way to improve upon this would be to use manualsegmentation per slice to reconstruct the 3-D vasculature, whichis discussed next. Another recent approach was made by Mrozetal. [43]. Interested readers are encouraged to research this algo-rithm. Manual and semiautomatic methods are used for vascularvisualization and segmentation (see [44] and [45]). Sample re-sults on manual segmentation are shown in Fig. 3. On the leftin Fig. 3, the manually selected threshold for TOF data for asingle slice image is shown, and the result can be seen on theright of Fig. 3. The process is repeated for the entire volume ona slice-by-slice basis. The output results are displayed in threedimensions (see Fig. 3, right).

Pros and Cons of Manual Vasculature Segmentation:Themajoradvantageof using the manual segmentation method wasthat traced manual methods are considered the ground truth,when traced by experienced technologists or radiologists. Thereare, however, issues such as intra- and inter-observer variabilitywhich must be taken into account. The majordisadvantagesofusing manual methods includes: 1) they were tedious to use,as the data sets were very large; 2) this was a slow process,as it took a long time to perform the tracing; 3) intraobservererrors were observed due to fatigue; 4) the threshold was ad-justed manually for every desired vessel, for every slice, for

every view (axial, sagittal, and coronal) which was an enormoustask to perform; 5) it was very difficult to track the tiny vesselsdue to their size and branching; 6) the quantification process forstenoses and aneurysms was cumbersome; 7) this was a repeti-tive process; and 8) it was a time-consuming process.

2) Computerized Thresholding and Shading:The surfacerendering-based technique for vessel thresholding and displayhas been done by several authors (see [30], [41], [42], and[46]–[48]). The basic principle was thresholding the volumetricdata set and obtaining the binary image slices with the vesselsidentified or detected. Finally, surface shading was performedbased on gradient methods (see Fig. 4). Sample results for renalimages can also be seen in Fig. 4. Other authors who performedthresholding on CT data and then surface shaded display (SSD)were Halpernet al. [46], Cline et al. [47], [49], Orkiszet al.[50] and Chapmanet al. [51].

Pros and Cons of Segmentation by Computerized Thresh-olding and Shading:The major advantage of this method wasits ability to show visually acceptable 3-D appearance of thevessels, however, it was conditional on the selected threshold.Large vessels particularly showed very good results using thismethod. The major disadvantages were that it was very diffi-cult to adjust the threshold for running the marching cubes al-gorithm (if the threshold was larger than the true value, then thinvessels got missed, while if the threshold was less than the truevalue, large vessels could not be shown) and, in addition, theocculsion problem was not solved. We will see ahead that someof the drawbacks will be removed by automatic thresholdingtechniques.

3) EM-Based Automatic Thresholding for Vascular Segmen-tation: Nobelet al. (see [1] and [2]) developed a technique forsegmenting the arteries from the MRA volume by automaticallythresholding the MRA volume based on the EM algorithm (see[53]). The algorithm consisted of the following steps: 1)MixtureModeling:This consisted of modeling the mixture as the tissuesof the brain MRA data set which consisted of two tissue types:artery class (class 0) and two Gaussian distributions (classes 1and 2). The model presented by Wilsonet al.was

(1)

where and were the mean and standard deviation of theGaussian distribution, respectively. Indexrepresented the twoGaussian distributions. was the weight of each classin


the mixture. 2)EM Algorithm: This step consisted of solvingthe iterative EM algorithm to estimate the mean, variance, andweight. We will only present the updating values for the param-eters , , and . For details on the EM algorithm,readers are referred to [52].

(2)

(3)

(4)

Note here that was the total number of voxels being consid-ered and was the intensity of the voxel, while the function

was the conditional probability of voxel that be-longed to class at the current iteration and was defined as:

. 3) ThresholdComputation:The threshold computed using the EM algorithmwas based on the condition that the conditional probability ofcoming from the uniform class wasgreater thanthe conditionalprobability of coming from the other two Gaussian distributions,i.e., , where took the values 1 and 2.Following this condition, we obtained the threshold for the voxel

belonging to the artery class if and only ifwas greater than

.

Pros and Cons of EM-based Thresholding Algorithm:Themajor advantageof this technique was its simplicity andstraightforwardness in use. The majordisadvantagesof thistechnique include: 1) it was computationally expensive; 2) thealgorithm presented in the paper did not show any validationscheme; and 3) the algorithm was applied to healthy volunteersonly. There was no discussion on the data sets, except that thedata set is a TOF type.

