# A Hybrid Geometric–Statistical Deformable Model for Automated 3-D Segmentation in Brain MRI

**ABSTRACT** We present a novel 3-D deformable model-based approach for accurate, robust, and automated tissue segmentation of brain MRI data of single as well as multiple magnetic resonance sequences. The main contribution of this study is that we employ an edge-based geodesic active contour for the segmentation task by integrating both image edge geometry and voxel statistical homogeneity into a novel hybrid geometric-statistical feature to regularize contour convergence and extract complex anatomical structures. We validate the accuracy of the segmentation results on simulated brain MRI scans of both single T1-weighted and multiple T1/T2/PD-weighted sequences. We also demonstrate the robustness of the proposed method when applied to clinical brain MRI scans. When compared to a current state-of-the-art region-based level-set segmentation formulation, our white matter and gray matter segmentation resulted in significantly higher accuracy levels with a mean improvement in Dice similarity indexes of 8.55% (p<0.0001) and 10.18% (p<0.0001), respectively.

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**ABSTRACT:**The survey outlines and compares popular computational techniques for quantitative description of shapes of major structural parts of the human brain, including medial axis and skeletal analysis, geodesic distances, Procrustes analysis, deformable models, spherical harmonics, and deformation morphometry, as well as other less widely used techniques. Their advantages, drawbacks, and emerging trends, as well as results of applications, in particular, for computer-aided diagnostics, are discussed.IEEE Journal of Biomedical and Health Informatics 07/2014; 18(4):1337-1354. · 1.98 Impact Factor -
##### Conference Paper: A 3D segmentation framework for an accurate extraction of the spongy and cortical bones from the MRI data

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**ABSTRACT:**In this paper we proposed a new framework for obtaining the spongy and cortical bones from the MRI data. The method focuses on the accurate extraction of the edges of the target tissues, which is the main drawback of the previous works. This framework first limits the searching area for the bone voxels from the whole data to a small strip around the edges of the cortical and spongy bones then applies a very accurate segmentation on the searching area using the newly developed deformable kernel Fuzzy C-Means (DKFCM) algorithm, which is proposed in this paper. Comparing the results of this work with previous segmentation methods on a testing dataset consisting of 10,485,760 voxels demonstrates the superiority of the proposed method especially on the edges of the spongy and cortical bone.2013 IEEE International Conference on Bioinformatics and Biomedicine (BIBM); 12/2013 - Brian J. Soher, William E. Wu, Assaf Tal, Pippa Storey, Ke Zhang, James S. Babb, Ivan I. Kirov, Yvonne W. Lui, Oded Gonen[Show abstract] [Hide abstract]

**ABSTRACT:**Concentration of the neuronal marker, N-acetylaspartate (NAA), a quantitative metric for the health and density of neurons, is currently obtained by integration of the manually defined peak in whole-head proton (1H)-MRS. Our goal was to develop a full spectral modeling approach for the automatic estimation of the whole-brain NAA concentration (WBNAA) and to compare the performance of this approach with a manual frequency-range peak integration approach previously employed. MRI and whole-head 1H-MRS from 18 healthy young adults were examined. Non-localized, whole-head 1H-MRS obtained at 3 T yielded the NAA peak area through both manually defined frequency-range integration and the new, full spectral simulation. The NAA peak area was converted into an absolute amount with phantom replacement and normalized for brain volume (segmented from T1-weighted MRI) to yield WBNAA. A paired-sample t test was used to compare the means of the WBNAA paradigms and a likelihood ratio test used to compare their coefficients of variation. While the between-subject WBNAA means were nearly identical (12.8 ± 2.5 mm for integration, 12.8 ± 1.4 mm for spectral modeling), the latter's standard deviation was significantly smaller (by ~50%, p = 0.026). The within-subject variability was 11.7% (±1.3 mm) for integration versus 7.0% (±0.8 mm) for spectral modeling, i.e., a 40% improvement. The (quantifiable) quality of the modeling approach was high, as reflected by Cramer–Rao lower bounds below 0.1% and vanishingly small (experimental - fitted) residuals. Modeling of the whole-head 1H-MRS increases WBNAA quantification reliability by reducing its variability, its susceptibility to operator bias and baseline roll, and by providing quality-control feedback. Together, these enhance the usefulness of the technique for monitoring the diffuse progression and treatment response of neurological disorders. Copyright © 2014 John Wiley & Sons, Ltd.NMR in Biomedicine 09/2014; 27(11). · 3.56 Impact Factor

Page 1

1838 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

A Hybrid Geometric–Statistical Deformable Model

for Automated 3-D Segmentation in Brain MRI

Albert Huang*, Student Member, IEEE, Rafeef Abugharbieh, Member, IEEE, Roger Tam,

and Alzheimer’s Disease Neuroimaging Initiative

Abstract—We present a novel 3-D deformable model-based ap-

proach for accurate, robust, and automated tissue segmentation of

brain MRI data of single as well as multiple magnetic resonance

sequences. The main contribution of this study is that we em-

ploy an edge-based geodesic active contour for the segmentation

task by integrating both image edge geometry and voxel statistical

homogeneity into a novel hybrid geometric–statistical feature to

regularize contour convergence and extract complex anatomical

structures. We validate the accuracy of the segmentation results

on simulated brain MRI scans of both single T1-weighted and

multiple T1/T2/PD-weighted sequences. We also demonstrate the

robustness of the proposed method when applied to clinical brain

MRI scans. When compared to a current state-of-the-art region-

based level-set segmentation formulation, our white matter and

gray matter segmentation resulted in significantly higher accuracy

levelswithameanimprovementinDicesimilarityindexesof8.55%

(p < 0.0001) and 10.18% (p < 0.0001), respectively.

Index Terms—3-D image segmentation, brain segmentation, de-

formable models, geodesic active contour.

I. INTRODUCTION

M

assessment and monitoring of patients with neurodegenerative

diseasessuchasParkinson’sdisease,Alzheimer’sdisease(AD),

epilepsy, schizophrenia, and multiple sclerosis (MS) [1]–[6].

