omisoidta, Hedicaversity

2013 Elsevier Inc. All rights reserved.

Available online at www.sciencedirect.com

Magnetic Resonance Imag ng 31Keywords: Magnetic resonance angiography; Cerebrovascular disorders; Fuzzy logic; Level-set segmentation

1. Introduction

Vascular diseases are a major cause of death anddisability worldwide and a large number of people sufferfrom a cerebrovascular incidence each year. Besidesischemic strokes, hemorrhages are the second major causefor cerebral strokes and account for approximately 1020%of all cases [1]. Most hemorrhages are thought to result fromthe rupture of small vessels in the presence of long standing

hypertonus or rupture of a pathological vessel wall of largerarteries or veins. Examples for such vessel pathologies areaneurysms [2] and arteriovenous malformations [3]. Espe-cially if diagnosed previous to a hemorrhagic event, aninterventional procedure may signicantly reduce thebleeding risk of such vessel pathologies.

Segmentations of the cerebral vessels are often required inthe clinical routine for improved diagnosis assistance,surgery planning, postoperative monitoring and researchpurposes [4]. In addition to this, cerebrovascular segmenta-Abstract

The aim of this work is to present and evaluate a level-set segmentation approach with vesselness-dependent anisotropic energy weights,which focuses on the exact segmentation of malformed as well as small vessels from time-of-flight (TOF) magnetic resonance angiography(MRA) datasets.

In a first step, a vesselness filter is used to calculate the vesselness dataset, which quantifies the likeliness of each voxel to belong to abright tubular-shaped structure and estimate the corresponding vessel directions from a given TOF dataset. The vesselness and TOF datasetsare then combined using fuzzy-logic and used for initialization of a variational level-set method. The proposed level-set model has beenextended in a way that the weight of the internal energy is locally adapted based on the vessel direction information. Here, the main idea is toweight the internal energy lower if the gradient direction of the level-set is similar to the direction of the eigenvector extracted by thevesselness filter. Furthermore, an additional vesselness force has been integrated in the level-set formulation.

The proposed method was evaluated based on ten TOF MRA datasets from patients with an arteriovenous malformation. Manualsegmentations from two observers were available for each dataset and used for quantitative comparison. The evaluation revealed that theproposed method yields significantly better segmentation results than four other state-of-the-art segmentation methods tested. Furthermore,the segmentation results are within the range of the inter-observer variation.

In conclusion, the proposed method allows an improved delineation of small vessels, especially of those represented by low intensitiesand high surface curvatures.Received 2 January 2012; revisedcDepartment of Diagnostic and Interventional Neuroradiology, University Medical Center Hamburg-Eppendorf, 20246 Hamburg, GermanydDepartment Computer Engineering, Faculty of Mathematics, Informatics and Natural Sciences, University of Hamburg,

22527 Hamburg, Germany

16 July 2012; accepted 17 July 20123D cerebrovascular segmentation cand level-sets with an

Nils Daniel Forkerta,, Alexander SchmDietmar Mllerd, Dennis Sring

aDepartment of Computational Neuroscience, University MbInstitute of Medical Informatics, Uni Corresponding author. Tel.: +49 40 7410 59828; fax: +49 40 741054882.

E-mail address: n.forkert@uke.uni-hamburg.de (N.D. Forkert).

0730-725X/$ see front matter 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.mri.2012.07.008ibining fuzzy vessel enhancementtropic energy weights-Richbergb, Jens Fiehlerc, Till Illiesc,einz Handelsb, Jan Ehrhardtb

l Center Hamburg-Eppendorf, 20246 Hamburg, Germanyof Lbeck, 23538 Lbeck, Germany

(2013) 262271tions come along with further benets such as an improvedregistration of angiographic datasets [5], possible blood owsimulations [6], improved vessel visualization using surface

2. State-of-the-art

263N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271In general, typical state-of-the-art vessel segmentationschemes can, for example, be distinguished into threshold-,scale-space- and deformable-model-based methods as wellas hybrid approaches that combine two or more of thesebasic techniques into one framework.

Threshold-based approaches aim to extract one globalthreshold or locally adaptive thresholds for segmenting vesselstructures. One comparably simple and fast threshold-basedapproach is the Z-buffer segmentation (ZBS) method asdescribed by Chapman et al. [13]. In this approach, amaximum intensity projection of the 3D TOF dataset iscomputed rst while the corresponding voxel coordinates aresaved in a Z-buffer image. After a consistency check of the Z-buffer, a set of seed points is extracted, which are used toobtain the nal segmentation via volume growing. Anothervolume-growing segmentation method was presented by Yiand Ra [14]. Here, the 3D dataset is separated into severalcube-shaped sub-volumes, which are used to calculate locally-adaptive thresholds that are then applied in a volume-growingprocess. Stochastic models are another common approach forthe extraction of a threshold. The basic idea of these models isto extract the histogram of a given image and t a mixture ofstatistical distributions that represent different tissues using theExpectation Maximization (EM) algorithm [15]. Wilson andNoble [16] proposed a stochastic model based on twoGaussian distributions, one for modeling the cerospinalmodels [7], quantication of pathologies [8] and preopera-tive denition a vessel-free path needed for brain tumorbiopsies and deep brain stimulations in case of epilepsy andParkinson disease [9].

