3D multimodal MRI brain glioma tumor and edema segmentation: A graph cut distribution matching approach

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Computerized Medical Imaging and Graphics xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Computerized Medical Imaging and Graphics

j ourna l h om epa ge : www.elsev ier .com/ locate /compmedimag

D multimodal MRI brain glioma tumor and edema segmentation: graph cut distribution matching approach

nes Njeha,∗, Lamia Sallemia, Ismail Ben Ayedd, Khalil Chtouroua,e, Stephane Lehericyb,c,amien Galanaudb,c, Ahmed Ben Hamidaa

Advanced Technologies for Medicine and Signals, ENIS, Sfax University, TunisiaNeuroimaging Research Center: CENIRICM, Pitie Salpetriere Hospital, Paris, FranceDepartment of Neuroradiology, Pitie Salpetriere, Paris, FranceGE Healthcare, London, ON, CanadaDepartment of Nuclear Medicine, CHU Habib Bourguiba, Sfax, Tunisia

r t i c l e i n f o

rticle history:eceived 11 April 2014eceived in revised form 15 August 2014ccepted 16 October 2014

eywords:raph cut distribution matchingegmentationRI

rain tumor

a b s t r a c t

This study investigates a fast distribution-matching, data-driven algorithm for 3D multimodal MRI brainglioma tumor and edema segmentation in different modalities. We learn non-parametric model distri-butions which characterize the normal regions in the current data. Then, we state our segmentationproblems as the optimization of several cost functions of the same form, each containing two terms: (i) adistribution matching prior, which evaluates a global similarity between distributions, and (ii) a smooth-ness prior to avoid the occurrence of small, isolated regions in the solution. Obtained following recentbound-relaxation results, the optima of the cost functions yield the complement of the tumor regionor edema region in nearly real-time. Based on global rather than pixel wise information, the proposedalgorithm does not require an external learning from a large, manually-segmented training set, as is the

demaraTS2012

case of the existing methods. Therefore, the ensuing results are independent of the choice of a trainingset. Quantitative evaluations over the publicly available training and testing data set from the MICCAImultimodal brain tumor segmentation challenge (BraTS 2012) demonstrated that our algorithm yieldsa highly competitive performance for complete edema and tumor segmentation, among nine existingcompeting methods, with an interesting computing execution time (less than 0.5 s per image).

© 2014 Elsevier Ltd. All rights reserved.

. Introduction

Glioma tumor could be considered as a primary malignantrain tumor that could seriously threaten an important numberf patients, with a survival prognosis not exceeding one year forigh-grade glioma [1,2]. Such tumors are often accompanied witheritumoral edema, which corresponds to an extensive perifocalwelling [3]. Magnetic Resonance Imaging (MRI) is the main modal-ty for evaluating the pathological regions. Segmenting preciselyhe tumor and edema regions in MRI is, therefore, an essentialre-processing task towards thorough and reproducible diagnosis

Please cite this article in press as: Njeh I, et al. 3D multimodal MRI brainmatching approach. Comput Med Imaging Graph (2014), http://dx.do

f brain tumors. Manual segmentation could be so prohibitivelyime-consuming, and could never be reproducible during clini-al routines. Therefore, automatic or semi-automatic segmentation

∗ Corresponding author.E-mail addresses: [email protected], [email protected] (I. Njeh).

ttp://dx.doi.org/10.1016/j.compmedimag.2014.10.009895-6111/© 2014 Elsevier Ltd. All rights reserved.

algorithms would be highly recommended in order to surmountsuch disadvantages. Several past research studies investigated suchproblem [4–6] by segmenting both the tumor and the edemaregions in one or multiple modalities (T1,T1C,T2 and Flair), andthis remains yet a challenging task. Most of the existing algorithmsare still not fast and not flexible enough, especially for realisticclinical scenarios and needs. One could notice some difficultiesinherent to the brain tumor segmentation because, in general,brain tumors have shape and intensity characteristics that mayvary dramatically from one subject to another, which impedesbuilding reliable models from training data. For instance, the braintumor region shape may be arbitrary, and does not necessarilyfall within a category (or class) of shapes that could be learnedfrom one finite set of training subjects as is the case of most med-

glioma tumor and edema segmentation: A graph cut distributioni.org/10.1016/j.compmedimag.2014.10.009

ical image segmentation problems. Furthermore, in some cases,tumors might have intensity profiles that would be so similar tothe other normal regions within the considered image. The pastresearch studies addressed different variants for this segmentation

dx.doi.org/10.1016/j.compmedimag.2014.10.009


http://www.sciencedirect.com/science/journal/08956111

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roblem and several of them used multi-modal MRI [6,7]; otherorks used only a single modality [8,11]. Among studies, one couldotice that several of them focused only on the tumor as a targetegion [9,10,13], whereas others addressed both the tumor and thedema segmentation [11]. Most of the existing methods require aime-consuming external learning phase, which requires building aarge, manually-segmented training set [6]. In [6], the authors usedhree MRI modalities (T1,T1C and T2) and texture characteristicso construct a multi-dimensional feature set. Then, they learned

