Medical Image Analysis 15 (2011) 214–225

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Medical Image Analysis

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A magnetic resonance spectroscopy driven initialization scheme for activeshape model based prostate segmentation

Robert Toth a, Pallavi Tiwari a, Mark Rosen b, Galen Reed c, John Kurhanewicz c, Arjun Kalyanpur d,Sona Pungavkar e, Anant Madabhushi a,⇑a Rutgers, The State University of New Jersey, Department of Biomedical Engineering, Piscataway, NJ 08854, USAb University of Pennsylvania, Department of Radiology, Philadelphia, PA 19104, USAc University of California, San Francisco, CA, USAd Teleradiology Solutions, Bangalore 560 048, Indiae Dr. Balabhai Nanavati Hospital, Mumbai 400 056, India

a r t i c l e i n f o

Article history:Received 27 February 2009Received in revised form 20 September2010Accepted 28 September 2010Available online 28 October 2010

Keywords:Prostate segmentationActive shape models (ASMs)Magnetic resonance spectroscopy (MRS)In vivo MRISpectral clustering

1361-8415/$ - see front matter � 2010 Published bydoi:10.1016/j.media.2010.09.002

⇑ Corresponding author. Address: 599 Taylor RoadTel.: +1 732 445 4500x6213; fax: +1 732 445 3753.

E-mail address: anantm@rci.rutgers.edu (A. Madab

a b s t r a c t

Segmentation of the prostate boundary on clinical images is useful in a large number of applicationsincluding calculation of prostate volume pre- and post-treatment, to detect extra-capsular spread, andfor creating patient-specific anatomical models. Manual segmentation of the prostate boundary is, how-ever, time consuming and subject to inter- and intra-reader variability. T2-weighted (T2-w) magneticresonance (MR) structural imaging (MRI) and MR spectroscopy (MRS) have recently emerged as promis-ing modalities for detection of prostate cancer in vivo. MRS data consists of spectral signals measuringrelative metabolic concentrations, and the metavoxels near the prostate have distinct spectral signalsfrom metavoxels outside the prostate. Active Shape Models (ASM’s) have become very popular segmen-tation methods for biomedical imagery. However, ASMs require careful initialization and are extremelysensitive to model initialization. The primary contribution of this paper is a scheme to automatically ini-tialize an ASM for prostate segmentation on endorectal in vivo multi-protocol MRI via automated iden-tification of MR spectra that lie within the prostate. A replicated clustering scheme is employed todistinguish prostatic from extra-prostatic MR spectra in the midgland. The spatial locations of the pros-tate spectra so identified are used as the initial ROI for a 2D ASM. The midgland initializations are used todefine a ROI that is then scaled in 3D to cover the base and apex of the prostate. A multi-feature ASMemploying statistical texture features is then used to drive the edge detection instead of just image inten-sity information alone. Quantitative comparison with another recent ASM initialization method by Cosioshowed that our scheme resulted in a superior average segmentation performance on a total of 388 2DMRI sections obtained from 32 3D endorectal in vivo patient studies. Initialization of a 2D ASM via ourMRS-based clustering scheme resulted in an average overlap accuracy (true positive ratio) of 0.60, whilethe scheme of Cosio yielded a corresponding average accuracy of 0.56 over 388 2D MR image sections.During an ASM segmentation, using no initialization resulted in an overlap of 0.53, using the Cosio basedmethodology resulted in an overlap of 0.60, and using the MRS-based methodology resulted in an overlapof 0.67, with a paired Student’s t-test indicating statistical significance to a high degree for all results. Wealso show that the final ASM segmentation result is highly correlated (as high as 0.90) to the initializationscheme.

� 2010 Published by Elsevier B.V.

1. Introduction

Prostatic adenocarcinoma (CaP) is the second leading cause ofcancer related deaths among men in the United States, with anestimated 186,000 new cases in 2008 (Source: American CancerSociety). The current standard for detection of CaP is transrectal

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hushi).

ultrasound (TRUS) guided symmetrical needle biopsy, which hasa high false negative rate associated with it (Catalona, 1991).Recently, multi-modal Magnetic Resonance (MR) Imaging (MRI)comprising both structural T2-weighted (T2-w) MRI (Madabhushiet al., 2005; Zhu et al., 2003) and MR Spectroscopy (MRS) (Kurha-newicz et al., 1996, 2002; Kumar et al., 2008; Vilanova and Barcelo,2007; Hom et al., 2006; Tiwari et al., 2009; Zaider et al., 2000; Kimet al., 2003; Coakley et al., 2003) have emerged as promisingmodalities for early detection of CaP (Kumar et al., 2008; Vilanovaand Barcelo, 2007). MRS measures the relative concentrations of

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Fig. 1. (a) 2D section of T2-weighted MR image with the prostate boundary in green. Metavoxels within the prostate are shown in red, and metavoxels outside the prostateare shown in blue. The top of the choline and creatine region is indicated by the left-most purple circle in each of (b)–(d), and the top of the citrate peak is denoted by theright-most purple circle in each of (b)–(d). (h) The mean MRS spectra from the prostate spectra (red) and the extra-prostatic spectra (blue) are shown. (i) Each datapointrepresents an MRS spectra (prostate in red, extra-prostatic in blue), in which principal component analysis was used to reduce the 256-dimensional spectra to 3-dimensionalspectra for visualization purposes.

1 Source: www.clinicaltrials.gov.

R. Toth et al. / Medical Image Analysis 15 (2011) 214–225 215

different biochemicals and metabolites in the prostate, andchanges in relative concentrations of choline, creatine, and citrateare highly indicative of the presence of CaP. It is important to notethat MRS acquisition has a lower resolution than MRI acquisition,and thus each MRS metavoxel (containing a spectral signal) isapproximately 13 times the size of an MRI voxel (containing a sin-gle intensity value).