The ability to diagnose and characterize these diseases in vivo

using MR image data promises exciting developments both

toward understanding the underlying pathologies, as well as

conducting clinical trials of drug treatments. One important

biomarker that is often used to assess patients with neurode-

generative disease is brain tissue volume. The typical rate of

globalbrainatrophyinMSpatientshasbeenshowntobe0.6%–

0.8% annually, which is two to three times the normal atrophy

rate [7]. Evidence has shown that white matter (WM) and gray

AGNETICresonance(MR)hasbecomethemainmodal-

ity for brain imaging that facilitates safe, noninvasive

Manuscript received August 20, 2008; revised December 11, 2008. First

published March 27, 2009; current version published June 12, 2009. This work

wassupportedinpartbytheNaturalSciencesandEngineeringResearchCouncil

(NSERC) Parts of the data used in the preparation of this article were obtained

from Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. As such,

investigators within ADNI contributed to the design and implementation of

ADNI and/or provided data but did not participate in analysis or writing of this

report. Asterisk indicates corresponding author.

∗A. Huang is with the Department of Electrical and Computer Engineer-

ing, University of British Columbia (UBC), Vancouver, BC V6T 1Z4, Canada

(e-mail: alberth@ece.ubc.ca).

R.AbugharbiehiswiththeDepartmentofElectricalandComputerEngineer-

ing, University of British Columbia (UBC), Vancouver, BC V6T 1Z4, Canada

(e-mail: rafeef@ece.ubc.ca).

R. Tam is with the Department of Radiology, University of British

Columbia (UBC), Vancouver, BC V6T 1Z4, Canada (e-mail: roger@msmri.

medicine.ubc.ca).

Digital Object Identifier 10.1109/TBME.2009.2017509

matter (GM) atrophy at different rates, and each correlates dif-

ferently to disability [8]–[10]; thus, accurate measurement of

the WM and GM brain tissues can provide valuable quantitative

indicatorsofdiseaseprogressionand,potentially,treatmentout-

comes [7],[11].Thus, the main goal of thispaper is tointroduce

an automatic algorithm for robust WM, GM, and cerebrospinal

fluid (CSF) segmentation to facilitate accurate measurement of

brain tissues.

Previously, to measure various tissue volumes in MRI head

scans, manual WM and GM segmentations were often per-

formed by skilled experts. Manual segmentation, however, is

extremely time-consuming, mostly limited to 2-D slice-based

segmentation, and prone to significant intra- and interrater vari-

ability[12].Inparticular,manualsegmentationcannotbepracti-

cally and efficiently performed in situations where precise mea-

surements on a large number of scans are required, such as in

clinical trials. Therefore, a fully automatic, highly accurate, and

robust tissue segmentation technique that provides systematic

quantitative analysis of tissue volumes in brain MRI is an in-

valuable tool in many studies of neurodegenerative diseases. A

wide variety of methods have been proposed for automating the

segmentation process over the past decade that provided either

semi- or fully automated frameworks for the segmentation of

brain tissues. A review of some of these methods can be found

in [13] and [14].

One popular family of brain tissue segmentation methods is

based on normalizing the brain scans by registering (or align-

ing) them to a predefined atlas of brain tissues. One exam-

ple is the popular statistical parametric mapping (SPM) tech-

nique, which relies on voxel-based morphometry (VBM) [15].

A number of extensions to the original SPM technique have

been proposed. For example, SPM is utilized to initialize an

expectation–maximization (EM) segmentation framework [16],

which has been extended to nonrigid registration [17]. Al-

though such atlas-based methods are typically robust to arti-

facts such as acquisition noise and distortions, concerns and

discussion [18]–[20] have ensued regarding the use of tem-

plates from one population when analyzing data from another

population. For example, morphing patient scans with patho-

logically enlarged ventricles to match a normal template could

potentially distort the surrounding tissues in an unpredictable

manner. Such structural differences might lead to systematic bi-

ases and misregistration errors that are difficult to quantify [19].

Suchconcernsintroduceyetanotherlevelofcomplicationsaris-

ing from image registration and atlas generation procedures that

add to the already nontrivial segmentation problem, especially

in the presence of anomalies such as tumors, lesions, and tissue

atrophy.

0018-9294/$25.00 © 2009 IEEE

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HUANG et al.: HYBRID GEOMETRIC–STATISTICAL DEFORMABLE MODEL FOR AUTOMATED 3-D SEGMENTATION IN BRAIN MRI1839

A second family of brain tissue segmentation methods as-

signs a label for each tissue based on image statistics either by

clustering [21] or by modeling the brain tissue intensity dis-

tributions as a finite mixture of distributions such as EM [22],

maximum a posteriori (MAP) [23], simulated annealing [24],

andGaussianmixturemodeling(GMM)[25].Otherapproaches

incorporate additional regional information, which is lacking

from these statistical methods, into their segmentation frame-

work. Such methods extend clustering or EM by integrating

with fuzzy connectedness [26], topological constraints [27],

Gibbs random field (GRF) [28], and hidden Markov random

field (HMRF) [29] in the segmentation task. A common diffi-

culty with many of these methods, particularly the random field

approaches, is the requirement for proper parameter settings in

a supervised setting.

A third family of brain tissue segmentation methods is based

on utilizing geometric information such as deformable models

or active contours [30] that delineates region boundaries using

a minimization of an energy functional [31], [32]. Deformable

models employing level sets [33] provide an effective implicit

representationratherthanexplicitparameterizationoftheevolv-

ing contour. However, a common problem of directly applying

the active contour approach in segmenting brain MR images

is leakage through weak or noisy edges that are ubiquitous,

especially for edge-based deformable models, e.g., geodesic ac-

tive contour [34], which describe the evolution of propagating

curveasafunctionofimagegradientfeatures.Someresearchers

incorporated image statistics into their deformable models in

various segmentation applications by utilizing coupled surface

principle [35], [36] and fuzzy logic [37], [38] to achieve better

stability. Others employed a region-based model [39] by utiliz-

ing regional homogeneity in a curve evolution perspective and

a hierarchical implementation on brain pathology images [40].

Morerecently,tissuesegmentationwasperformedandquantita-

tively evaluated [41]–[43] by using the multiphase 3-D level set

segmentation(M3DLS)algorithm[41].M3DLSutilizesamulti-

phaseextension[44]oftheregion-baseddeformablemodel[39]

based on the Mumford–Shah functional [45] by iteratively de-

forming two closed curves separating four regions. This mini-

mal partitioning approach assumes piecewise constant or piece-

wise smooth data and optimizes a sum of terms, including the

lengths and areas for the two closed curves, and the sums of

square intensity differences from the means for all four sepa-

rated regions. This minimization is also performed in a level set

framework [33] implicitly. Further extending this model to N-

phase allows separation of 2Nregions but the number of classes

to be segmented is limited to two to the power of the number of

closed curves defined. Moreover, complexity increases as more

level sets are required and the rate of convergence is typically

slow [46].