B. Fitting-Based Segmentation Techniques:Moments and Spline Models

This class of indirect method consisted of estimating thevessel contours perpendicular to the vessel axis. These vesselcontours were represented by generalized cylinders, B-splines,or triangulated surfaces (see [54]–[58]).

1) Moment-Based Approach for Vascular Segmenta-tion: Coatrieux et al. [3]–[5] developed an algorithm forblood vessel detection and quantification in MRA data sets.The algorithm consisted of the following steps: 1) Initial seedplacement for tracking the 3-D vasculature. 2) Correction ofthe values by computing the orientation , which theprojected axes of the cylinder made with the- and -axes,respectively. These values were computed based on the momentsand were: and

,

where ’s are moments about the axes andwas a constant.The ’s were given as: ,

,and , where was defined as

(5)

where, and was the binary

indicator which had a value of one inside the sphere andzero outside the sphere. was the density function given as

. 3)The diameter of the vessel was computed using the following

expression: ,where was the size of the window, was the vessel intensityand was the background intensity. 4) The next step consistedof finding if the next voxel belonged to the vessel. The test wasmade using the thresholding procedure, if the intensitywasgreater than or less than the threshold, where was given as

(6)

where was the minimum value of the diameter that has tobe detected.

Pros and Cons of the Moment Based Technique: The majoradvantagesof the system include: 1) the method presented atechnique to detect the vascular network in MRA data sets;2) the method provided the local parameters characterizing thenormal or abnormal morphology of a vessel based on a cylinder-shaped model; and 3) the algorithm was independent of thewindow size. The majordisadvantagesof the system were: 1)the model was not capable of understanding the forking or bifur-cation behavior of the vessels (it was very difficult to design allthe possible 3-D configurations, at least the detection of thesedeviations from the model and the reinitialization of the trackingprocedure along these branches); 2) the window must be adap-tive in size and only one vessel should be observed during thetracking procedure; and 3) the fundamental assumption in themodel was that the tissues consisted of only two classes: back-ground and foreground. Consequently, the methodology did notwork for more than a two class problem and, usually in abnormalpathology, there are more than two classes.

2) Vessel Segmentation Using Spline-BasedModels: Recently, Frangiet al. [59]–[62] developed a fittingmodel-based method for segmentation of vessels from TOFMRA data sets. The method was called “fitting model-based”because it used an energy minimization model for fittingthe “initial spline” toward the “goal spline” for vesselsegmentation. The initial spline was the raw spline whichthe user placed by selecting a few points in 3-D space. Thegoal spline was the spline which was estimated after fittingand consisted of a state of minimum energy. The algorithm


consisted of the following steps: 1) The first step consisted offinding the central vessel axis (CVA). This was modeled as

, where was the representationfor B-spline curve of degree with control points, wasthe control points, was the th B-spline basis functionof order and . This snake model was deformedtoward the center of the vessel (goal state) by minimizationof the energy function , where represents the energy dueto the central vessel axis fitting and mathematically given as

, where was the internalenergy of the spline which was the combination of stretchingand bending given as .Note that and were the stretching and bendingconstants. The stretching and bending terms were standard dueto Kasset al. [90] as the first and second partial derivatives ofthe central vessel axis contour. This was mathematicallyexpressed as and

, where. The external energy term,

was defined mathematically as:, where

and was the discriminantfunction which depended upon the cross-sectional geometry ofthe vessel. This discriminant function was actually developedby Frangi et al. [59] and was mathematically expressed as:

, where , ,

and .Pros and Cons of the Spline-Based Methods:The majorad-

vantageof the system was its simplicity in implementation. Themajordisadvantagesof the system were: 1) the method was sus-ceptible to errors due to the energy constants; 2) the basis func-tion needed to be carefully selected; and 3) the accuracy of thesystem depended upon the external energy term due to the imageintensities and was susceptible to errors for noisy data.