An example of a MR spectra signature associated with a T2-wMRI image is show in Fig. 1. The spectra corresponding to threemetavoxels within the prostate are shown in red, and three spectracorresponding to metavoxels outside the prostate are shown incyan. The average spectra of the extra-prostatic metavoxels isshown in Fig. 1h as a blue line, and the average spectra of the pros-tatic metavoxels is shown as a red line. It can be seen that the pros-tatic MRS spectra are greatly different from the extra-prostaticMRS spectra. Finally, in Fig. 1i a scatter plot of the MRS spectrafor a given slice is shown, in which the prostatic spectra are indi-cated by red dots and the extra-prostatic spectra are indicated byblue dots. To visualize the 256-dimensional spectra in threedimensions, principal component analysis was used. This scatterplot shows an example of how the prostatic and extra-prostaticspectra are distinct.

As of 2009, there are approximately 16 ongoing clinical trials inthe US aiming to demonstrate the role of MR in a diagnostic, clin-ical setting.1 Recent literature suggests that the integration of MRIand MRS could potentially improve sensitivity and specificity forCaP detection (Hom et al., 2006). In fact, when combined withMRI, using MRS data could yield prostate cancer detection specific-ity and sensitivity values as high as 90% and 88% respectively (Tes-ta et al., 2007). Recently, computer-aided diagnosis (CAD) schemeshave emerged for automated CaP detection from prostate T2-wMRI (Madabhushi et al., 2005; Chan et al., 2003) and MRS (Tiwariet al., 2007, 2008, 2009). In Tiwari et al. (2009), we showed thatspectral clustering of the MRS data could be used to distinguish be-tween prostatic and extra-prostatic voxels with accuracies as highas 98%. This paper improves upon the methodology presented inTiwari et al. (2009) to drive a segmentation scheme for the prostatecapsule on T2-w MRI.

With the recent advancements of prostate MR imaging, severalprostate segmentation schemes have been developed (Zhu et al.,2003; Chiu et al., 2004; Costa et al., 2007; Ladak et al., 2000; Huet al., 2003; Pathak et al., 2000; Gong et al., 2004; Cosio, 2008;

216 R. Toth et al. / Medical Image Analysis 15 (2011) 214–225

Gao et al., 2010). Segmentation of the prostate is useful for a num-ber of tasks, including calculating the prostate volume pre- andpost-treatment (Hoffelt et al., 2003; Kaminski et al., 2002), for cre-ating patient specific anatomical models (Nathan et al., 1996), andfor planning surgeries by helping to determine just how far outsidethe capsule they might need to go in order to capture any possibleextra-capsular spread of the tumor. Additionally, identifying theprostate capsule is clinically significant for determining whetherextra-capsular spread of CaP has occurred. Manual segmentationof the prostate, however, is not only laborious, but is also subjectto a high degree of inter-, and intra-observer variability (Warfieldet al., 2002, 2004). The aim of this work is to automatically identifythe spectra within the prostate in order to initialize a multi-featureactive shape model (ASM) for precise segmentation of the prostatecapsule.

2. Previous work and motivation

Previous work on automatic or semi-automatic prostate seg-mentation has been primarily for transrectal ultrasound (TRUS)images (Chiu et al., 2004; Ladak et al., 2000; Hu et al., 2003; Pathaket al., 2000; Gong et al., 2004; Cosio, 2008). Ladak et al. (2000) andHu et al. (2003) presented semi-automated schemes in which sev-eral points on the prostate contour are manually selected to initial-ize a deformable model for prostate segmentation. Manualintervention is then used to guide the segmentation. Pathak et al.(2000) similarly presented an algorithm to detect prostate edgeswhich were then used as a guide for manual delineation on pros-tate ultrasound images. In Gong et al. (2004), deformable ellipseswere used as the shape model to segment the prostate from TRUSimages. Recently, some researchers have attempted to developprostate segmentation methods from in vivo endorectal prostateMR imagery (Costa et al., 2007; Gong et al., 2004; Flores-Tapiaet al., 2008; Makni et al., 2008; Liu et al., 2009; Betrouni et al.,2008; Klein et al., 2008; Zwiggelaar et al., 2003; Gao et al., 2010).Klein et al. (2008) presented a segmentation algorithm in whichthe prostate boundary is obtained by averaging the boundary ofa set of training images which are best registered to a test image.Costa et al. (2007) presented a 3D method for segmenting the pros-tate and bladder simultaneously to account for inter-patient vari-ability in prostate appearance. In Zwiggelaar et al. (2003), polartransformations were used in conjunction with edge detectiontechniques such as non-maxima suppression to segment the pros-tate. A recent paper by Gao et al. (2010) uses a more advanced reg-istration task to first align the prostate shapes, and hence creates amore accurate statistical shape model. The appearance of the pros-tate is learned using both the distance to the center of the prostateas well as the voxels’ intensity information in a Bayesian frame-work, which showed very promising results on a number of stud-ies. One possible limitation with some of these prostatesegmentation schemes (Costa et al., 2007; Gong et al., 2004; Kleinet al., 2008; Zwiggelaar et al., 2003) is in their inability to deal withvariations in prostate size, shape, and across different patient stud-ies. Further, some of these methods are often susceptible to MR im-age intensity artifacts including bias field inhomogeneity andimage intensity non-standardness (Madabhushi et al., 2005,2006; Madabhushi and Udupa, 2006).

A popular segmentation method is the active shape model(ASM), a statistical scheme that uses a series of manually land-marked training images to generate a point distribution model(Cootes et al., 1995). Principal component analysis (PCA) is thenperformed on this point distribution model to generate a statisticalshape model (Cootes et al., 1995). A texture model is created neareach landmark point of each training image, and the Mahalanobisdistance between the test image and the training model is mini-

mized to identify the boundary of an object (Cootes et al., 1995;Cootes and Taylor, 1994, 2004). The Mahalanobis distance is a sta-tistical distance measurement and routinely used in conjunctionwith ASMs to estimate dissimilarity between training and test im-age intensities at user selected landmark points. After findingboundary points by minimizing the Mahalanobis distance, theshape model is deformed to best fit the boundary points, and theprocess is repeated until convergence.