In this paper, we propose a MR brain tissue segmentation

approach that integrates both geometric and statistical image

features into an edge-based deformable model formulation to

achieve accurate segmentation results. By utilizing this novel

hybrid image feature, we present one solution to the challeng-

ing problem of stabilizing the active contour. Similar existing

work used a topology preservation principle enforced at non-

simple points in a geometric deformable model [47], or a curve

shorteningpriorforsmoothnessinalevelsetframeworktomin-

imize leakage [40], [48]. Here, we do not explicitly apply any

smoothness and topological constraints (e.g., topology preser-

vation at nonsimple points) to the geometric deformable models

but rather rely on the proposed hybrid feature to regularize the

level sets. Other approaches used prior knowledge such as a

distance penalizing term in the level set function between two

boundary classes [35], a fuzzy decision system on contour dis-

tance to an anatomical target or atlas [37], or a dissimilarity

measure between the contour and a shape model in the en-

ergy term [49]. Here, we demonstrate our proposed approach in

segmenting complex anatomical structures such as WM, GM,

and CSF without a priori knowledge. Hence, the proposed ap-

proach is truly automated and data-driven in both statistical and

geometric sense. Furthermore, we compare the segmentation

performance of our proposed edge-based level setmethod tothe

region-based M3DLS approach [41] on real clinical MRI scans.

WedemonstratetheimprovedWM,GM,andCSFsegmentation

accuracy and robustness when using the proposed method.

The paper is organized as follows: In Section II, we introduce

our novel hybrid geometric–statistical feature implemented on

the edge-based geodesic active contour formulation. Our modi-

fied deformable model is then used to design a new automated

3-D brain tissue segmentation algorithm for both single and

multiple MR sequence data. In Section III, we present quanti-

tative and qualitative results and analysis obtained on simulated

and real clinical MRI images, as well as comparisons to results

reported by using M3DLS. We then conclude in Section IV.

II. METHODS

Inthissection,wepresentour3-Dbrainsegmentationmethod

thatintegratesbothgeometricandstatisticalfeaturesinanedge-

based geodesic active contour framework. We describe the pro-

posedmodelinitsgeneralform.Wethenpresentasegmentation

framework for brain MRI for both single and multiple MR se-

quence data.

A. Edge-Based Deformable Model

In this study, we utilize the geodesic active contour model

[34] rather than the region-based formulation [39] due to its

computation soundness and extendibility. The geodesic model

delineates region boundaries by describing the evolution of a

curve or surface C from an initial position C0 as finding the

minima of the Riemannian curve distance

?1

?L(C)

where g is a general feature function, |∇I| is the gradient norm

of intensity I, and q is the parameterization of the curve C.

The right side of the equation describes the parameterized curve

C(q) such that the Euclidean length of C can be represented

as L(C) =

Euclidean arc length or the Euclidean metric. Note that this

min

0

g (|∇I (C (q))|)|C?(q)|dq

= min

0

g (|∇I (C (q))|)ds

(1)

?|C?(q)|dq =

?ds, where ds = |C?(q)|dq is the

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1840 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

geodesic formulation of the active contour relies on g, the speed

and halting feature for the evolving surface in 3-D applications

derived based on the geometric gradient feature of an image.

Generally, g is chosen as a positive-valued function of the in-

tensity gradient as in (2), whereˆI is a smoothed version of I

and ρ = 1 or 2 [34]. Other similar monotonically decreasing

functions, such as the sigmoid function (3) with parameters α

(width of intensity window) and β (center of intensity window)

are also often utilized [50].

g(I) = (1 + |∇ˆI|ρ)−1

?

The value of this feature function determines the propagation

ofthesurfacebysearchingfortheminimalRiemanniandistance.

An ideal edge would ultimately have a feature value of zero at

all the pixel points along this boundary. However, propagation

relying solely on edge feature is typically sensitive to noisy and

weak edges that are frequently observed in medical images. In

particular, with the presence of complex anatomical structures,

it is often impossible to automatically and accurately derive the

desired geometric edge term to prevent contour leakage into the

surroundingregions.Consequently,achievingaccuratesegmen-

tation results with edge-based geodesic active contour requires

eitheruserinterventionorcarefuladjustmentofparameterssuch

that the ideal boundary is minimal. This process is subjective

and ideal parameters are often difficult to derive for a fully

automated segmentation framework.

(2)

g(I) = 1 + exp

?

|∇ˆI| − β

α

??−1

.

(3)

B. Proposed Hybrid Geometric–Statistical Feature

We propose to transform the feature function g in the tradi-

tional geodesic active contour formulation into a hybrid feature

function by incorporating geometric image features with voxel

statistics to help automate and regularize the evolving contours.

The minimization of the active contour is thus represented by

(4)

?L(C)

where for gray-scale intensity MR images, P(I|Φ) represents

theprobabilitydistributionfunctionofamixturemodel(5)from

which voxel statistics are drawn, assuming that all voxels are

identically and independently distributed and the image is to be

described with K class labels.

min

0

g (|∇I (C(q))|,P(I |Φ))ds

(4)

P(I) =

K

?

k=1

P(k)P(I |Φk)

(5)

where P(k) represents the prior probability of the class label

k and P(I|Φk) is the conditional density function of the kth

class given Φ, the parameter set of the distribution. We employ

Gaussian distributions as

?

which require a parameter set Φ = {µ, σ}, where µ and σ

are the mean and standard deviation. This parameter estimation

P(I |Φ) =

1

σ√2π

?

exp

?−(I − µ)2

2σ2

?

(6)

problem for GMM is solved by applying the EM algorithm [51]

to the image intensity histogram.

The design of g in (4) utilizes both a geometric term and

a statistical term. Geometrically, the presence of strong image

gradients indicates significant structuralcontent. Asaresult,the

contour propagation speed slows to a halt. On the other hand,

a lack of edge features often indicates the presence of a homo-

geneous region. Statistically, high voxel probability indicates a

high likelihood of the voxel belonging to the class of interest,

warranting a fast contour propagation. If the voxel likelihood is

reduced, the contour propagation is slowed down accordingly.