C. Scale-Space Fuzzy Connectedness Technique for VascularSegmentation

Recently, Udupaet al. (see [11]) developed an algorithm forsegmentation of vessels in 3-D based on scale-space fuzzy con-nectedness (see the literature on fuzzy connectedness applied tomedical image segmentation [8]–[11] and [13]). The algorithmfor 3-D vessel segmentation consisted of the following steps:1) -Affinity image generation; 2) -connectivity scene gen-eration. Computation of the scale was done by solving the fol-lowing equation:

(7)

where was the number of pixels inand was the homogeneity function used

for defining . This meant that while was greater thanor equal to , keep incrementing. The scale was thus the lastvalue of . The connectivity scene generation consisted of thefollowing: Set all the elements of the scene to be zero, while

Fig. 5. 3-D vascular segmentation using nonscale and scale fuzzy techniquesfor two views (top row and bottom row). Left: Nonscale-based fuzzy vesselextraction. Middle—1: Scale-based fuzzy vessel extraction. Middle—2:Nonscale-based fuzzy vessel extraction. Right: Scale-based fuzzy vesselextraction (Courtesy of Dr. Udupa, University of Pennsylvania, Philadelphia,PA [9]).

the object was set to one. Push all the elements suchthat to . Now the loop was run while wasnot empty. During this loop was computed. If wasgreater than , was assigned the value andthe pixels were loaded in the queue, where .3) Surface rendering using the shell-rendering technique (see[12]). Fig. 5 shows the results of running the fuzzy connected-ness algorithm on MRA data sets. As can be seen in this figure,the scale-space method (right column) performed better thanthe nonscale space (left column) method.

Pros and Cons of Scale-space Fuzzy Technique:The majoradvantagesof scale-space fuzzy connectivity technique in-cluded: 1) the technique demonstrated that the scale-spacemethod performed better than the nonscale-space-basedmethod; 2) this technique was utilized for separating arteriesfrom veins; and 3) the method had been run on over 1500patient studies for different applications such as brain whitematter (WM) segmentation and fibroglandular tissue seg-mentation in breast X-ray digitized mammograms. The majordisadvantagesof scale-space fuzzy connectivity techniqueincluded: 1) the fuzzy connectivity was used only for CE-MRAdata sets; 2) user interactiveness was needed for parameterestimation; and 3) the fuzzy connectedness technique needed auser selected threshold for computing the connected scene.

Recently, Kobashiet al. [14] came up with a fuzzy approachto blood vessel segmentation.

D. Geometric Deformable Models for VasculatureSegmentation

Recently, Lorigoet al. [15] presented an algorithm for brainvessel reconstruction based on curve evolution in 3-D, alsoknown as “codimension two,” in geodesic active contours (see[17]). This method used two components: 1) mean curvatureflow (MCF) and 2) the directionality of vessels. The meancurvature flow component was used to derive the Eulerianrepresentation of the level-set equation. Ifwas the signeddistance transform (SDT) and wasthe eigenvalues of the projection operator: ,where and was a nonzero vector,


Fig. 6. Segmentation results using Lorigoet al.’s technique [15], [16]. (Left) Axial results. (Middle) Coronal results. (Right) Sagittal results (Courtesy of ProfessorGrimson, MIT, Cambridge, MA).

Fig. 7. Wavefront propagation input and output. (Left) input image. (Middle) output image (Courtesy of Dr. Quek, Wright University, Dayton, OH). (Right)Cline’s [7] method for segmentation of vessels based on 3-D mathematical morphology. The ellipses represent the process and the rectangles represent the objectsor input–output. As seen in this figure, the main steps are: 1) thresholding; 2) morphological smoothing; 3) mask generation; 4) volume subtraction;5) intersectionestimation; and 6) connectivity and display.

then using these eigenvalues, the Eulerian representa-tion of the curve evolution was given by Lorigoet al. as

. The second componentwas the normal of these vessels projected onto the plane andwas given as the product of with the projection vector .This projection vector was computed using the Hessian of theintensity image, and was given as ,where was the edge detector operator. Adding these twocomponents, the complete level-set equation was

(8)where was the directionality term which was the dot productof and which was the angle between these two vectors.

was the scale term. Note that the second term was like anangular balloon force which navigated the deformation process.The results of running the above algorithm can be seen in Fig. 6which shows the axial, coronal, and sagittal results, respectively.

Pros and Cons of Geometric Deformable Model Technique:The majoradvantagesof this technique include: 1) the methodsuccessfully demonstrated the segmentation of vessels of thebrain; 2) the method used the directional component in the levelset framework, which was necessary for segmenting twisted,convoluted, and occluded vessels; and 3) the technique wasused to compute vessel radii, a clinically useful measurement.The disadvantagesof geometric deformable model based

on the level set framework are: 1) not much discussion wasavailable on the computation of the scale factor; 2) themethod has yet to show the analytical model since the outputof the system showed relatively thinner vessels compared toMIP12 and thresholding schemes; and 3) since no comparisonwas made between segmented results and the ground truth, thishas not been validated.