While ASMs have been employed for a variety of different seg-mentation tasks related to biomedical imagery (Zhu et al., 2003,2005; Cootes et al., 1993; Smyth et al., 1997; Montagnat and Del-ingette, 1997; de Bruijne et al., 2003; Mitchell et al., 2002), theyhave a major shortcoming in that they tend to be very sensitiveto model initialization (Wang et al., 2002) and sometimes fail toconverge to the desired edge. Manual initialization can be tediousand subject to operator variability. Over the last few years, someresearchers have been exploring schemes for accurate and repro-ducible initialization of ASM’s (Cosio, 2008; Brejl et al., 2000;Cootes et al., 1994). Seghers et al. (2007) presented a segmentationscheme where the entire image is searched for landmarks. Theyhowever concede that accurately initialized regions of interest(ROIs) would greatly improve their algorithm’s efficiency and accu-racy. Gao et al. (2010) use a single user click to initialize their pros-tate segmentation scheme, and would undoubtedly benefit froman automatic method for localizing the prostate in MR imagery.van Ginneken et al. (2002) pointed out that without a priori spatialknowledge of the ROI, very computationally expensive searcheswould be required for ASM initialization, contributing to a slowoverall convergence time. Multi-resolution ASMs have also beenproposed, wherein the model searches for the ROI in the entirescene at progressively higher image resolutions (Cootes et al.,1994). Brejl et al. (2000) presented a shape-variant Hough trans-form to initialize an ASM, but the scheme can be very computa-tionally expensive. Cosio (2008) presented an ASM initializationmethod based on pixel classification which was applied to seg-menting TRUS prostate imagery. The method employs a Bayesianclassifier to discriminate between prostate and non-prostate pixelsin ultrasound imagery. A trained prostate shape is then fit to theedge of the prostate, identified via the Bayesian classifier. A GeneticAlgorithm (Mitechel, 1998) is employed to minimize the distancebetween the trained prostate shape and the edge of the prostate.

The second major shortcoming of ASM’s is their inability to con-verge to the desired object boundary in the case of weak imagegradients. The appearance model normally uses the intensities ofthe image to learn a statistical appearance model. However, therehave been several studies in which using statistical texture fea-tures and more advanced appearance models have shown to yieldimproved accuracy over just using image intensities (Zhu et al.,2005; Seghers et al., 2007; van Ginneken et al., 2002; Toth et al.,2008, 2009). In addition, since the ASM models the object borderusing a multi-dimensional Gaussian, a large number of trainingimages are required for accurate model generation (Ledoit andWolf, 2004).

In this paper we present a novel, fully automated ASM initiali-zation scheme for segmentation of the prostate on multi-protocolin vivo MR imagery by exploiting the MR spectral data. Note thatfor the studies considered in this work, the MRS data was acquiredas part of routine multi-protocol prostate MR imaging and not spe-cifically for the purposes of this project. While the resolution of MRand MRS data are different, the identification of prostate spectra byeliminating non-informative spectra outside the prostate providesan initial accurate ROI for the prostate ASM. We leverage the ideafirst introduced in Tiwari et al. (2008, 2009), in which spectral clus-tering was employed to distinguish between prostatic and extra-prostatic spectra. We achieve this through replicated k-meansclustering of the MR spectra in the midgland. Replicated k-means

Table 1List of notation and symbols used.

Symbol Description Symbol Description

C MRI scene bC MRS scene

R. Toth et al. / Medical Image Analysis 15 (2011) 214–225 217

clustering aims to overcome limitations associated with the tradi-tional k-means algorithm (sensitivity to choice of initial clustercenters). For each slice, the largest cluster (identified as the non-informative cluster) is eliminated. The mean shape of the prostateis then transformed to fit inside the remaining spectra, whichserves to provide the initial landmark points for a 2D ASM. In addi-tion, since the spectral data severely degrades away from the mid-gland of the prostate, we limit the clustering to the midgland. Theresulting initialized shape is then rescaled to account for thechange in size of the gland towards the base and the apex.

The ASM is performed in 2D because our limited number of 3Dstudies (32 in total) would prevent accurate statistical models frombeing generated in 3D. However, while we only had access to 32 3Dstudies, this constituted a total of 388 2D image slices. According toLedoit and Wolf (2004), the ratio of the number of Gaussian dimen-sions (in our case 5) to the number of samples (in our case either388 or 32) must be significantly less than 1. We therefore reasonedthat while 32 3D samples would be insufficient to create an accu-rate 3D appearance model, the 388 slices would suffice to generatean accurate 2D statistical appearance model. In addition, we haveopted to use multiple statistical texture features to better detectthe prostate border. Statistical texture features have been shownto improve ASM accuracy (Seghers et al., 2007; van Ginnekenet al., 2002; Toth et al., 2008, 2009). We calculate gray level statis-tics (such as mean and variance) of the neighborhood surroundingeach landmark on the prostate border and use these statistics togenerate our appearance model.

Note that as in traditional ASM schemes, the off-line trainingphase needs to only be done once. In this paper we compare theASM segmentation performance using our MRS-based initializa-tion scheme against corresponding results obtained via the initial-ization method recently presented by Cosio (2008). In Cosio (2008),only four patients were evaluated, with a total of 22 TRUS imageslices, resulting in a mean MAD value of 1.65 mm. Note that whilethe Cosio method was originally presented for US data, in thiswork, we evaluate it in the context of prostate MR imagery.2 Thepopular Cootes et al. (1995) ASM was employed with both initializa-tion schemes. Both schemes were rigorously evaluated via a 5-foldrandomized cross validation system, in which the manual delinea-tions of the prostate by an expert radiologist were used as the surro-gate for ground truth. We also rigorously evaluted the results of thereplicated k-means clusteirng algorithm with the results from twoother popular clustering schemes – hierarchical and mean-shiftclustering.

The rest of the paper is organized as follows. In Section 3 weprovide a brief overview of our MRS-based ASM initializationscheme. In Section 4 we present the details of our methodologyfor identifying the prostate ROI via spectral clustering of MRS data.Section 5 describes the methodology for our ASM segmentationsystem. Section 6 describes the experimental set up and evaluationmethods, in addition to our implementation of the ASM initializa-tion method by Cosio (2008). In Section 7 we present both thequalitative and quantitative results, followed by a brief discussionof our findings. Finally, concluding remarks and future directionsare presented in Section 8.