The contribution of voxel likelihood to the contour propagation

exhibits an inverse behavior to that of image gradients. Since

both geometric and statistical features are essential to the con-

tour stability, they can be combined into a single hybrid feature

function by modeling the aforementioned behavior as

g(I) = sigmoid(|∇I|)sigmoid−1(P(I |Φ))

?

α

= 1 + exp

?

|∇ˆI| − β

??−1 ?

−ln

?1 − P(I |Φ)

P(I |Φ)

??

(7)

where the first term is the traditional geometric feature as in

(3) and the second term models the inverse behavior of voxel

likelihood to image gradients using an inverse sigmoid function

with magnitudes between −1 and 1. Complementarily, these

two components in the new hybrid feature help regularize the

evolvingcontourinboththegeometricandstatisticalsense.The

minimization of (4) is then achieved by computing the Euler–

Lagrange equation [34]

?1

?L(C0)

whereκistheEuclideancurvature,?N istheinwardunitnormal,

and C0is the initial curve or surface, and performing steepest

gradient search (9), to deform C toward a minima

d

dt

0

g (C(q))|C?(q)|dq|t=0

?

=

0

[∇g(C0) ·?N]?N − g(C0)κ?N

?

· C0ds

(8)

∂C

∂t

= g(I)(φκ + c)?N − ε(∇g ·?N)?N

where {ψ, c, ε} are the free parameters introduced to govern

curvature, propagation, and advection strengths, respectively.

With the designed hybrid feature, the algorithm uses only the

propagationterm.Othertermsareshownhereforcompleteness.

This curve evolution equation is then embedded in a level set

function u and solved for the steady state solution:

C (0) = C0

(9)

∂u

∂t= g(I)(φκ + c)|∇u| + ε∇g(I) · ∇uu(0) = u0.

(10)

The numerical implementation is based on the curve evo-

lution algorithm via level sets [33], which utilizes an upwind

piecewise continuous approximation scheme to provide a nu-

merically stable solution in the presence of singularities.

As summarized in Table I, the rationale behind using this

new hybrid feature is to enable handling of situations where

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HUANG et al.: HYBRID GEOMETRIC–STATISTICAL DEFORMABLE MODEL FOR AUTOMATED 3-D SEGMENTATION IN BRAIN MRI1841

TABLE I

EFFECTS OF REGULARIZING CONTOUR PROPAGATION USING GEOMETRIC AND

STATISTICAL FEATURES

the image gradient is high (small sigmoid(|∇I|) value) and the

posterior probability of voxel is low, in which the voxel is con-

sidered to be a significant feature but lies outside of the desired

region. We, therefore, aim to steer the contour slowly away

from this voxel by assigning a small negative feature value. On

the other hand, if the posterior probability is high, this indi-

cates a significant feature within the desired region; therefore, a

small positive feature value is assigned. In contrast, if the image

gradient is low (large sigmoid(|∇I|) value) and the posterior

probability is low, the voxel is considered to be a weak gradi-

ent feature that lies outside of the desired region, warranting a

large negative feature value such that contour can be quickly

steered away from that region. If the posterior probability is

high, a homogeneous area in the desired region is indicated, and

is rewarded with a large positive feature value for fast contour

expansion.Insummary,theproposedhybridfeatureprovidesan

adaptive active contour propagation based on local information

reflecting both geometry and statistical homogeneity.

C. Segmentation of Brain MRI

Based on the proposed active contour model, we develop a

fully automated 3-D brain tissue segmentation algorithm for

MR images. The segmentation procedures (Fig. 1) are a gener-

alization and extension of earlier work [52]. We first present the

proposed algorithm for T1-weighted (T1w) MRI scans, which

are most often used for brain tissue segmentation due to the

generally high WM and GM contrast and the reduced effects

of WM lesions in patients with neurodegenerative diseases. We

later extend the proposed method to simultaneously incorporate

additional MR sequence data, such as T2-weighted (T2w) and

PD-weighted (PDw) images, in addition to T1w.

To segment the brain tissues, we first estimate the GMM

parameters such that each mixture distribution represents one

single class. Based on these estimated distributions, the normal-

ized posterior probability of each voxel is calculated. We derive

the hybrid geometric–statistical feature as described above by

combining both the voxel statistics and the image gradient in-

formation. To initialize the active contour, we first introduce a

voxel threshold tson the posterior probability to further regu-

larize this contour initialization by effectively removing voxels

outside of the desired region boundaries due to noise or partial

volume artifacts. Based on the thresholded masks, we form the

skeleton representation using standard 2-D morphological se-

quential thinning (3 × 3 kernel) and sequential pruning (3 ×

3 kernel) [53] iteratively until no further changes occur. This

is done slice-by-slice in 2-D as morphological operations are

performed on discrete numbers of voxels, and to do this in 3-D

Fig. 1.

Asterisk (∗) denotes the proposed novel hybrid geometric–statistical image

feature described in Section II-B.

Block diagram of the proposed MRI brain segmentation algorithm.

on anisotropic scans would require resampling of the acquired

data,whichwouldpotentiallyintroduceadditionalartifacts.The

hybridfeatureandthecontourinitializationaredeterminedindi-

viduallyforeachtissuetobesegmented,andeachcontouristhen

propagated independently. After the contours converge, minor

overlaps and gaps occurred between the individually evolving

contour boundaries are re-assigned to a single label by com-

paring the individual z-scores, the difference between voxel

intensity to the sample mean normalized by the sample stan-

dard deviation, of all tissue classes. A brief description of the

algorithm is described as follows:

Step 1: Given raw MRI scan U.

Step 2: Preprocess with intensity inhomogeneity correction,

noise filtering, and brain extraction to obtain V .

Step 3: Calculate gradient norm |∇I| of pixel intensity I in V .

Step 4: For k = 1 to K, tissue class labels:

1) determine the GMM distribution parameter set by

using EM: Φk= {µk,σk};

2) for each I, calculate normalized probability

P(I|Φk).

Step 5: For k = 1 to K, tissue class labels:

1) derivehybridgeometric–statisticalfeature:gk(I) =

g(|∇I|,P(I|Φk));

2) deriveinitialcontourC0,kbythresholdingP(I|Φk)

at tS= 0.1 and skeletonizing;

3) propagate curve Ckfrom C0,kon gk(I) until con-

vergence to obtain class label image Lk(I).