E. Mathematical Morphology Approach for VesselSegmentation

Masutaniet al. [6] and then Cline [7] recently presented thealgorithm based on mathematical morphology for estimationof the blood vessels from MRA data sets. This was basedon the following four fundamental equations of mathemat-ical morphology: dilation (ORing), erosion (ADing), andclosing and opening expressed as ;

; ; and. Fig. 7 (right) shows the algorithmic

steps used for segmentation of the 3-D vessels from MRAdata sets. The algorithm is self-explanatory, however, thesteps are discussed briefly: 1)Thresholding Process:this stepconsisted of binarization of the input gray scale volume basedon user threshold; 2)Morphological Smoothing:consisted oferoding the binary volume using the structuring element like asphere followed by dilating the resulting volume with the same

12The MIP algorithm is a very popular technique. An example can be seen in[41].


structuring element; 3)Mask Generation:This step consistedof mask generation, which consisted of dilating the smoothedvolume (computed from the previous step); 4)Subtraction:thisconsisted of volume subtraction, where the smoothed volumewas subtracted from the masked volume; 5)Intersection:computed by subtracted volume intersected by the originalvolume; and 6)Connectivity and Display:This step consistedof running of the connectivity algorithm over the intersectedvolume and finally demonstrating the MIP of this volume forthe 3-D vessel display.

Pros and Cons of Mathematical Morphology-Based Method:The mathematical morphology method had theadvantagein itssimplicity and straightforwardness to use. However, this methodhad the followingdisadvantages: 1) initial stages needed userinteraction; 2) no research had been done on the size of the struc-turing elements; nor 3) was there any description on the valida-tion of the algorithm.

F. Skeleton-Based With Multiscale Vessel Model

Krissianet al. [63]–[65] recently developed a 3-D segmen-tation method for brain vessel segmentation using MRA. Thealgorithm can be classified as a model-based technique usingthe scale-space framework. The algorithm consisted of the fol-lowing steps: 1)Framing Initial Model: the model used was acylinder with the axis of the cylinder along the-axis with thecross section being a Gaussian function. This was representedusing the following equation:

(9)

where was a constant which depended upon choosing the sizeand location of the vessel and represented the in-tensity at the center of the vessel. The reason for choosing thismodel was that when this model convolved with the Gaussiankernel of standard deviation, the resulting image was anothervessel which matched this model with a different radius. 2)Mul-tiscale Response Computation:This step had two parts: Part oneconsisted of the preselection of the candidates using the eigen-values of the Hessian matrix . Part two con-sisted of computation of the scale-space response at one scaleand was given as

(10)

where . ranges from zero to .3) Local Extrema Computation:This step consisted of findingthe multiscale response and was given as

(11)

where was the scale-space response at a scale,, and therange of the scale was from to . was computed as

(12)

where and were the eigenvectors of the Hessian matrix.4) Skeletonization and Visualization:This consisted of skele-tonization of the vessels.

Pros and Cons of Multiscale with Vessel Model: The majoradvantagesof using this method were that the algorithm usedthe multi-scale approach for vascular segmentation and the al-gorithm showed good behavior on junctions and tangent vessels.The majordisadvantagesof multiscale with vessel model werethat the initial model taken was a cylinder, which was too simplefor the complex vascular nature of the network, plus, there wasno discussion on the validation.

G. 2-D Vessel Boundary Tracking Using Deformable Models:Wave

Recently, Queket al.[22] introduced a technique for segmen-tation of vessels in X-ray angiograms. This technique was sim-ilar to the concept of the propagation of the zero-level set con-tours in the level set framework. For complete details on levelsets, see the review article in [99], but sample results of Queketal.’s method can be seen in Fig. 7.

H. Nonskeleton-Based Approach Using Differential Geometry

A series of papers have appeared written by Dericheet al.(see [23]–[28], see also [66]–[68]). These papers are based onthe concept of differential geometry (see [69] and [70]). Thealgorithm used was based on computing the principal curva-tures and finding the ridge lines. Principal direction is definedas the direction of the vessel where the curvature change wasat a minimum. The principal direction was estimated using theWeingarten matrix, which was the product of , where

and were given as the 3 3 matrix. was given asand

was given as . Oncethe was computed, the eigenvalues and eigendirections werecomputed. This was computed for each voxel position in thevolume. An identification stage of , , and wascomputed to determine the directional derivatives of the max-imum and medium principal curvatures (DMC, DmC), whichwere given as and

. The zero crossing of the above equations define the twosurfaces in 3-D and their intersections as 3-D thin network.This zero-crossing was then computed as

. The method was actually run over thevolume which was obtained by the convolution of the decom-posed higher order derivatives, originally developed by Deriche.