Due to the fact that the manual delineation of vesselstructures is time-consuming and error-prone, the automaticsegmentation of vascular structures has been in the focus ofresearch for several years. Numerous factors have to be takeninto consideration for the development of an automaticsegmentation approach. Among others, these factors includethe high complexity of vessel shapes, including diameter andcurvature, especially in case of pathological structures, as wellas noise and other imaging artifacts, different vessel contrasts,the representation of surrounding organs and general aspectslike image dimension or resolution [10]. Therefore, a generalmethod that can extract the vascular system from any kind ofangiographic dataset is not available.

Due to the high blood-to-background contrast [11], the 3Dtime-of-ight (TOF) magnetic resonance angiography(MRA) is a commonly used MR imaging technique inclinical practice for diagnosis of the cerebral vascular system[12] and numerous vessel segmentation approaches havebeen proposed in the past that can be used for delineation ofvessel structures from this image sequence. A rough overviewof the state-of-the-art of vessel segmentation techniques isgiven in the following.uid, bone and background and the second for the braintissue and eyes, and one uniform distribution for arteries andsubcutaneous fat. Hassouna et al. [17] found that an improvedtting accuracy can be achieved if using four distributions. Inthis work, a Rayleigh distribution was used to model thebackground and three Gaussian distributions were used todesign the remaining tissue distributions, whereas theGaussian distribution modeling the high intensity regioncorresponds to vascular structures. After thresholding, aMarkov random eld is employed in a post-processing step.Intensity-based segmentation techniques are usually simple toimplement, fast and are able to delineate malformed vessels,which are represented by high intensities. However, theseapproaches tend to be sensitive for noise artifacts leading toholes within the segmentation and leakages to non-vasculartissues. Moreover, intensity-based approaches often fail tosegment small vessels that are represented by low intensities.

Scale-space-based methods are another common generaltechnique for cerebrovascular segmentation. Here, especiallyline-lter methods [1820] have been used extensively in thepast. The main idea of these approaches is to convolve theangiographic image with Gaussian derivatives of differentstandard deviations to obtain information about the localimage geometry. The different scales are used to deal withdifferent vessel sizes. Commonly, the Hessian matrix is usedto obtain the required second-order derivative informationbut the use of the Weingarten matrix has also been proposedas an alternative [21]. Certain relations of the eigenvalues ofthe matrix are used to discriminate tubular structures in theimage, while the corresponding eigenvectors can be used toestimate the vessel orientation in space. The enhanced so-called vesselness images have been used for direct visuali-zation [19], thresholding [18] or active contour segmentation[20]. Scale-space approaches allow an improved small-vesselextraction but usually fail to delineate malformed vessels,which do not exhibit a typical tubular vessel shape.

Deformable-model-based approaches deform an initialcontour or surface by internal and external forces. Generally,the internal forces keep the evolving contour smooth, whilethe external energy drives the contour towards dened imagefeatures. Due to the fact that the parameterization of activecontours is very challenging for vascular segmentation in3D, implicit active contours such as level-sets are morefrequently used for this purpose. Several level-set vesselsegmentation schemes have been proposed in the past thatdiffer regarding the integration and extent of shape priors andusage of gradient features or global intensity statistics. Onewell known level-set segmentation approach that utilizes astrong shape prior is the curve evolution method proposed byLorigo et al. [22]. The main idea of this approach is to evolveline structures in the 3D image domain. To account for thespecial characteristics of vessels, the width-limited surface isevolved by constraining its lowest curvature. In contrast tothis, Vasilevskiy and Siddiqi proposed a level-set frameworkfor vascular segmentation that is based on ux-maximizingow [23]. Here, the main idea is to align the surface normal

264 N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271to the intensity gradient direction. Gooya et al. [24] extendedthis approach by adding region statistical measures. Level-set segmentation schemes are topologically exible but maylead to insufcient small vessel delineation as edge andintensity information may be too weak such that the internalenergy is stronger than the external energy.

Several more approaches for the cerebrovascular seg-mentation have been proposed in the past. A good overviewof recent segmentation techniques is for example given bySuri et al. [25] or Lesage et al. [21].

The aim of this work is to present and evaluate acerebrovascular segmentation scheme fusing the benets ofintensity-, scale-space- and deformable-model-based ap-proaches. Fig. 1 shows the single steps of the proposedmethod that will be described in more detail in the following.