Step 6: ForeachI,ifLk(I) = 1formorethanonekorLk(I) =

null for all k, assign Lk(I) = 1 for k with the highest

z-score.

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1842 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

TABLE II

PARAMETER SENSITIVITY OF A SIMULATED BRAIN VOLUME (9% NOISE,

40% INHOMOGENEITY)

In step 5, the performance gain by setting ts> 0 is demon-

stratedinTableII,andweshowthatfor0.1 ≤ ts≤ 0.6,thefinal

segmentationaccuracyinasimulatedbrainvolumeisshownnot

to be sensitive to the parameter value tested but is necessary for

removing extreme outliers before skeletonizing is performed.

The parameter is set to ts= 0.1 for all subsequent experiments,

both simulated and clinical.

D. Extension to Multiple MR Sequence Data

To further demonstrate the flexibility of the proposed seg-

mentation approach, we extend our method so that information

from multiple MR sequences with different contrast properties

can be incorporated when the data is available. Assuming regis-

tered images, we first replace the geometric feature component

in the proposed hybrid active contour feature (7) with the mul-

tidimensional vector gradient norm derived from all available

data sequences. To derive the statistical active contour feature

term, the GMM parameters and the voxel statistics are individ-

ually estimated for each contrast modality m given M input

modalities. Since our main goal is to improve the ability to dif-

ferentiate between various tissue labels, we derive an pairwise

intensity contrast term Cm

ference between the EM estimated means µ of labels i and j

over the observed intensity range of [IMax...IMin] (11) and

then normalize (12).

i,jas a ratio of absolute intensity dif-

Cm

i,j=

|µm

Im

i− µm

Max− Im

Cm

i,j

?M

j|

Min

(11)

¯Cm

i,j=

m=1Cm

i,j

.

(12)

This intensity contrast factor is used as an optimized weight-

ing factor to linearly combine individual posterior probability,

P(I |Φm

posterior probability. This is done by using all relevant pair-

wise contrast terms, defined between label k and all others.

This ensures that the MR sequence with greater contrast re-

ceives a greater weight with respect to other lower contrast MR

modalities used. Equation (13) shows how the final posterior

probability is computed as a function of the means and vari-

ances of each tissue and modality. In the case where tissues at

different modalities exhibit equal variances, more emphasis is

placed on the scan that possesses the greater difference between

the expected values of the tissues of interests, thereby facilitat-

ing separation. In the other case where the differences in the

sample means are equal, the differences in variance are taken

into account inherently in the individual posterior probability

terms. The resulting probability replaces the posterior proba-

bility derived from single contrast input in the segmentation

k) as in (13), for label k in modality m to form a new

procedure.

P(I |Φk) =

?M

m=1

?K

m=1

i=1¯Cm

?K

i,kP(I |Φm

i=1¯Cm

i,k

k)

?M

.

(13)

E. Data Preprocessing

We employed the nonparametric nonuniform intensity nor-

malization(N3)algorithm[54]forintensityinhomogeneitycor-

rectionusingdefaultparametersettings(widthofdeconvolution

kernel = 0.15, number of iterations = 50, sampling factor = 4,

characteristic distance = 200 mm, stopping criteria = 0.001).

All scans were then noise filtered using an edge-preserving

Perona–Malik anisotropic diffusion filter [55] (number of iter-

ations = 4, conductance = 3.0) to further enhance the image

signal-to-noiseratio.Brainmasksweregeneratedusingthepro-

vided ground truths consistent with other published methods to

facilitate direct comparisons, or alternatively, many methods

are also available for this brain extraction task [56]–[58]. For

the clinical datasets where the ground truths are not available,

the brain masks were generated with the brain extraction tool

(BET) [56] using default parameter settings.

III. RESULTS AND DISCUSSION

We applied our proposed segmentation to both simulated and

real clinical MRI scans, and demonstrated in the following sec-

tions: 1) the accuracy of the proposed segmentation method on

simulated T1w brain MRIs; 2) the segmentation improvement

on multiple MRI sequences; 3) the accuracy of the proposed

method on real clinical MRI scans of normal adults; and 4)

the qualitative performance of the proposed methods on clinical

MRI scans of MS and AD patients.

We first validated our proposed method on 18 simulated T1w

BrainWeb[59]MRIimages(with0%/1%/3%/5%/7%/9%noise,

0%/20%/40% inhomogeneity, 181 × 217 × 181 dimension,

1 × 1 × 1 mm3spacing). We also performed multisequence

segmentation based on six T1w/T2w/PDw MRI triplets (with

0%/1%/3%/5%/7%/9% noise, 0% inhomogeneity). Second, 18

real high-resolution clinical T1w MRI scans from the Inter-

net Brain Segmentation Repository (IBSR) [60] (coronally ac-

quired, 256 × 128 × 256 dimension, 0.837 × 0.837 mm2to

1 × 1 mm2in-plane spacing, 1.5 mm slice thickness) were also

segmented. For both datasets, the “ground truth” is known for

comparisons. For the BrainWeb dataset, the ground truth is the

phantom atlas used to generate the simulated scans, whereas for

the IBSR dataset, the ground truth is the provided expert-guided

manual segmentation label for each of the clinical scans. Lastly,

fromtheMSMRIResearchGroup(MS/MRI),realclinical1.5T

spoiled gradient (SPGR) MRI scans (axially acquired, 256 ×

256×120–160dimension,0.937×0.937×1.50mm3spacing)

were taken at multiple sites. Real clinical 1.5 T magnetization

prepared rapid gradient echo (MP-RAGE) MRI scans (sagit-

tally acquired, 256 × 256 × 166 dimension, 0.937 × 0.937 ×

1.20mm3spacing)werealsoobtainedfromtheADNeuroimag-

ingInitiative(ADNI)oftheLONIimagedataarchive(IDA)[61]

initiated by the National Institute on Aging (NIA), the National

Institute of Biomedical Imaging and Bioengineering (NIBIB),

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HUANG et al.: HYBRID GEOMETRIC–STATISTICAL DEFORMABLE MODEL FOR AUTOMATED 3-D SEGMENTATION IN BRAIN MRI1843

the Food and Drug Administration (FDA), private pharmaceuti-

calcompanies,andnonprofitorganizations.Theseclinicalscans

weresegmentedandqualitativelyevaluated.Forallexperiments,

the parameters for the level set evolutions are set at {ψ = 0.0,

c = 1.0, ε = 0.0} to reinforce propagation and effectively re-

move boundary attraction and smoothness regularizations. The

convergence criteria for the gradient descent optimization is

defined as either less than 0.5% root-mean-square change in

the level set function or, if not achieved, a maximum of 100

iterations reached.