Pros and Cons of the Differential Geometry-Based Tech-nique: The major advantagesof the system were that thesystem was fast, and used the higher order derivatives in termsof sine and cosines. The drawback was that the minimumdirection was not estimated at the center of the vessel. Also,the technique was not very robust toward handling differentdiameters of vessels. This method did not use the scale-spaceconcept.

Although direct techniques are robust, accurate, and veryattractive, there lies a major weakness with these techniques,i.e., they are computationally very expensive, and, therefore, areslow when it comes to real-time data analysis. Consequently,researchers are aggressively working on developing indirectmethods, which have proven to be faster.


III. SKELETON (INDIRECT) VASCULAR

SEGMENTATION TECHNIQUES

Skeleton or indirect-based techniques utilize the prin-ciple of building the skeleton of the vessels (see [75]–[85]).Section III-A presents the skeleton-based technique whichuses edge-based fusion for vessel cross section estimation.Section III-B presents the skeleton-based technique which usesdeformable model for vessel cross section estimation. Finally,this section concludes with the skeleton-based approach usingtraining models, covered in Section III-C.

A. Skeleton-Based With Scale-Space Edge-Based Fusion

Recently, Viergeveret al.(see [31], [71], and [72]) developeda fast delineation technique for vessel reconstruction fromdifferent modalities such as computerized tomography angiog-raphy (CTA), phase contrast (PC)-MRA and contrast enhanced(CE)-MRA. The algorithms consisted of the following steps:1) Manual Initialization: This step consisted of manuallyintroducing the start and end points of the central vessel axis.2) Computation of the nextcandidate pointalong the vessel.3) Estimation of the Plane Perpendicular to this CandidatePoint: Here, the step vector was first computed which consistedof the product of , where was a predeterminedconstant and was the minimum diameter estimated of thevessel. The step vector was extended in the direction of thevector which joined the previous vessel center to the currentvessel center. The perpendicular to this extended step vectorwas the the perpendicular plane in which the search regionwas defined. 4)Estimating the Vessel Center in a Search Regionin this Perpendicular Plane: The vessel center was computedby finding the center likelihood measure which was defined as

(13)

where was the center likelihood measure,was the totalnumber of rays or lines in the search region, andwere the absolute value of the rays which originate from thecenter toward the border of the vessel along the lines, whichcorresponded for the line. The rays and were com-puted in opposite directions using the gradient change of thegray-scale intensity. The rays originated from the point sourcein radial directions. An average of lines were drawnfrom the likelihood central point. The gradient component wascomputed as , where was therate of change of image intensity along the radial direction and

was the product of the radial vectorand the gradientof the image intensity . Note that the gradient of the orig-inal image was computed using Lindeberg’s method [73], [74]which was mathematically given as: , where

was the scale factor andwas the Gaussian smoothing func-tion. Thus, given the at all the points in the search region, the location where was at a maximum gave the vessel

center location. 5)Check of Termination Conditions: Here onechecks for the adaptation toward the central vessel axis andchecking toward the termination conditions. If they were met,then the system exited, or else the process was repeated.

Pros and Cons of the Scale-Space Edge-Based FusionMethod: The major advantagesof the system included:1) The system was fast, since it found the central vesselaxis in around 10 s. 2) One of the important aspects aboutthis algorithm was the introduction of the smoothnessconstraint which was responsible for tracking the suddencurvatures of the vessels. So basically, the direction of thetracking process was controlled by the new step vector,

(called the smoothed step vector) and was given as, where

was the scale factor and had a range from zero to one. The largerthe values of the , the more robust the tracking process was tothe abrupt changes in the direction of the central vessel axis.On the other hand, the smaller the values of, the algorithmprevented the tracking of highly curved vessels. 3) Winket al.[31] also suggested a more robust method for computing theway to the vessel center in the search region. This was basedon thesearch treemethod, that explored different extensionsto the current central vessel axis simultaneously and at a largerdepth. This meant that for every position in this search tree, the

was computed. The tracking process now proceeded inthe direction leading to the highest sum of center likelihoodsalong the tree. Although this method was more efficient, it wascomputationally expensive.