3. Methods and materials

3.1. Material and preprocessing

Overall, 11 datasets of patients with an arteriovenousmalformation of various volumes were available for this

work. All MR imaging measurements were performed on a3T Trio scanner (Siemens, Erlangen, Germany) using aneight-channel-phased array-head-coil. Among others, 3DTOF MRA image sequences were acquired for each patient.

The TOF image sequences used in this study were acquiredusing a TR 36ms, TE 6 ms, ip angle 25, bandwidth 178 Hz/Px, 6/8 slice partial Fourier, ow compensation, ve slabssequence each consisting of 40 partitions with an image in-plane resolution of 0.47 mm and 0.5 mm slice thickness.

Informed consent was obtained from all patients. The studywas approved by the local ethics committee (No. 2706/2005)

Prior to segmentation, each TOF image sequence waspreprocessed using the histogram-based slab boundaryartifact reduction method proposed by Kholmovski et al[26] to reduce slice-related intensity variations caused bythe multi-slab acquisition. After this, in-slice intensity non-uniformities, for example caused by poor radio frequencycoil uniformity, were corrected using the N3 algorithm [27]Finally, a skull-stripping algorithm especially designed forTOF image sequences [28] was applied in the last step ofthe preprocessing to exclude non-cerebral tissues from theTOF-images.

Fig. 1. Illustration of the single processing steps of the proposed method..

.

.

3.2. Vesselness parameter extraction

In this work, the vesselness lter proposed by Sato et al.[18] is used to enhance tubular structures in the TOF imagesequence and obtain information about the vessel direction in3D space. Briey described, this lter analyzes theeigenvalues of the Hessian matrix:

H =Txx Txy TxzTyx Tyy TyzTzx Tzy Tzz

24

35 1

where Txx, Txy,Tzz represent the second-order partial de-rivatives of the TOF image T(x) with x=(x,y,z) and theimage domain 3. Let the eigenvalues of H be denedby 1, 2 and 3 and the corresponding eigenvectors by e1, e2and e3. In this case, e1 represents the direction where thesecond derivative achieves its maximum (see Fig. 2), whichgives an estimation of the course of a vessel in 3D space. Thisdirection information will be included in the level-setapproach in the following. The fact that tubular structures

response of the vesselness lter stronger if the TOF intensity islow whereas the TOF intensity is weighted stronger in case oflow vesselness values. The resulting fuzzy image exhibits highvalues for all vessels, especially for small and malformedvessels, while low values are assigned to the brain tissue. Toobtain the initial vessel segmentation, which is required for thelevel-set segmentation process, global intensity thresholdingusing a threshold of init is applied to the fuzzy image.

Despite the improved display of vessels in the fuzzyparameter image, the optimal threshold selection remainschallenging. Lower thresholds lead to an improved smallvessel detection but also come along with an increasingamount of false-positives caused by noise. In contrast to thishigher thresholds decrease the number of false-positives butalso lead to a decreased detection of small vessels. The level-set procedure described in the following was especiallydesigned to overcome this trade-off and enable satisfyingsmall vessel delineations from the calculated fuzzy param-eter images while reducing false-positive segmentations.

tion o

265N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271should exhibit a 1 close to 0 and large negative values for 2and 3 is used to calculate the vesselness measure for eachvoxel. Practically, the Hessian matrix is calculated using thesecond derivatives of a Gaussian of different standarddeviations, which enables an enhancement of tubularstructures of different diameters. The vesselness imagesobtained for the different scales can be combined to a nalvesselness image using a voxel-wise maximum operator.

3.3. Initial cerebrovascular segmentation

To fuse the benets of the pre-processed TOF imagewith thecorresponding vesselness image, both datasets are combinedvoxel-wisely using fuzzy logic based on an analyticallydesigned rule base as described in [29]. The main idea of therule base used for fuzzy value calculation is to weight the

Fig. 2. Slice from a TOF image sequence and 3D visualiza3.4. Level-sets with vesselness-dependent anisotropicenergy weights

A variational level-set based segmentation approach inthe style of [30] was used in this work for the extraction ofthe nal cerebrovascular segmentation from 3D TOF datasets. Here, the surface of an object is expressed implicitly asthe zero level-set of the level-set function :withb0in the object. The optimal level-set was computed in thiswork by minimizing the energy functional

J := E F; + | ; + V ; 2where F(x) is the value calculated by fuzzy-based combina-tion of intensity and vesselness information. The functionalconsists of two terms representing the internal | and external

f the rst eigenvectors calculated by the vesselness lter.,

Here, the parameter c controls the principle smoothingapplied, while its actual inuence is weighted by the secondterm. Fig. 3 illustrates the basic idea of this locally adaptiveinternal energy weight. If is close to 0 or , the weight

converges against zero and no smoothing is applied, whichallows the level-set to evolve into small vessels. On the otherhand, if the vectors are orthogonal, is equal to c and thesegmentation is smoothed as usual.