The average surface distance between the ground truth and

the computed segmentation was computed for each test scan by

approximate nearest neighbor searching [62]. In addition, the

Dice similarity index [63] was also chosen for the quantitative

evaluation of the 3-D brain segmentation results to facilitate

direct comparisons to other published results

Dicesimilarityindex :

2T+

2T++ F++ F−

× 100%.

(14)

We denote the true positives, true negatives, false positives,

and false negatives as T+,T−,F+, and F−, respectively, be-

tween the known ground truth and the segmentation results. We

compared our segmentation results with those of the M3DLS

method [41].

A. Segmentation Validation Using Simulated Brain MRI

Wefirstvalidatedathree-class(WM,GM,andCSF)segmen-

tation using the proposed method on the simulated T1w brain

MRI data. Segmentation was performed using the traditional

geometric feature only, the statistical feature only, and the pro-

posed hybrid feature on all 18 datasets with varying noise and

intensity inhomogeneity levels. For the edge-only level set evo-

lution, the parameter set {ψ = 2.0, c = 1.0, ε = 4.5} was used

to enforce a stronger smoothness constrain; otherwise, contours

leaking through weak edges were often observed. For the sta-

tistical feature term only, the parameter set {ψ = 0.0, c = 1.0,

ε = 0.0} was used, same as the hybrid approach. Qualitative

results in Fig. 2 demonstrated very good resemblance between

the provided phantom label and the segmentation results based

on the hybrid feature. Table III shows that, on average, over all

noise and inhomogeneity levels, the proposed method achieved

consistently accurate segmentation results for both WM and

GM with similarity indexes of 93.71% (σ = 2.11%, average

distance = 0.27mm) and 92.59% (σ = 2.40%, average distance

= 0.30mm). Segmentation of structures such as CSF by using

the proposed approach also achieved considerable (>70%) sim-

ilarity of 77.75% (σ = 6.15%, average distance = 2.24 mm).

The CSF results were not as stable as WM and GM mainly due

to the much smaller structural volume, leading to increased sen-

sitivity to estimation errors in the active contour initialization

and feature derivation. Nonetheless, the overall segmentation

results were on par if not better than other previously published

results [16], [27], [64].

To statistically evaluate the differences of segmentation re-

sults between the proposed hybrid approach, and the contours

based on geometric-only and statistical-only features, we calcu-

Fig. 2.

images showing the provided phantom label, raw images and the segmentation

results obtained by using the proposed hybrid feature. We show three slices for

both the best case (0% noise, 0% inhomogeneity) and worst-case (9% noise,

40%inhomogeneity)scenarios.White,lightgray,anddarkgraycolorsrepresent,

respectively, the WM, GM, and CSF classes in the tissue and phantom labels.

We note the results from the hybrid approach resemble the phantom for both

the best and worst input scenarios.

Qualitative segmentation performance of two simulated T1w brain

lated the p-values (p < 0.05 indicates a statistically significant

difference in the group means). Compare to results from us-

ing only the traditional geometric feature, the proposed hybrid

approach achieved significantly higher similarity indexes and

reduced surface distance across all scans. On average, the pro-

posed method achieved increased similarity indexes of 5.36%

(p = 0.0002) in WM, 7.23% (p < 0.0001) in GM, and 9.30%

(p < 0.0001) in CSF segmentation results with reduced sur-

face distance of 3.99 mm (p < 0.0001) in WM, 0.27 mm (p <

0.0001) in GM, and 4.86 mm (p < 0.0001) in CSF. Compare

to results from using only the statistical feature, the proposed

hybridapproachonlyachievedslightlybettersimilarityindexes.

However, we observed that, on average, the proposed method

was able to significantly reduce the average surface distance by

4.44mm(p<0.0001)inWMand3.79mm(p<0.0001)inCSF.

These results showed that using the geometric term alone was

highly sensitive to image artifacts and require contour regular-

ization, and using the statistical term alone caused the contours

to deviate from the true edges. Only when incorporating both

features we can evolve the contour in the appropriate statistical

space while maintaining high geometric relevance at the same

time.ProcessingasingleBrainWebvolumetakesapproximately

55 min (dual 3.20 GHz Xeon PC with 3.25 GB memory) to 75

min(3.60GHzPentium4PCwith2GBmemory),comparableto

the processing time required by other conventional techniques.

B. Segmentation Improvement Using Multiple MR Sequences

We next performed a three-class (WM, GM, and CSF)

segmentation using the proposed method on the simulated

T1w/T2w/PDw brain MRI data. Segmentation was performed

on six datasets with varying noise levels and 0% intensity

inhomogeneity. Qualitative results in Fig. 3 illustrated very

good resemblance between the provided phantom label and the

segmentation results. Table IV demonstrates the quantitative

segmentation accuracies. On average, over all noise levels,

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1844 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

TABLE III

QUANTITATIVE EVALUATION OF SEGMENTATION RESULTS OBTAINED BY USING THE GEOMETRIC FEATURE, THE STATISTICAL FEATURE, AND THE PROPOSED

HYBRID APPROACH ON 18 SIMULATED T1W BRAINWEB SCANS

Fig. 3.

quence (T1w, T2w, PDw) brain images showing the provided phantom label,

raw images (0% noise, 0% inhomogeneity), and the segmentation results ob-

tained by using the proposed approach. White, light gray, and dark gray colors

represent,respectively,theWM,GM,andCSFclassesinthetissueandphantom

labels. We show three slices for the test case and note improved segmentation

results on multiple MR sequence.