C Set of spatialcoordinates in C

bC Set of metavoxel

coordinates in bCc A spatial location in C c A metavoxel in bCf(c) Intensity value at c bFðcÞ Spectral content at c

S+ � C Prostate spatiallocations (from experts)

D Distribution from asum of Gaussians

SD � C Prostate spatiallocations

D 2 {MRS, Cos} Initialization methodemployed

X Set of landmark points X Mean training

3. System overview

3.1. Notation

We define a spectral scene bC ¼ ðbC ; bFÞ where bC is a 2D grid ofmetavoxels. Note that a metavoxel is a voxel at the lower spectral

(X � C) landmark points

X0D

Initialized landmarks XFinalD

Final segmentatedlandmarks

2 The extension of the scheme in Cosio (2008) to MR imagery was made possible bythe lead author (Cosio) of Cosio (2008).

resolution. For each spatial location c 2 bC , there is an associated256-dimensional valued spectral vector bFðcÞ ¼f jðcÞjj 2 f1; . . . ;256gh i

, where f jðcÞ represents the concentrationof different biochemicals (such as creatine, citrate, and choline).We define the associated T2-w MR intensity image sceneC ¼ ðC; f Þ, where C represents a set of spatial locations (voxels),f(c) is the MR image intensity function associated with everyc 2 C, and c = (xc, yc). The distance between any two adjacent meta-voxels, c; d 2 bC ; kc � dk2 (where k�k2 denotes the L2 norm) isroughly 13 times the distance between any two adjacent spatialvoxels c,d 2 C. We define X = {c1 . . .cN} � C as the set of N landmarksused to define a given prostate shape. The mean landmark coordi-nates across all training images is given as X ¼ f�c1; . . . ; �cNg. The j-neighborhood of pixels surrounding each c 2 C is denoted as N jðcÞ,where for 8d 2 N jðcÞ; kd� ck2 6 j; c R N jðcÞ. Finally, we denoteas D 2 {MRS, Cos} the MRS-based ASM presented in this work andthe Cosio method (Cosio, 2008) respectively. A table of commonlyused notation and symbols employed in this paper is shown inTable 1.

3.2. Data description

Our data comprises 32 multi-protocol clinical prostate MR data-sets including both MRI and MRS endorectal in vivo data. Thesewere collected during the American College of Radiology ImagingNetwork (ACRIN) multi-site trial (Mr imaging, xxxx) and fromthe University of California, San Fransisco. The MRS and MRI stud-ies were obtained on 1.5 Tesla MRI scanners, and the MRI studieswere axial T2-w images. The 32 3D studies comprised a total of388 2D slices, with a spatial XY resolution of 256 � 256 pixels, or140 � 140 mm. The ground truth for the prostate boundary onthe T2-w images was obtained by manual outlining of the prostateborder on each 2D section by a solitary expert radiologist, one withover 10 years of experience in prostate MR imagery.

3.3. Brief outline of ASM initialization schemes

Fig. 2 illustrates the modules and the pathways comprising ourautomated initialization system. First, replicated k-means cluster-ing is performed on the spectra in the midgland, identified as themiddle slices. The largest cluster obtained is identified as thenon-informative cluster corresponding to the extra-prostatic spec-tra and removed. The remaining spatial locations corresponding tothe resulting spectra are denoted by SMRS. The prostate shape is fitto the region corresponding to these informative spectra. The clus-tering results are then extended to the base and apex slices.

Fig. 2. Pathways and modules involving in the MRS-based ASM initialization scheme for prostate segmentation on multi-protocol in vivo MRI.

218 R. Toth et al. / Medical Image Analysis 15 (2011) 214–225

4. Methodology for MRS-based ASM initialization scheme

4.1. Clustering of spectra (calculation of SMRS)

The crux of the methodology is to determine a set of prostatevoxels (SMRS) based on a clustering of the spectroscopic data. Thisalgorithm is described in the form of a sequence of steps below.

1. For a given 2D MRS slice bC ¼ ðbC ; bFÞ, we first obtain the MRspectra

bF ðcÞ ¼ f ðcÞjj 2 f1; . . . ;256gh i

:

2. The metavoxels c 2 bC , are aggregated into k clustersVa � bC ; a 2 f1; . . . ; kg, by applying k-means clustering to allbFðcÞ; 8c 2 bC . k-means clustering aims to minimize the sum ofdistances to the clusters’ centroids, for all clusters. Formally, ititeratively estimates

argminV1 ;...;Vk

Xk

a¼1

Xc2Va

bF ðcÞ � 1jVaj

Xc2Va

bF ðcÞ����������

2

: ð1Þ

3. Since the k-means algorithm is dependent on the starting loca-tions of the centroids (i.e. which Va each c initially belongs to),the result is sometimes a local minima instead of a global min-ima. To overcome this limitation, the clustering was repeated25 times with random initial locations of the centroids, andthe resulting clustering which yields the minimum value fromEq. (1) is selected. Repeating the clustering more than 25 timesdid not significantly change the results.

4. The dominant cluster is identified as being extra-prostatic (non-informative), and the metavoxels in this cluster are removed.This is akin to the approach used in Tiwari et al. (2009), inwhich it was found that the dominant cluster is the non-infor-mative cluster. The set of remaining metavoxels is then definedas,

3 For interpretation of color in ‘Figs. 1–10’, the reader is referred to the web versionf this article.

bSMRS ¼ cjc 2 Va; a – argmaxa

jVaj� �

: ð2Þ

The set of MRI voxels corresponding to metavoxels in bSMRS are thenidenfitied. For our data, we found that k = 3 clusters yielded the bestresults. Fig. 3a shows the 3 clusters V1 � V3 as colored metavoxels.The largest cluster is shown in green, and would be eliminated,yielding bSMRS as the cluster comprising blue and red metavoxels.While bSMRS denotes the set of metavoxels, the voxels associatedwith bSMRS are denoted as SMRS and are shown in red3 in Fig. 3b.

4.2. Fitting the prostate shape (calculation of X0)

Cosio (2008) employed the Genetic Algorithm to optimize thepose parameters of the prostate shape to fit a given binary mask.We found that using the objective function described belowyielded an accurate initialization for a given set of prostate pixelsSMRS. The mean shape X constitutes a polygon, and the set of voxelsinside this polygon is denoted as SX. More generally, for a given setof affine transformations T, which represent scaling rotation andtranslation, the set of voxels within that polygon are denoted asSTðXÞ. The objective function we use aims to maximize the true po-sitive ratio, so that the initialization is given as

X0D ¼ TðXÞ; where T ¼ argmax

T

SD \ STðXÞ

SD [ STðXÞ

" #; ð3Þ

where D 2 {MRS,Cos}. The optimization of Eq. (3) is performed viathe Genetic Algorithm (Mitechel, 1998). The entire initializationprocess for D = MRS is shown in Fig. 3.