Finally, the energy functional includes a vesselness forceterm:

V : = V H x cos2 x V x

pdx: 8

This energy term is used to actively drive the contouralong with the vessels. More precisely, the principleinuence of this term is weighted by the parameter V

which is locally adapted by the angle and the vesselnessvalue V(x) at the actual location. The weight of this term ishighest in case is close to 0 or and high vesselnessvalues such that a level-set evolution into structures with

266 N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271energy E as well as an additional term representing thevesselness force V.

The region-based external energy term, which drives thecontour towards dened image properties, is dened as:

E F; : = 1H x log pV F x + H x log pBG F x dx;

3

where H denotes the Heaviside function, which is used todescribe inside and outside of the object. Using thisformulation an integration of a priori knowledge aboutintensity distributions inside (pV) and outside (pBG) thevessels becomes possible. These intensity distributions canbe estimated by sampling the fuzzy values inside and outsidean initial cerebrovascular segmentation using a Parzen-Window strategy [31] with Gaussian kernels:

pj g = 1jGjj giGj1

2

p exp ggi 2

22

!4

where j {V", BG"} and G denotes the set of sampledfuzzy values.

More precisely, two thresholds were used in this work:one for initialization of the level-set segmentation (init) andone for estimating the fuzzy value probabilities (prob) withthe Parzen-Window technique. Higher values should bepreferred for init such that the initial segmentation containsmostly true vessels. In contrast to this, lower thresholds arerecommended for prob, which is supposed to enable animproved evolution into non-segmented vessels.

The internal energy is typically used to keep the objectboundaries smooth. However, small vessels are oftenrepresented by low intensities and edge values. In such acase, the internal energy is typically stronger than theexternal energy, which may lead to an insufcient evolutioninto small vessels, even in case of a low prob. One solutionto avoid this problem is to lower the weight for the internalenergy, which enables improved small vessel delineationsbut also results in more leakages into non-vascular tissues.Thus, a local adaption of the internal energy weight may leadto an improved level-set evolution into small vessels whilepreventing false-positive leakages into non-vascular tissues.

For this reason, the internal energy is dened in this work by:

| ;

: = jjH x jjdx: 5The function :[0,c] in this formulation is used to

locally adapt the weight of the internal energy depending onthe angle between e1, the rst eigenvector calculated bythe vesselness lter, and . It is dened by:

x : = c 1cos2 x 6with

cos x = e1 x 1jj x jj 7high vesselness values are favorable.The described energy functional was optimized in this

work using an iterative update scheme.

3.5. Implementation details, experiments and evaluation

Ten of the 11 available TOF datasets were independentlysegmented by two observers using volume growing andmanual correction in the orthogonal slices. These manualsegmentations were used for interobserver comparison as wellas for evaluation of the automatic segmentations. Theremaining TOF dataset was segmented by only one observerand used for parameter optimization but not for the evaluation.

The basic vesselness images used in this work for fuzzyimage generation and vessel direction estimation werecalculated by computing the Hessian operator over vesigma log-scales ([0.25,1.5]). All parameters required for

Fig. 3. Illustration of the vesselness-dependent anisotropic smoothingprocedure. No smoothing is applied in Case (a), normal smoothing is appliedin Case (b).,

the proposed level-set model were optimized using the TOFdataset that was only segmented by one observer. Thefollowing parameters have been used for segmentation of theremaining ten TOF datasets: init=92, prob=80,

V=5, c=0.5and 100 iterations for the level-set evolution.

Aside from the automatic segmentation using thedescribed fuzzy-based level-set segmentation (FLS) ap-proach with anisotropic energy weights, each preprocesseddataset was also segmented using four other automaticsegmentation approaches for comparison of the proposedmethod: the intensity-based ZBS approach [13], the moresophisticated intensity-based stochastic model segmentation(SMS) method [17], the fuzzy image segmentation (FIS)

distance from each centerline voxel to the closest vesselboundary was calculated using the distance transformdescribed by Danielsson [34]. Finally, the closest 3Dcenterline voxel was determined for each voxel part of thevascular segmentation and used for denition of the vesselradius at this location.

4. Results

Table 1 shows the results of the quantitative evaluation ofthe segmentation results using the Dice-coefcient. Here, itcan be seen that the two observers agree with a mean Dice-coefcient D of 0.791 (standard deviation =0.039).

essel s

SMS

0.7470.7010.8020.7710.6690.8170.6830.7610.5420.756

267N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271used for initialization of the presented level-set approach andthe level-set curve evolution segmentation (CES) approach[22]. The calculated fuzzy image and the correspondingfuzzy image segmentation were also used for initialization ofthe curve evolution segmentation as implemented in thevascular modeling toolkit [32].