Qualitative segmentation performance of a multiple simulated MR se-

the proposed method achieved consistently accurate segmen-

tation results for WM, GM, and CSF with similarity in-

dexes of 96.24% (σ = 1.13%, average distance = 0.15 mm),

94.14% (σ = 1.24%, average distance = 0.24 mm) and 81.57%

(σ = 2.82%, average distance = 1.56 mm), respectively. When

compared to the experiment on single simulated T1w brain

images, segmentation using multiple MR sequence data pro-

vided an average improvement in similarity indexes of 1.29%

(p = 0.0479),0.44%(p = 0.4627),and3.55%(p = 0.1403)for

WM, GM, and CSF, respectively. The segmentation improve-

TABLE IV

QUANTITATIVE EVALUATION OF SEGMENTATION RESULTS OBTAINED BY USING

THE PROPOSED METHOD ON 6 SIMULATED T1W/T2W/PDW SCANS

ments are not statistically significant, which is not surprising

given that the synthetic T1w brain images by themselves al-

ready have the strong image contrast required to distinguish

between the majority of WM and GM tissues. Additional MR

sequencessuchasT2wandPDwinthiscase,helpedimprovethe

overall robustness by achieving a much better balance between

the WM, GM, and CSF estimation as observed by the T+and

T−performance. Table III(column 1)shows thatwithonly T1w

scans as inputs, the differences between the T+ and T−were

7.77%, 8.67%, and 24.09%, respectively, for WM, GM, and

CSF, whereas with T1w, T2w, and PDw inputs (Table IV), these

differences were much reduced to 2.84%, 0.24%, and 6.95%.

C. Segmentation Comparisons Using Clinical MR Scans

of Normal Adults

We applied the proposed method to segment 18 clinical IBSR

brain images. The images were segmented using a three-class

(WM, GM, and CSF) segmentation. The qualitative results are

shown in Fig. 4. The tissue labels were then postprocessed due

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HUANG et al.: HYBRID GEOMETRIC–STATISTICAL DEFORMABLE MODEL FOR AUTOMATED 3-D SEGMENTATION IN BRAIN MRI1845

Fig. 4.

images (IBSR #08) showing the raw images, the expert-guided manual seg-

mentation label, and the segmentation results obtained by using the traditional

edge feature and the proposed hybrid approach. We show three slices for the

three-class segmentation case and the postprocessed case. White, light gray,

and dark gray colors represent, respectively, the WM, GM, and CSF classes in

the segmentation labels. We note the good resemblance between the segmenta-

tion results and the raw image, and between the postprocessed results and the

expert-guided manual segmentation labels.

Qualitative segmentation performance of a real clinical T1w brain

to a known limitation of the provided manual segmentation

labels. It has been reported previously [41] that the expert-

guided manual segmentation label contains much of the cortical

CSF being mislabeled as GM. We have confirmed this with

our own observations. As observed from Fig. 4, we note that

the original segmentation results matched closely with what

can be visually observed from the raw images. However, this

observation did not correspond well to the provided expert-

guidedmanualsegmentationlabelduetotheexistinglimitation.

Ifquantitativeevaluationwastobeperformedonthisresult,both

GM and CSF would produce much lower accuracies than what

were actually present.

Toenableavalidcomparisonbyretainingonlytheventricular

CSFforcomparison,weemployedthefollowingpostprocessing

scheme:

Step 1: Re-assign segmented CSF labels close to (≤5 mm) any

background labels as GM.

Step 2: Definearectangularregionofinterest(30%ofthemask

width in the superior–inferior orientation and 50% for

both left–right and anterior–posterior) around the brain

mask centroid. Apply 2-D morphological thinning (3

× 3 kernel) [65] on CSF pixels outside the region of

interest in coronal slices, and singly links are removed.

Step 3: Identify the largest 3-D connected component as the

desired ventricular CSF. Apply 3-D morphological di-

lation(3×3×3kernel)tothisfinalmask,andre-assign

all original CSF labels outside as GM.

This postprocessing scheme allowed us to generate re-

sults comparable to the provided manual label. We show in

Table V that the results obtained by using the proposed method

achieved similarity indexes of 87.55% (σ = 2.92%, average

distance = 0.54 mm), 93.18 (σ = 0.92%, average distance =

0.38 mm), and 77.39% (σ = 11.15%, average distance =

3.12 mm) for WM, GM, and CSF, respectively, averaged across

the 18 images tested. To statistically compare the segmentation

TABLE V

QUANTITATIVE EVALUATION OF SEGMENTATION RESULTS ON 18 REAL

CLINICAL T1W IBSR SCANS

performance of our hybrid active contour approach against the

region-based active contour M3DLS algorithm, a one-sample t-

testwasperformedtocalculatethep-values(standarddeviations

werenotreportedbyM3DLS[41]).Bothmethodsareautomatic

and based on 3-D level set implementation with the key differ-

ence in the active contour formulation and the optimization

functional. The proposed method achieved significantly higher

accuracies with an average improvement of 8.55% (p < 0.0001)

in WM and 10.18% (p < 0.0001) in GM segmentation similar-

ities. CSF results were not reported with the M3DLS method;

however,ourproposedapproachachievedconsiderable(>70%)

similarity. Furthermore, the segmentation results achieved by

M3DLS were conservative with low true positives. This can be

mainly attributed to the fact that the optimization functional in

M3DLS modeled each class as piecewise constant by taking

only the intensity square differences from the means. However,

variations within each segmented class are not considered, such

that if, intrinsically, WM contains significantly larger intensity

variance than GM, voxels belonging to WM would potentially

be mislabeled as GM if the voxel intensities are closer to the

estimated GM mean. This lead to undersegmentation in WM

(undersegmentation in GM is attributed to the known limitation

in the manual labels), and M3DLS is required to postprocess

the segmentation results by incorporating an additional mor-

phological dilation step [42]. On the other hand, by integrating

both geometric and statistical features into an edge-based de-

formablemodel,theproposedhybridapproachcapturesboththe

image edge geometry and the voxel statistical homogeneity, and

achieved higher segmentation accuracies with less additional

computation complexity.