4.3. Estimation of X0MRS in the base and apex

The MRS spectra lose their fidelity towards the base and theapex of the prostate. This is demonstrated in Fig. 4a, in which thethree resulting clusters (V1, . . . , V3) are shown via red, green, andblue metavoxels respectively. It was found that the spectra in themidgland of the prostate yielded accurate estimations of SMRS. Forthis reason, we perform our clustering algorithm in the midgland

o

Fig. 3. (a) MRS metavoxels bC (shown as colored boxes) overlaid onto the T2-w image C where each color represents a different class resulting from the replicated k-meansclustering scheme. The voxels associated with the informative metavoxels (SMRS) are shown as a red overlay in (b), with the resulting shape initialization X0

MRS

� �shown as a

green line in (b) and (c).

R. Toth et al. / Medical Image Analysis 15 (2011) 214–225 219

of the prostate, the results of which are then extended to the baseand apex. Note that since the 2D T2-w MRI slices tend to cover theprostate from base to apex, we have found that in our studies, themiddle slice typically corresponded to the midgland. Hence weused the middle slice as our anchor midgland slice. We observedthat the area of the prostate decreases to 80% its size in the base,and 30% its size in the apex. Fig. 4b demonstrates this taperingoff of the gland in the base and apex. Fig. 4b is a histogram showingthe size of the prostate relative to the central slice for all groundtruth segmentations. Hence, to calculate X0

MRS for the remainingslices, X0

MRS is first calculated for slice 5, and is linearly scaled downto 80% its size for the first third of the 2D sections, and to 30% itssize for the latter third of the gland.

5. Multi-feature ASM based segmentation

5.1. Basic shape model

Following model initialization X0D

� �, an ASM search (Cootes

et al., 1995) is performed to segment the prostate from a new im-age. An ASM is defined by the equation

X ¼ Xþ P � b; ð4Þ

where X represents the mean shape, P is a matrix of the first fewprincipal components (Eigenvectors) of the shape, created usingPrincipal Component Analysis (PCA), and b is a vector defining theshape, which can range from between �3 and +3 standard devia-tions from the mean shape. Therefore, X is defined by the variableb. Given a set of landmark points Xi

D; ðD 2 fMRS; CosgÞ for iterationi, the goal is to find landmark points bXi closest to the object border.The shape is then updated using Eq. (4) where

Fig. 4. (a) Example of a clustering result in the base of the prostate, in which thethree colors represent Va, a 2 {1, 2, 3}. The results demonstrate the degradation ofquality of MR spectra in the prostate near the base, a phenomenon which alsooccurs near the apex. (b) A 2D histogram of the relative size of the prostate as afunction of the slice index from base to apex reveals that the prostate is largest inthe center and tapers off towards the extrema.

b ¼ PT � bXi � Xi� �

; ð5Þ

where each element of b can only be within ±3 standard deviationsof the mean shape. The final ASM segmentation is denoted as XFinal

D .The training of the ASM to determine X and P is performed by man-ual delineation of the prostate boundary followed by manual align-ment of 100 equally spaced landmark points along this boundary(N = 100). It should be noted that this needs to only be performedonce in an off-line setting, and once an ASM is trained it can beused for repeated segmentations without significant manualintervention.

5.2. Basic appearance model

We define the set of intensity values near c as gðcÞ ¼ff ðdÞjd 2 N jðcÞg. Over all training images, the mean intensity val-ues for a given landmark point cn, n 2 {1, . . . , N}, are denoted as gn,with the covariance matrix denoted as Rn. We define the set of pix-els near cn 2 Xi along the normal to the shape as cN ðcnÞ. The stan-dard cost function for a given pixel to the training set is theMahalanobis distance. Therefore, bXi is defined as

bXi ¼ fdnjn 2 f1; . . . Ngg; where dn

¼ argmine2bN ðcnÞ

ðgðeÞ � �gnÞT � R�1n � ðgðeÞ � �gnÞ

h i: ð6Þ

5.3. Multi-feature appearance model

Our previous work and that of others in employing multiple im-age features to drive the ASM model has shown that multi-featureASM’s are more likely to latch on to weak edges and boundariescompared to the traditional intensity driven ASM (Seghers et al.,2007; van Ginneken et al., 2002; Toth et al., 2008, 2009). In thiswork, in addition to using image intensity values g(c), we also ex-tracted the mean, standard deviation, range, skewness, and kurto-sis of intensity values with local neighborhoods associated withevery c 2 C. If E represents the expected value of an image feature,then the feature vector (G(c)) associated with each c 2 C is definedas,

GðcÞ ¼

8><>:�gðcÞ; E ðgðcÞ � �gðcÞÞ2h i1=2

; max gðcÞ

�min gðcÞ;E ðgðcÞ � �gðcÞÞ3h i

E ðgðcÞ � �gðcÞÞ2h i3=2 ;

E ðgðcÞ � �gðcÞÞ4h i

E ðgðcÞ � �gðcÞÞ2h i2

9>=>;: ð7Þ

Our cost function in Eq. (6) thus uses G instead of g.

Table 2Performance measures used.

Measure Formula

Overlap jSXD \ SXE j=jSXD [ SXE jSensitivity jSXD \ SXE j=jSXE jSpecificity jC � SXD [ SXE j=jC � SXE jPositive predictive value (PPV) jSXD \ SXE j=jSXD jMean absolute distance (MAD) 1

N

PNn¼1 kcn � dnk; cn 2 XD; dn 2 XEð Þ

Hasudorff distance (HAD) maxn kcn � dnk; cn 2 XD; dn 2 XEð Þ

Table 3Experimental set ups for calculation of SMRS.

Experiment Description

E1 Hierarchical clusteringE2 Mean-shift clusteringE3 Replicated k-means clustering

220 R. Toth et al. / Medical Image Analysis 15 (2011) 214–225

6. Experiments and performance measures

6.1. Performance measures

For each image, a single expert radiologist segmented the pros-tate region, yielding ground truth landmarks XE. For a given shapeX, the set of pixels contained within the shape is denoted as SX. Weemploy the performance measures shown in Table 2.