The Dice coefcient:

D A;B = 2jABjjAj + jBj 9

was used for quantitative evaluation of the availablesegmentations, whereas A and B denote two segmentations.Dice-values close to 1 indicate a good consensus. The Dice-coefcient was used for inter-observer comparison as well asfor quantitative comparison of the automatic segmentationresults to the manual gold standard segmentations.

Two-sided t-tests were used to test for signicantdifferences between the quantitative Dice-values of the inter-observer comparison and those of the automatic segmentationevaluation. A P value less than .05 was assumed to indicatestatistical signicance. Statistical analysis was performedusing SPSS (version 18.0, SPSS, Chicago, IL, USA).

Furthermore, the number of voxels belonging to smallvessel structures with a radius of less than 0.5 mm wascalculated for all manual and automatic segmentations forevaluation purposes. For extraction of this parameter in avoxel-wise manor, the available segmentations were rstused to calculate the corresponding 3D centerlines using themethod proposed by Lee et al. [33]. In a second step, the

Table 1Quantitative results of the inter-observer comparison (IOC) and automatic v

Dataset IOC ZBS

1 0.732 0.4922 0.824 0.6043 0.808 0.5984 0.767 0.6625 0.748 0.4676 0.838 0.4737 0.785 0.7468 0.753 0.3789 0.827 0.48310 0.825 0.600No signicant differences were found regarding the Dice-coefcients of the automatic segmentation methods com-pared to the manual segmentations of the two observers(0.36bPb.87). Therefore, the mean Dice-coefcients Dstated in the following have been averaged over bothobservers and all ten datasets.

The worst automatic segmentation results were achievedby the ZBS method (D=0.55, =0.11). Compared to this, theintensity-based SMS approach lead to signicantly bettercerebrovascular segmentation results (D=0.725, =0.081,Pb.0001). However, on average all three remainingsegmentation methods using the fuzzy-image as input leadto better segmentation results regarding the Dice-coefcient.Comparing these three segmentation techniques, it becomesapparent that both level-set segmentation techniques lead toa quantitative improvement of the FIS (D=0.762, =0.038)used for initialization of both techniques. A comparison ofthe two level-set methods reveals that the CES algorithmperformed worse (D=0.783, =0.037) than the proposedFLS with anisotropic energy weights (D=0.806, =0.028).The FLS even lead to segmentation results, which areslightly better than the determined inter-observer agreement.Overall, the FLS performed signicantly better than anyother automatic segmentation approach tested in this study(ZBS: Pb.0001, SMS: P=.0004, FIS: P=.048, CES: P=.0004), while no signicant difference to the results of theinter-observer comparison was found (P=.305).

Overall, the quantitative results show that the FLS lead tothe best segmentation results in 9 of the 10 datasets

egmentations using the Dice-coefcient: ZBS, SMS, FIS, CES and FLS

FIS CES FLS

0.720 0.729 0.7630.816 0.835 0.8380.761 0.787 0.8050.790 0.792 0.8150.767 0.773 0.7850.711 0.794 0.7900.790 0.816 0.8320.756 0.764 0.7850.799 0.814 0.8520.711 0.722 0.790

268 N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271evaluated, while the SMS performs best in the remainingcase (Dataset 6).

These results can also be conrmed visually (see Fig. 4).Here, it becomes apparent that the ZBS is only capable ofextracting vessels with rather large diameters. Overall, theSMS approach segments more vessels than the ZBS but alsoleads to more false-positives caused by noise (see centralregion). In contrast to this, the three segmentation schemesusing the fuzzy-images as basis are able to segment manysmall vessels while no obvious noise artifacts are present.However, the result of the proposed FLS exhibits most vessel

Fig. 4. 3D visualizations from the axial and sagittal view using volume rendering orow), Z-buffer (second row, left) and stochastic model segmentation (second row rrow, right) and fuzzy-level-set segmentation (last row).structures, which is especially obvious in the top left regionin the axial view.

These visual results can be further conrmed by thesecond quantitative evaluation counting the number of voxelsassociated to small vessel structures with a radius less than0.5 mm (see Table 2). The results show that the twoobservers delineated an average of 90928 voxels per dataset,which were determined to belong to small vessel structures.Comparing the results of the automatic segmentations, itbecomes apparent that the ZBS lead to the worst small vesselextraction (=28482 voxels). The results reveal that the

f one selected TOF dataset masked with the two manual segmentations (rstight), fuzzy image (third row, left) and Curve-Evolution segmentation (third