The majordisadvantagesof the system included: 1) Therewere too many parameters to adjust. They were:, parameterwhich controlled the vector step, a constant which premul-tiplied the vector step to find the search region, smoothnessconstraint, and , the total number of rays which originatedfrom the likelihood vessel center. 2) The system did not takeinto consideration anya prior knowledge for segmentation ofthe vessels. 3) The system did not show how the vessels wereclassified. 4) The computation time was linearly proportionalto the number of rays originating from the vessel center in thesearch region. 5) It would have been better if the result showedthe effect of the scale parameter, since it played a critical rolein the tracking process. 6) There was no experimental compar-ison made between Winket al.’s [31] method and the indirectmethods or other direct methods.

B. Skeleton-Based With Parametric-Based Model Fusion

Although deformable models13 have been into existence since1988, most of the applications were done in segmenting internalbrain structures, or isolated structures. Not much was done inthis area applied to vasculature segmentation. Authors who didresearch in this application were Steinet al. [87] and Bulpittet al. [88]. Steinet al. [87] developed a technique to segmentnervus alveolaris inferior (NAI) present in the jaw-neck area.This algorithm consisted of the following steps: 1)ROI Re-duction:This step consisted of running the mathematical mor-phology operation to preprocess the CT images to reduce thesearch region where the nerve was to be segmented. 2)MinimumPath Estimation (Guide Wire Estimation):This step consistedof finding the most favorable path (called guide wire) betweenthe starting and ending nodes or points. They used Dijkstra’s

13The three major advantages of deformable models are: 1) ability to fuseregularizers; 2) ability to model the constrain in the imagery; and 3) ability toextend 2-D models to 3-D and 4-D.


algorithm for this purpose. 3)Balloon Inflation: The last stepconsisted of applying the balloon force over the guide wire toinflate the guide wire to estimate the nerve structure.

Pros and Cons of Skeleton with Parametric-Based FusionMethod: The major advantages of the system included: 1) Thesystem logically used the correct steps for estimation of thenerves: ROI reduction, guide wire estimation, and balloon infla-tion. 2) The system was fast since the region of process was re-duced, based on mathematical morphology. 3) The system tookadvantage of interpolation since the data was tilted. 4) The con-cept of the soft classification was used, unlike the hard classifi-cation. This gave the advantage that a path could go throughsmall regions that showed a low probability of containing anerve based on their own gray level. The majordisadvantagesof the system were there was no discussion on the mathematicalmorphology operations, therefore, it was not clear what the sizewas of the structuring elements, and there was no discussion onthe snake algorithm as to what the values were of the constantsused in the minimization of the energy.

Bulpitt et al. [89] recently used the deformable model tosegment the branching vessels in abdominal aortic aneurysms(AAA). Similarly, Rueckertet al. [91] extended the classicaldeformable model of Kasset al.’s [90] for tracking aorta.Interested readers are encouraged to explore that paper further.

C. Skeleton-Based Approach Using Training Models

Very recently, Toledoet al. [92] developed a technique forsegmenting the coronary vessels in angiograms. This techniqueused deformable models (for details on deformable models, seethe extensive review by Suriet al. [93]), where the external en-ergy was computed based on the training data set. The energyminimization was done using the following classical equation:

(14)

where the first and second terms are the smoothing andstretching energies. The third term is the external energy termcomposed from the training data matrix,. The way is com-puted is as follows: first, the higher order Gaussian derivativesare computed to preserve the edges, ridges, and valleys whichare then convolved to give the scale-space representation.Then, the tensor is computed for the direction computation.This is similar to computing the Hessian of the scale-spacerepresented image (see Suriet al. [94] or Frangiet al. [62]).Then the eigenvalues are computed from this tensor matrixwhich gives the directions of the vessels. Now the isbuilt for all the points ( index) at all the scales (-index). Theratio is computed using the Mahanabolis distance in

direction, which becomes an attractive force for the initialvessel contour. Thus, (14) is optimized to yield the new contourpoints of the vessels.

Pros and Cons of Training-Based Snake Models: This tech-nique is a novel concept of bringing together the training modelwith the deformable model and thus the external energy termcomputation. The main weakness of this method is that it is com-putationally very expensive since it has to undergo training datacollection, computation, tensor computation, and then the it-erative optimization for the final contour position estimation.