Performance measures 1–4 are area based performancemeasures, in which a higher value indicates a more accurate seg-mentation, while performance measures 5 and 6 are edge basedperformance measures which evaluate proximity of the ASM ex-tracted boundary compared to the manually delineated boundary.A lower value in measures 5 and 6 reflects a more accuratesegmentation.

6.2. Comparison of clustering algorithms

We compared the efficacy of the replicated k-means clusteringscheme with hierarchical clustering (Hastie et al., 2009) andmean-shift clustering (Comaniciu and Meer, 2002). Hierarchicalclustering generates a dendrogram based off the Euclidean distancebetween spectra, and hierarchically combines spectra which have alow distance between them into a single cluster. The process is re-peated until a pre-specified number of clusters remain (Hastie et al.,2009). Mean-shift clustering attempts to iteratively learn the den-sity of the feature space and yields a clustering result based of themanifold instead of a pre-specified number of clusters (Comaniciuand Meer, 2002). Each methodology was used to calculate SMRS inthe midgland, and these estimations of X0

MRS in the midgland werecompared to the ground truth segmentations XE for all studies.Table 3 summarizes the clustering experiments performed.

6.3. Comparison of initialization methods

6.3.1. Cosio based initialization (calculation of X0Cos)

Cosio developed an automated ASM initialization scheme (Co-sio, 2008) to segment prostate ultrasound images. We extendedthe Cosio (2008) scheme to MR imagery in order to comparethis scheme against our MRS-based initialization method.4 Thecrux of the methodology is to classify the pixels in the imagesbased on a Bayesian classification scheme using a mixture of Gaus-sians to represent the distribution of prostate and non-prostatepixels.

1. A set of 10 images was expertly segmented, resulting in a set ofvoxels within the prostate, denoted as S+ # C and a set of pixelsoutside the prostate, denoted as S- = C � S+.

2. Each voxel c = (xc, yc) had a three dimensional vector con-structed from its x and y coordinates and its intensity valueFxy(c) = [xc, yc, f(c)].

4 Extension of the scheme in Cosio (2008) to MR imagery was performed with theassistance of the first author in Cosio (2008), Fernando Cosio

3. The distribution for prostate pixels (Dþ) and non-prostate pixels(D�) based on the spatial-intensity vector Fxy(c) = [xc, yc, f(c)]was then estimated by using the Expectation–Maximizationfunction to generate a mixture of 10 Gaussians. The distributionis given as D �

P10b¼1Nðlb;r2

bÞ, where N is a 3-D normal distribu-tion such that lb 2 R3 and r2

b 2 R3�3.4. For each of the images considered, Bayes’ law (Duda et al., 2001)

was then used to determine the posterior conditional probabil-ities of a given voxel c 2 C belonging to the prostate class(Pðwþjc;DþÞ) and the non-prostate class (Pðw�jc;D�Þ), wherew denotes the class. The set of pixels SCos represents those pixelsin which the likelihood of belonging to the prostate class wasgreater than the likelihood of being part of the non-prostateclass, so that

SCos ¼ cj lnðPðwþjc; DþÞÞ þ lnðPðwþÞÞ > lnðPðw�jc;D�ÞÞfþ lnðPðw�ÞÞg: ð8Þ

The methodology presented in Section 4.2 was then used to calcu-late X0

Cos.

6.3.2. Comparing ASM segmentations using different initializationschemes

To test the ASM, each initialization method (D 2 {MRS, Cos}) re-sulted in an initialization X0

D for each image, and a final ASM seg-mentation XFinal

D . To evaluate ASM performance in the absence ofany automated initialization, we placed the mean prostate shapein the center of the image yielding a third initialization, D = Mid.A 5-fold cross validation was performed as follows. The 32 3Dstudies were randomly split into five groups of about six studies.For each group of studies, the remaining 26 were used for trainingthe ASM, and the segmentation was performed for each slice ineach of the six studies. This was repeated for each group resultingin segmentations for all 388 images. The segmentations were com-pared to the ground truth XE in terms of the six performance mea-sures in Table 2. A paired Student’s t-test was then carried out foreach of the performance measures to determine the level of statis-tical significance. The t-test was performed over all 388 images (or,stated differently, with 387 degrees of freedom). Finally, the corre-lation (R2 value) between each final segmentation result

XFinalD ; D 2 fMRS;Cos;Midg

� �and the initialization result was cal-

culated for each performance measure, to determine the correla-tion between the final segmentation with respect to theinitialization. A high R2 value would indicate that the model is verysensitive to the initialization.

6.4. Comparison of multi-resolution ASM’s

For each of the initialization methods (D 2 {MRS, Cos, Mid}), amulti-resolution ASM was also performed. A Gaussian image pyra-mid was constructed with 4 image resolution levels (ranging from32 � 32 pixels to 256 � 256 pixels), and at each image level a dis-tinct ASM model is constructed. The result from the final pyramid(the full-resolution image) was used as XFinal

D , and 5-fold cross val-idation and statistical significance tests were performed as de-scribed above. Finally, the correlation (R2 value) was alsocalculated, the hypothesis being that if the multi-resolution

Table 4Experimental set ups for the ASM experiments performed.

Experiment X D Description

E4 X0D

MRS MRS initialization

E5 XFinalD

ASM

E6 XFinalD

Multi-resolution ASM

E7 X0D

Cos Cosio initialization

E8 XFinalD

ASM

E9 XFinalD

Multi-resolution ASM

E10 X0D

Mid Initialized by placing X in the middle of CE11 XFinal

DASM

E12 XFinalD

Multi-resolution ASM

Fig. 5. Shown above are the qualitative results from E1 � E3 in columns 1, 2, and 3 reassignment, and the white shape represents X0. For reference, column 4 shows the grou

Fig. 6. SD is shown in red for two different studies (1 study per row), for D = Cos in thinitialization X0

D is shown in white, and the ground truth segmentation XE is shown in c

R. Toth et al. / Medical Image Analysis 15 (2011) 214–225 221

framework was able to overcome poor or lack of initialization, thenthe R2 values would be lower for the multi-resolution experiments.In essence, we were aiming to explore whether a multi-resolutionapproach would make redundant the need for initialization.The entire set of ASM experiments performed are summarized inTable 4.