methods as well as human observers. It was previously

ximal

MS

81284132046031773353967763830049467466150288269935

269N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271reported by Nowinski et al. [35] that the sensitivity for smallvessel extraction using their method is as low as 16.5% and itwas estimated that a manual renement would take 8 weeks.Therefore, perfect ground-truth segmentations are usually notavailable for typical clinical datasets. To the authors'knowledge, an evaluation of inter-observer agreement forcerebrovascular segmentations has not been performed to date.The inter-observer agreement evaluation based on ten TOFdatasets performed in this study revealed a mean Dice-coefcient of 0.791, which seems like a good result regardingthe fact that overlap measures are known to be not optimal forthin structures like vessels. Unfortunately, better suitedSMS extracted considerably more small vessels (=73213voxels) while the FIS (=82286 voxels) and FLS performedeven better (=86660 voxels). In contrast to this, a loss ofsmall vessels was found for the CES, which can be ascribedto a thickening of the vessel segmentation in some partswhile other thin vessel structures of the initial segmentationwere eliminated by the CES (=42184 voxels). Neverthe-less, the CES generally lead to a better adaption of thesegmentation to the vessel boundaries such that the Dicesimilarity measure is still improving compared to the initialfuzzy-image segmentation.

5. Discussion

The concurrent and exact delineation of small andmalformed vessels is a very challenging task for automatic

Table 2Number of voxels segmented belonging to small vessel structures with a ma

Dataset IOC ZBS S

1 106482 328582 116061 36825 13 90638 325174 99450 334165 113376 282586 87046 227657 61541 276818 69327 120239 73461 24989 110 91901 33497validationmetrics for this certain purpose are not available yet.Nevertheless, the evaluation revealed that the proposed

level-set segmentation technique leads to results comparableto those achieved by human observers. The presentedsegmentation method did not perform superior comparedto the other segmentation approaches tested in this work inonly one case. This one dataset exhibits a large apical locatedarteriovenous malformation and many large dilated drainingveins, which lead to a suboptimal intensity non-uniformitycorrection and also to an insufcient vessel enhancement.Therefore, the intensity-based stochastic model segmenta-tion, which does not rely on the vesselness image, performedbest in this case.The second quantitative evaluation counting the numberof voxels belonging to vessel structures with a maximalradius of 0.5 mm revealed that the integration of the locallyadaptive internal energy weight leads to an improved smallvessel delineation compared to the results of the curveevolution level-set method, which does not include thisproperty. The mean number of voxels belonging to suchsmall vessel structures is also comparable to that achieved bythe human observers. The mean number of voxelscorresponding to small vessel is even higher than that ofthe manual segmentations if excluding the problematicdataset 6 from this analysis. However, this quantitativemeasure is also not quite optimal for comparing cerebrovas-cular segmentations as a general underestimation of thevessels diameters would also lead to a misleadingly increaseof segmented voxels belonging to small vessels. Further-more, noise-dependent over-segmentations may also in-crease this number. This problem was for example observedfor the fuzzy image segmentation method, which generallyleads to smaller estimates of the vessel diameters comparedto the other methods. However, comparing these quantitativeresults with visual impression from 3D visualizationssuggest that this parameter still gives a good indication forthe ability of a method to segment small vessels.

Fuzzy techniques have been integrated into varioussegmentation methods for different problems, e.g., Refs.[3638]. The presented method is not the rst work, whichcombines fuzzy control techniques with level-set methods.For example, Ciofolo and Barillot [39] presented a fuzzycontrol driven level-set method for the segmentation of brain

diameter of 0.5 mm for the manual and automatic segmentations

FIS CES FLS

101022 46065 104703114445 52349 12216992085 46207 9207190595 43218 100586105975 52163 11270647430 39963 4451851939 41040 5688574430 34372 8322265835 28186 6643079106 38282 83306tissue. In this approach, a priori atlas knowledge wascombined with image-based intensity information. Rivest-Hnault and Cheriet [40] also proposed a brain segmenta-tion, combining a level-set method and fuzzy techniques. Intheir work, fuzzy C-means clustering was used forinitialization of a level-set approach. However, to theauthors' knowledge, a level-set segmentation method incombination with fuzzy logic has not been proposed yet forthe problem of cerebrovascular segmentation.

It has to be emphasized that the proposed method stillexhibits some drawbacks. Turbulent and fast blood ow mayresult in a local reduction of TOF intensities. This problemcan be observed in some of the large vessels and

reference gold-standard segmentations. To the authors'

270 N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271knowledge such an extensive evaluation with this numberof manual segmentations has not been performed yet.Therefore, the current database may serve as the basis forthe evaluation of other previously published methods as wellas new automatic cerebrovascular segmentation approaches.

In conclusion, the proposed method allows a signicantlybetter extraction of the cerebrovascular system compared tothe other state-of-the-art methods evaluated in this study,which is even comparable to human observer segmentations.The integration of locally adaptive energy weights togetherwith an additional vesselness force allows improved smallvessel delineations compared to level-set methods withoutthis additional properties.

References

[1] Thrift AG, Dewey HM, Macdonell RA, McNeil JJ, Donnan GA.Incidence of the major stroke subtypes: initial findings from the NorthEast Melbourne stroke incidence study (NEMESIS). Stroke 2001;32(8):17328.