Besides the above weakness, the training data is sensitive to thepoints collected for the vessels. There was no discussion of thiskind in the paper by Toledoet al. [92].

IV. CHALLENGES, THE FUTURE, AND SUMMARY :VASCULAR SEGMENTATION

Challenges:The state-of-the-art vasculature segmentationtechniques are filled with scale-space framework,14 fuzzyconnectivity, classification, geometric frameworks and skele-tonization of the tubular structures. Even though we are able tosucceed to a large extent on the segmentation of the vessels,there still lie ahead greater challenges and unresolved issues invascular segmentation. Some of the challenges in vasculaturesegmentation techniques include: 1) The ability to integrate thefuzzy connectivity or regularizers in the geometric frameworkfor robust vasculature segmentation. 2) The ability to trackthe vessels to the second and third layers of branching. 3) Theability to distinguish arteries and veins from the TOF data.4) The development of methods which can incorporate thelocal object size in defining the connectedness, object materialinhomogeneity, noise, blurring, and background variations.

The Future:Even though the application of geometric tech-niques such as level sets and PDEs have gone well in the fieldsof medical imaging and biomedicine, we are still far away fromachieving stable 3-D volumes and a standard segmentation inreal-time. By standard, we mean that which can segment the3-D volume with a wide variation in pulse sequence parame-ters. In the near future, we will see the modeling of front prop-agation that takes into account the physical constraints of theproblem, for example, minimization of variation geodesic dis-tances, rather than simple distance transforms. We will also seemore incorporation of likelihood functions and adaptive fuzzymodels to prevent leaking of the curves/surfaces. A good ex-ample of integration of the low-level processes into the evo-lution process would be given as

, where ,where is the low-level process from edge detection, opticalflow, stereo disparity, texture, etc. The better the , themore robust would be the level set segmentation process. Wealso hope to see more papers on level sets where the segmen-tation step does require a reinitialization stage (see [109] and[110]). It would also, however, be helpful if we can incorpo-rate a faster triangulation algorithm for isosurface extraction in3-D segmentation methods. Another issue in the future lies inthe user interactiveness of the system design. No matter whatcomputer algorithm is presented, the user interaction is alwaysa help in improving the accuracy of the system. The interpre-tation of the results is very essential. An attempt was made byQueket al.[111] who designed an architecture, called attention-ally-based interpretation model (AIM) for interpretation of theneurovascular system. We need such kinds of vascular interpre-tation systems which will help to better patient care.

Summary:In Part I of the paper, we introduced the importanceof angiography, the motivations of performing MRA, and the

14We could not cover the cardiac application and tracking in this paper. Therehas been a recent attempt by Rueckertet al. [91] to track the Aorta and paperson tracking and search heuristics (see [112]–[117]).


major difficulties in vascular segmentation. Here, in Part II, wepresented the state-of-the-art vascular segmentation taxonomywhich consisted of primarily two broad classes,skeleton or indi-rect-basedandnonskeleton or direct-based. We then presentedthree differentskeleton or indirecttechniques along with theirmathematical foundations, algorithms and their pros and cons.Following this was the presentation of eight different techniquesin the class ofnonskeleton or directmethods. Extensive discus-sion was given on geometric and fuzzy frameworks for vascularsegmentation. Finally, this paper concluded with the currentchallenges and the future on vascular segmentation techniques.

ACKNOWLEDGMENT

The authors wish to thank Dr. E. Keeler and Dr. L. Kasub-oski from Philips Medical Systems, Inc., Cleveland, OH, andProf. L. Shapiro, University of Washington, Seattle, for theirmotivations. The authors also thank Professor Grimson, MIT,Medical Labs., and Professor Udupa, University of Pennsyl-vania, Department of Radiology, for the useful discussions onfuzzy connectivity and images. The authors thank Academicand IEEE Press for granting permissions to reproduce the nec-essary figures, S. Lipton for proofreading the manuscript, andPhilips Medical Systems, Inc., for the MR data sets.

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Jasjit S. Suri (S’90–M’91–SM’00), photograph and biography not available atthe time of publication.

Kecheng Liu, photograph and biography not available at the time of publication.

Laura Reden, photograph and biography not available at the time ofpublication.

Swamy Laxminarayan (M’79–SM’94), photograph and biography not avail-able at the time of publication.

a review on mr vascular image processing: skeleton versus nonskeleton approaches: part ii

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