7. Results and discussion

7.1. Comparison of clustering algorithms (E1 � E3)

Fig. 5 shows some qualitative results from E1 � E3 for a mid-gland slice, which was used to calculate SMRS. In all the images,

spectively for two different studies. The color of each metavoxel reflects its classnd truth XE in white.

e first column ((a) and (d)), and D = MRS in the second column ((b) and (e)). Theolumn 3 ((c) and (f)) for reference.

222 R. Toth et al. / Medical Image Analysis 15 (2011) 214–225

the red cluster indicates the largest cluster which is removed, sothat bSMRS corresponds to all metavoxels that are not red. Whileall the clustering methodologies found a set of metavoxels within

Fig. 7. Quantitative results for E1 � E3 are shown for the six performance measures over 3yellow represents E3. The standard deviations over 32 studies are shown with black bar

(a)

(b)Fig. 8. (a) Results from the initialization schemes comparing X0

D to X0E for each slice, in wh

significance results are shown in Table 5. (b) Results from the ASM’s comparing XfinalD to X

yellow. The statistical significance results are shown in Table 6. Standard deviations ove

the prostate, it is obvious that only the replicated k-means cluster-ing algorithm was able to properly identify most of the prostatemetavoxels. The superior performance of replicated clustering over

2 midgland slices, in which the blue bar represents E1, the red represents E2, and thes.

ich E4 is shown in blue, E7 is shown in red, and E10 is shown in yellow. The statisticalE for each slice, in which E5 is shown in blue, E8 is shown in red, and E11 is shown inr 388 slices are shown as black bars in both (a) and (b).

Table 5Statistical significance results (in terms of p values) between all initialization schemes (D 2 {MRS, Cos, Mid}) are shown below, in which a paired Student’s t-test was used tocompare two different X0

D (D 2 {MRS, Cos, Mid}) results for all six performance measures, over 388 slices. The accompanying data is shown in Fig. 8a.

Comparison Sensitivity Specificity Overlap PPV Hausdorff MAD

E4; E7 4.8 � 10�6 5.8 � 10�4 1.6 � 10�4 1.9 � 10�12 1.3 � 10�4 3.4 � 10�6

E4; E10 1.3 � 10�75 0 0 2.5 � 10�8 5.9 � 10�1 4.7 � 10�1

E7; E10 6.9 � 10�114 3.8 � 10�96 8.4 � 10�14 1.7 � 10�55 7.5 � 10�10 1.7 � 10�8

Table 6Statistical significance results (in terms of p values) between all non-multi-resolution ASM schemes below, in which a paired Student’s t-test was used to compare two differentXfinal

D results for all six performance measures, over 388 slices. The accompanying data is shown in Fig. 8b.

Comparison Sensitivity Specificity Overlap PPV Hausdorff MAD

E5; E8 2.2 � 10�2 8.8 � 10�8 9.0 � 10�6 7.8 � 10�16 2.1 � 10�5 4.5 � 10�8

E5; E11 4.6 � 10�63 1.2 � 10�4 0 1.8 � 10�2 1.6 � 10�8 0E8; E11 1.3 � 10�90 0 0 3.3 � 10�15 4.6 � 10�1 4.3 � 10�4

Table 7Statistical significance results (in terms of p values) comparing each Xfinal

D result to the corresponding multi-resolution XfinalD segmentation result for all six performance measures

over 388 slices. The non-multi-resolution experiments (E5 ; E8; E11) are shown in Fig. 8b and the accompanying multi-resolution experiments (E6 ; E9; E12) are shown in Fig. 9.

Comparison Sensitivity Specificity Overlap PPV Hausdorff MAD

E5; E6 2.3 � 10�1 9.0 � 10�7 2.3 � 10�3 2.2 � 10�2 7.4 � 10�6 3.5 � 10�4

E8; E9 1.5 � 10�12 8.7 � 10�1 0 1.8 � 10�3 8.3 � 10�4 5.8 � 10�9

E11; E12 1.0 � 10�6 7.6 � 10�13 3.3 � 10�1 1.2 � 10�10 1.9 � 10�1 4.1 � 10�1

Table 8The correlation (R2 value) between Xfinal

D and X0D is shown for each performance

measure to determine how much of an effect the initialization had on the final ASMsegmentation result.

Performance measure ASM Multi-resolution

E5 E8 E11 E6 E9 E12

Sensitivity .81 .71 .80 .65 .80 .84Specificity .91 .78 .84 .71 .84 .87Overlap .76 .89 .87 .59 .91 .90PPV .84 .90 .91 .70 .94 .94Hausdorff .88 .86 .82 .68 .85 .84MAD .86 .88 .86 .63 .91 .89

R. Toth et al. / Medical Image Analysis 15 (2011) 214–225 223

the two other algorithms might have to do with the fact that wewere unable to identify the optimal parameter values for themean-shift and hierarchical clustering schemes. Although weexperimented with several different parameter settings, the hierar-chical and mean-shift clustering algorithms ended up clusteringmost of the background metavoxels with the prostate metavoxels.The replicated k-means clustering, however was able to groupmost of the prostate metavoxels together for a value of k = 3. Notethat k = 3 appeared to work better than k = 2, owing perhaps tosome heterogeneity of tissues (cancerous and benign areas) withinthe prostate.

For each of the 32 studies, X0 was calculated for the midglandslice, and compared to XE. The quantitative results for a single mid-land slice are shown in Fig. 7 over all 32 studies. The most impor-tant thing to note is the extremely high sensitivity of the replicatedk-means compared to the other clustering algorithms, suggestingthat the mean-shift and hierarchical clustering tended to under-segment the prostate voxels. In addition, the overlap measure ofthe replicated k-means, which takes into account both false posi-tive and false negative pixels, was higher than any of the otheralgorithms, suggesting a more accurate overall initialization.