[2] Wiebers DO, Whisnant JP, Huston III J, Meissner I, Brown Jr RD,Piepgras DG, et al. Unruptured intracranial aneurysms: natural history,clinical outcome, and risks of surgical and endovascular treatment.Lancet 2003;362(9378):10310.

[3] Fiehler J, Illies T, Piening M, Saring D, Forkert N, Regelsberger J,et al. Territorial and microvascular perfusion impairment in brainarteriovenous malformations. Am J Neuroradiol 2009;30(2):35661.

[4] Handels H, Ehrhardt J. Medical image computing for computer-supported diagnostics and therapy. Advances and perspectives.Methods Inf Med 2009;48(1):117.

[5] Sring D, Fiehler J, Ries T, Forkert ND. Rigid 3D-3D registration ofTOF MRA integrating vessel segmentation for quantification ofrecurrence volumes after coiling cerebral aneurysm. Neuroradiology2012;54(2):1716.

[6] Groden C, Laudan J, Gatchell S, Zeumer H. Three-dimensionalpulsatile flow simulation before and after endovascular coil emboli-zation of a terminal cerebral aneurysm. J Cereb Blood Flow Metab2001;21(12):146471.arteriovenous malformation structures. Due to the fact thatthe vesselness lter response in such vessels is also low, thecurrent method is not capable of segmenting themsuccessfully. However, this does only occur seldom and amanual correction of this does not require a long time.

Even though the proposed method was especially developedwith the goal to achieve improved malformed as well as smallvessel delineations, gaps within the nal segmentations can stillbe observed. Experienced human observers are capable ofdelineating the course of a vessel even if it is interrupted byparts of very low intensities, which is problematic for thepresented method. Therefore, depending on the requiredsegmentation quality, a post-processing may be necessary.

It has to be pointed out that so far only one TOF datasetwith a corresponding manual segmentation from oneobserver has been used for parameter optimization. There-fore, further improvements may be possible by moresophisticated parameter training methods.

However, most previous segmentation methods have beenevaluated using visual inspection or only a small number of[7] Shapiro LB, Tien RD, Golding SJ, Totterman SM. Preliminary results ofa modified surface rendering technique in the display of magneticresonance angiography images. Magn Reson Imaging 1994;12(3):4618.

[8] Ries T, Wegscheider K, Wulff A, Radelfahr K, Sring D, Forkert ND,et al. Quantification of recurrence volumes after endovasculartreatment of cerebral aneurysm as surrogate endpoint for treatmentstability. Neuroradiology 2011;53(8):5938.

[9] Brunenberg EJ, Vilanova A, Visser-Vandewalle V, Temel Y,Ackermans L, Platel B, et al. Automatic trajectory planning for deepbrain stimulation: a feasibility study. Med Image Comput ComputAssist Interv 2007;10(Pt 1):58492.

[10] Kirbas C, Quek F. A review of vessel extraction techniques andalgorithms. ACM Comput Surv 2004;36(2):81121.

[11] Al-Kwifi O, Emery DJ, Wilman AH. Vessel contrast at three Tesla intime-of-flight magnetic resonance angiography of the intracranial andcarotid arteries. Magn Reson Imaging 2002;20(2):1817.

[12] Davis WL, Warnock SH, Harnsberger HR, Parker DL, Chen CX.Intracranial MRA: single volume vs. multiple thin slab 3D time-of-flight acquisition. J Comput Assist Tomogr 1993;17(1):1521.

[13] Chapman BE, Stapelton JO, Parker DL. Intracranial vessel segmen-tation from time-of-flight MRA using pre-processing of the MIP Z-buffer: accuracy of the ZBS algorithm. Med Image Anal 2004;8(2):11326.

[14] Yi J, Ra JB. A locally adaptive region growing algorithm for vascularsegmentation. Int J Imaging Syst Technol 2003;13(4):20814.

[15] Dempster AP, Laird NM, Rubin DB. Maximum likelihood fromincomplete data via the EM algorithm. J R Stat Soc Ser B 1977;39(1):138.

[16] Wilson DL, Noble JA. An adaptive segmentation algorithm for time-of-flight MRA data. IEEE Trans Med Imaging 1999;18(10):93845.

[17] Hassouna MS, Farag AA, Hushek S, Moriarty T. Cerebrovascularsegmentation from TOF using stochastic models. Med Image Anal2006;10(1):218.

[18] Sato Y, Nakajima S, Shiraga N, Atsumi H, Yoshida S, Koller T, et al.Three-dimensional multi-scale line filter for segmentation andvisualization of curvilinear structures in medical images. Med ImageAnal 1998;2(2):14368.

[19] Frangi AF, NiessenWJ, Vincken KL, Viergever MA.Multiscale vesselenhancement filtering. Lect Notes Comput Sci 1998;1496:1307.