D. Segmentation Performance Using Clinical MR Scans of MS

and AD Patients

Lastly, we applied the proposed method to segment clin-

ical MRI brain scans of MS and AD patients. The images

were segmented using a three-class (normal appearing WM,

GM grouped with diseased WM, and CSF) segmentation. The

qualitative results are shown in Fig. 5, demonstrating that the

proposed approach appears stable on clinical scans. Fig. 5(a)

shows a typical clinical MRI scan of a MS patient, whereas

Fig. 5(b) illustrates an example scan of a MS patient with en-

largedlateralventricles.Bothscansweresegmentedwithoutany

gross misclassifications. In addition, we demonstrated segmen-

tation results from an MRI scan where the brain extraction step

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1846 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

Fig. 5.

results obtained by using the proposed approach. We show two slices each for the three-class segmentation. White, light gray, and dark gray colors represent,

respectively, the normal appearing WM, GM grouped with diseased WM, and CSF classes in the segmentation labels. We note the approach is stable on (a) a

typical MS patient scan (TE/TR = 3.176/7.655 ms, TI = 450 ms, Flip Angle = 0◦), (b) an MS patient scan with enlarged ventricles (TE/TR = 4.000/11.000 ms,

TI = 0 ms, Flip Angle = 0◦), and (c) an MS patient scan with an inaccurate brain mask (TE/TR = 3.917/8.110 ms, TI = 0 ms, Flip Angle = 0◦). AD patient

scans at (d) year one (TE/TR = 3.95/9.124 ms, TI = 1000 ms, Flip Angle = 8◦) and (e) year two (TE/TR = 3.98/9.124 ms, TI = 1000 ms, Flip Angle = 8◦).

Qualitative segmentation performance of real clinical T1w brain images (UBC MS/MRI and LONI IDA) showing the raw images and the segmentation

inaccurately included part of the eyes in the brain mask in

Fig. 5(c). This error in the brain mask did not seem to cause

visible problems for the algorithm in the adjacent brain tissue.

Furthermore, Fig. 5(d) and (e) shows segmentation results of

scans from an AD patient one year apart. We again noticed vis-

ibly consistent segmentation in the tissue labels in the presence

of tissue atrophy/ventricle enlargement over time. In our T1w

test scans, the intensity difference between GM and diseased

WM is subtle, and separating these two class types is likely

not possible without additional MRI sequences that are more

sensitive to WM pathology, such as PDw or T2w, or relying on

prior probability maps such as those derived from a training set.

We have left these experiments for future work. In its current

form, the proposed method can potentially be used for the as-

sessment of disease severity by providing stable and consistent

segmentations of CSF and normal appearing WM.

IV. CONCLUSION

We proposed a 3-D brain MR segmentation method based on

deformable models and demonstrated accurate and stable brain

tissue segmentation on single as well as multiple MR sequence

scans. The main contribution of our work is that we employed a

geodesic active contour formulation by integrating both image

geometry and voxel statistics into a hybrid geometric–statistical

feature, which acts as a stabilizing regularizing function for the

extraction of complex anatomical features such as WM, GM,

and CSF. We validated our technique first by using both single

andmultiplesimulatedbrainMRIsequencedata.Improvedseg-

mentation accuracy and robustness were shown in results from

the proposed hybrid approach against those using individual ge-

ometric or statistical features only. Furthermore, on real clinical

MRI datasets, we also demonstrated improved accuracy over

a state-of-the-art approach, the region-based M3DLS. We also

demonstrated consistent and robust results when segmenting

MRI scans of both MS and AD patients.

Issues identified for possible future work include enhancing

the statistical distribution estimation process by using complex

intensitydistributionestimationmethodssuchasnonparametric

and partial volume models, and extending additional segmen-

tation classes, hierarchy or feature cues for segmentation of

anomalies such as WM lesions or tumors.

ACKNOWLEDGMENT

The authors thank the UBC MS/MRI Research Group

for data collection and sharing. In addition, ADNI (Prin-

cipal Investigator: M. Weiner; National Institutes of Health

(NIH) Grant U01 AG024904; a complete listing of investi-

gators is available at www.loni.ucla.edu/ADNI/Collaboration/

ADNI_Citation.shtml). ADNI was funded by the National In-

stitute on Aging, National Institute of Biomedical Imaging and

Bioengineering, Pfizer, Inc., Wyeth Research, Bristol-Myers

Squibb, Eli Lilly and Company, GlaxoSmithKline, Merck &

Company,Inc.,AstraZenecaAB,NovartisPharmaceuticalsCor-

poration,Alzheimer’sAssociation,EisaiGlobalClinicalDevel-

opment, Elan Corporation plc, Forest Laboratory, and ISOA,

with participation from U.S. Food and Drug Administration.

ADNI industry partnerships are coordinated through NIH with

the Veterans Health Research Institute (NCIRE) as the grantee

organization. ADNI study was coordinated by Alzheimer’s Dis-

ease Cooperative Study at University of California, San Diego.

ADNI data are disseminated by the LONI at University of Cal-

ifornia, Los Angeles (www.loni.ucla.edu/ADNI).

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Albert Huang (S’05) received the S.M. degree in

engineering science from Harvard University, Cam-

bridge, MA, in 2002, and the B.A.Sc. degree in elec-

trical and computer engineering in 2000 from the

University of British Columbia (UBC), Vancouver,

BC, Canada, where he is currently working toward

the Ph.D. degree at the Department of Electrical and

Computer Engineering.

From 2000 to 2004, he was an Algorithm De-

veloper at the Harvard Communications/Molecular

and Cellular Biology Laboratories, and Sony Taiwan

Limited. His current research interests include signal and image processing.

RafeefAbugharbieh(M’03)receivedtheBachelor’s

degree in electrical engineering from Jordan Univer-

sity, Amman, Jordan, in 1995, the Master’s degree

(with distinction) in digital communication systems

from Chalmers University, Gothenburg, Sweden, in

1997,andtheDoctoraldegreefromtheDepartmentof

Signals and Systems, Chalmers University, in 2001.

In2004,shejoinedasanAssistantProfessorinthe

Department of Electrical and Computer Engineering,

University of British Columbia (UBC), Vancouver,

BC, Canada., where she cofounded the Biomedical

Signal and Image Computing Laboratory (BiSICL), in 2005, and is currently

the Co-Director. Her current research interests include image processing and

analysis particularly in medical imaging applications.

Dr. Abugharbieh has been a member of the IEEE Engineering in Medicine

and Biology Society (EMBS) since 2003. She is also an Associate Founding

Member of the IEEE EMBS Vancouver Section (2004) and an Associate Editor

for Image and Vision Computing.

Roger Tam received the Ph.D. degree in computer

science from the University of British Columbia

(UBC), Vancouver, BC, Canada, in 2004.

He is currently an Assistant Professor in the De-

partment of Radiology, UBC, and is also a member

of the UBC MS/MRI Research Group, a pioneering

research laboratory in the field of MRI analysis for

the study of multiple sclerosis. His current research

interests include medical image processing, compu-

tational shape modeling, and scientific visualization.

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