7.2. Comparison of initialization schemes (E4; E5; E7; E8; E10; E11)

Fig. 6 shows SD in red with X0D in white for D 2 {Cos, MRS} for

two different studies, with XE shown in the third column ((c) and(f)) for reference. It can be seen that both perform quite well inlocating the prostate pixels. This was further tested quantatitivelyover all 388 slices, results of which are shown in Fig. 8. Fig. 8 illus-trates that in many cases the MRS initialization yielded superior re-sults. It should be noted that the specificity was extremely high inmost cases due to the large size of the image compared to the sizeof the target object (jCj =�jSXj). Our model yielded an averageoverlap value of 0.66, while the Cosio method had a value of0.62. Comparison of our segmentation system with other MR pros-tate segmentation schemes show that our system performs compa-rably to other related techniques. Zhu et al. (2003) have overlapcoefficients ranging from about 0.15 to about 0.85, while our mean

overlap is 0.66. Costa et al. (2007) used prior knowledge from theMRI scan to localize an ROI containing the prostate, resulting in amean sensitivity and PPV of 0.75 and 0.80 respectively for the pros-tate. Our model achieved mean sensitivity and PPV values of 0.81and 0.79 respectively. Comparing the initialization schemes(X0

D; D 2 fMRS;Cos;Midg) revealed that all results were statisticallysignificant to a high degree, except for the edge based performancemeasures between D = MRS and D = Mid, shown in Table 5. Whencomparing the actual ASM segmentations, all results were statisti-cally significant except for the Hausdorff distance between D = Cosand D = Mid, shown in Table 6. In Table 8, it can be seen that theASM is extremely sensitive to the initialization, with the lowestR2 value being 0.71.

7.3. Comparison of multi-resolution ASM’s (E6; E9; E12)

Fig. 9 shows the result from the multi-resolution ASM’s over388 images using a 5-fold cross validation scheme. These resultswere then compared to the values reported in Fig. 8b via the useof a statistical significance test, shown in Table 7. Apart from afew scenarios (sensitivity of D = MRS, specificity of D = Cos, andoverlap and edge performance measures of D = Mid), the multi-res-olution approach generally improved the ASM segmentation re-sults significantly. Finally, the R2 values from the multi-resolution experiments were calculated, and they were all extre-

Fig. 9. Results from the multi-resolution ASM experiments XfinalD , in which E6 (the multi-resolution ASM using the MRS initialization) is shown in blue, E9 (the multi-resolution

ASM using the Cosio initialization) is shown in red, and E12 (the multi-resolution ASM using the Midgland initialization) is shown in yellow. The results from the tests ofsignificance, in which each multi-resolution test (shown above) was compared to each non-multi-resolution test (shown in Fig. 8b) are given in Table 7. Standard deviationsover all 388 slices are shown as black bars.

Table 9Efficiency table noting the mean time, in seconds for a single image. For MRS, the timenoted is the total time calculating SMRS for a single midgland slice, using k-meansclustering replicated 25 times. For Cosio, the time is the calculation of SCos for a singlemidgland slice, given that the distributions have already been calculated. Thecomputer system had a 2.8 GHz processor and 32 GB of RAM, running MATLAB 2009bwith the Ubuntu Linux operating system.

MRS Cosio ASM

Mean time (s) 1.3 0.08 0.14

224 R. Toth et al. / Medical Image Analysis 15 (2011) 214–225

mely high (with the lowest being 0.59). It is interesting that in theD – MRS experiments, the R2 values actually increased with themulti-resolution framework, and additional studies will have tobe carried out to investigate this further. Overall, while a multi-res-olution framework is useful for accurate segmentations, the factthat the multi-resolution results were still correlated to the initial-ization suggests that a multi-resolution framework by itself is notsufficient for addressing the lack of accurate model initialization.

In addition, Table 9 shows that while the Cosio scheme was veryefficient, the MRS initialization scheme only required approxi-mately 1 second to accurately initialize the prostate ROI (using a2.8 GHz, 32 GB RAM system with MATLAB 2009b and the UbuntuLinux operating system). In a clinical setting, the need for rapid ini-tialization of a segmentation scheme is motivated by the need forreal time biopsy guidance, real time registration of ultrasound withMRI, and radiation therapy applications, all of which use segmen-tation of the prostate gland as a first step (Barqawi et al., 2007;Chen et al., 2010; Zhou et al., 2010).

8. Concluding remarks

In this paper, we have presented a fully automated and accurateASM initialization scheme for prostate segmentation from multi-protocol in vivo MRI/MRS data. With the increasing use of MRimaging of the prostate, several institutions are beginning to ac-quire multi-modal MR prostate data, including MR spectroscopy(Kurhanewicz et al., 1996; Kumar et al., 2008; Vilanova and Bar-celo, 2007; Hom et al., 2006; Tiwari et al., 2009). The primary novelcontribution of our work is in leveraging information from oneimaging protocol (spectroscopy) to drive the segmentation of theprostate on a different protocol (T2-weighted structural MRI). Tothe best of our knowledge this is the first instance of multi-modalinformation being used in this fashion for ASM initialization. Ourmethod uses replicated k-means clustering to cluster the MRSspectra in the midgland. For the studies we considered, the central

slice was ssumed to be the midgland. This may not always be thecase, and future work will entail developing an automated, moreintelligent scheme for selecting the midgland slice. We then elim-inate the background spectra, fit the shape to the remaining spec-tra, and extend our initializations to the base and apex of theprostate. We employed a multi-feature ASM to perform the seg-mentation, wherein multiple statistical texture features were usedto complement image intensities. We compared our MRS initializa-tion method against a recent image feature driven ASM inititializa-tion method by Cosio (2008) and found that our scheme resulted insignificantly better segmentations. Future work will entail evaluat-ing our scheme on a larger cohort of data.

Acknowledgments

This work was made possible via grants from the WallaceH. Coulter Foundation, New Jersey Commission on CancerResearch, National Cancer Institute (Grant Nos. R01CA136535-01,ARRA-NCl-3 R21CA127186, R21CA127186, R03CA128081-01,R01CA140772-01A1, and R03CA143991-01), the Cancer Instituteof New Jersey, and the Life Science Commercialization Award fromRutgers University. The authors would like to thank Fernando Cosioin his assistance implementing his initialization methodology.Finally, the authors would like to acknowledge the ACRIN trial forproviding the MRI/MRS data.

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