[20] Lorenz C, Carlsen IC, Buzug TM, Fassnacht C, Weese J. A multi-scaleline filter with automatic scale selection based on the Hessian matrixfor medical image segmentation. Lect Notes Comput Sci 1997;1252:15263.

[21] Lesage D, Angelini ED, Bloch I, Funka-Lea G. A review of 3D vessellumen segmentation techniques: models, features and extractionschemes. Med Image Anal 2009;13(6):81945.

[22] Lorigo LM, Faugeras OD, GrimsonWE, Keriven R, Kikinis R, NabaviA, et al. CURVES: curve evolution for vessel segmentation. MedImage Anal 2001;5(3):195206.

[23] Vasilevskiy A, Siddiqi K. Flux maximizing geometric flows. IEEETrans Pattern Anal Mach Intell 2002;24(12):156578.

[24] Gooya A, Liao H, Matsumiya K, Masamune K, Dohi T. Effectivestatistical edge integration using a flux maximizing scheme forvolumetric vascular segmentation in MRA. Inf Process Med Imag2007;20:8697.

[25] Suri JS, Liu K, Reden L, Laxminarayan S. A review on MR vascularimage processing: skeleton versus nonskeleton approaches: Part II.IEEE Trans Inf Technol Biomed 2002;6(4):33850.

[26] Kholmovski EG, Alexander AL, Parker DL. Correction of slabboundary artifact using histogram matching. J Magn Reson Imaging2002;15(5):6107.

[27] Sled JG, Zijdenbos AP, Evans AC. A nonparametric method forautomatic correction of intensity nonuniformity in MRI data. IEEETrans Med Imaging 1998;17(1):8797.

[28] Forkert ND, Saring D, Fiehler J, Illies T, Moller D, Handels H.Automatic brain segmentation in time-of-flight MRA images. MethodsInf Med 2009;48(5):399407.

[29] Forkert ND, Schmidt-Richberg A, Fiehler J, Illies T, Moller D,Handels H, et al. Fuzzy-based vascular structure enhancement in time-of-flight MRA images for improved segmentation. Methods Inf Med2011;50(1):7483.

[30] Schmidt-Richberg A, Handels H, Ehrhardt J. Integrated segmentationand non-linear registration for organ segmentation and motion fieldestimation in 4D CT data. Methods Inf Med 2009;48(4):3449.

[31] Parzen E. On estimation of a probability density function and mode.Ann Math Stat 1962;33:106576.

[32] Piccinelli M, Veneziani A, Steinman DA, Remuzzi A, Antiga L. Aframework for geometric analysis of vascular structures: application tocerebral aneurysms. IEEE Trans Med Imaging 2009;28(8):114155.

[33] Lee TC, Kashyap RL, Chu CN. Building skeleton models via 3-Dmedial surface/axis thinning algorithms. Graph Models Image Process1994;56(6):46278.

[34] Danielsson P. Euclidean Distance Mapping. Comput Graph ImageProcess 1980;14:22748.

[35] Nowinski WL, Volkau I, Marchenko Y, Thirunavuukarasuu A, NgTT, Runge VM. A 3D model of human cerebrovasculature derived

from 3T magnetic resonance angiography. Neuroinformatics 2009;7(1):2336.

[36] Lin GC, Wang CM, Wang WJ, Sun SY. Automated classification ofmultispectral MR images using unsupervised constrained energyminimization based on fuzzy logic. Magn Reson Imaging 2010;28(5):72138.

[37] Udupa JK, Wei L, Samarasekera S, Miki Y, van Buchem MA,Grossman RI. Multiple sclerosis lesion quantification using fuzzy-connectedness principles. IEEE Trans Med Imaging 1997;16(5):598609.

[38] Shen S, Szameitat AJ, Sterr A. An improved lesion detection approachbased on similarity measurement between fuzzy intensity segmentationand spatial probability maps. Magn Reson Imaging 2010;28(2):24554.

[39] Ciofolo C, Barillot C. Atlas-based segmentation of 3D cerebralstructures with competitive level sets and fuzzy control. Med ImageAnal 2009;13(3):45670.

[40] Rivest-Henault D, Cheriet M. Unsupervised MRI segmentation ofbrain tissues using a local linear model and level set. Magn ResonImaging 2011;29(2):24359.

271N.D. Forkert et al. / Magnetic Resonance Imaging 31 (2013) 262271

3D cerebrovascular segmentation combining fuzzy vessel enhancement and level-sets with anisotropic energy weights1. Introduction2. State-of-the-art3. Methods and materials3.1. Material and preprocessing3.2. Vesselness parameter extraction3.3. Initial cerebrovascular segmentation3.4. Level-sets with vesselness-dependent anisotropic energy weights3.5. Implementation details, experiments and evaluation

4. Results5. DiscussionReferences