statistical model for tumor and normal tissues, thereby obtain-ng a 3D supervised segmentation of the brain tumor. Several othertudies addressed both edema and tumor in order to provide richerlinical information that could be somehow useful. For instance,he authors of [11] presented a Bayesian formulation for incorpo-ating soft model assignments so as to delimit brain tumor anddema. The study in [9] presented an unsupervised change detec-ion method based on gray level histograms for brain tumor anddema segmentation. Comparatively to our proposed approach,arious other tumor/edema segmentation algorithms were pre-ented at the MICCAI BraTS 2012 challenge. The authors of [5]sed a standard forest classification based on spatially non-localeatures along with initial probability estimates for individual tis-ue classes. The initial tissue regions probabilities were thereforeased on local intensity information alone, and one parametricMM-based model was used for the estimation step. Another com-etitor in the challenge [4] integrated random forest classificationith hierarchical conditional random field regularization within an

nergy minimization scheme. The authors of [19] presented a semi-utomatic tumor-cut algorithm. The user would be consequentlyequired to provide the maximum diameter of the edema regionisible on FLAIR images, and subsequently, a level set methodould be then used to segment the target regions. Although effec-

ive in some cases, such mentioned training-based algorithms coulde faced to one evident difficulty in extracting the substantialariations within tumor shape and intensity. The ensuing resultsepended on the characteristics, the variability, and the mathe-atical description of the training set. For instance, an unseen

umor different from all those within the training set may not beound.

In this work, we propose a novel distribution-matching, data-riven algorithm for 3D multimodal MRI brain glioma tumor anddema segmentation. We estimate a non-parametric model distri-ution that characterizes the normal regions in the current data.hen, we state our segmentation problems as the optimizationf several cost functions of the same form, each involving twoerms [15] (i) a distribution matching prior, which evaluates alobal similarity between distributions, and (ii) a smoothness prioro avoid the occurrence of small, isolated regions in the solu-ion. Obtained via recent bound-relaxation results, the optimaf the cost functions yield the complement of the tumor regionr edema region in nearly real-time. Based on global ratherhan pixel wise information, the proposed algorithm does notequire an external learning from a large, manually-segmentedraining set, as is the case of the existing methods. Therefore,he ensuing results are independent of the choice of a traininget. Quantitative evaluations over the publicly available train-ng and testing data set from the MICCAI Multimodal Brainumor Segmentation 2012 challenge (BraTS 2012) demonstratehat the proposed algorithm yields a competitive performance.ver the real data of the mentioned challenge, our algorithmas well ranked for complete edema and tumor segmentation

mong the nine competing methods [14]. Our work builds on


he Bhattacharyya-similarity bound derived by our co-author in preliminary conference paper [26]. The following lists the mainontributions of this study and the differences between our worknd [26]:

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(1) The main contribution of [26] is theoretical and focuses on theoptimization aspects of the work. Specifically, it details the deriva-tion of a bound of the Bhattacharyya measure, which allows usinggraph cuts. However, the proof-of-concept experiments in [26]were limited to color photographs and were based on an unre-alistic assumption where the model distribution is learned fromthe ground truth. There are no medical imaging applications in[26]. In this work, we extend the application of the Bhattacharyyabound to the real problem of 3D Multimodal MRI Brain GliomaTumor and Edema Segmentation.(2) We report completely novel results, including quantitativeevaluations/comparisons on the publicly available training andtesting data set from the MICCAI multimodal brain tumor segmen-tation challenge (BraTS 2012). The results demonstrate that theproposed algorithm can yield a highly competitive performanceamong nine other competing algorithms.(3) In this submission, we added new algorithmic components,which were designed specifically for multi-modal edema segmen-tation. The work in [26] cannot be applied directly to our problem;it did not consider any medical imaging application.(4) To the best of our knowledge, our work is the first to investigatethe idea of distribution matching in the context of brain tumorsegmentation. Furthermore, it is the first to design a distributionmatching algorithm in an interactive way, where the prior modelis learned interactively from the current image data. Unlike theexisting brain tumor segmentation methods, our work removesthe need for and dependence on extensive learning from a large,manually segmented training set. In practice, this is an importantadvantage over the existing brain tumor segmentation algorithms.

The remainder of this paper is arranged as follows. Section 2introduces the Multimodal Brain Tumor Segmentation Benchmark(BraTS2012 data). Section 3 describes the segmentation method-ology. Section 4 reports the experimental results and contains adiscussion. Finally, the conclusion’s section draws several perspec-tives of this work.

2. Materials: multimodal brain tumor segmentationbenchmark (BraTS2012 data)

The results reported in this research were based on approvedevaluations using the Multimodal Brain Tumor SegmentationBenchmark (BraTS 2012 data) [14]. This section describes in detailsthe data sets, notations and evaluation metrics that we used inthis work. The Multimodal Brain Tumor Segmentation data set wasintroduced in the MICCAI 2012 Challenge by B. Menze, A. Jakab, S.Bauer, M. Reyes, M. Prastawa and K. Van Leemput [14]. This largeand publicly available training and testing dataset was very usefuland allowed us to compare efficiently our algorithm to others par-ticipating in the challenge. In the remainder of the paper, we willrefer to this dataset as BraTS2012. We followed the standard evalu-ation protocol used for all algorithms via an online system providedby the Virtual Skeleton Database [17].

2.1. BraTS2012 data principle

BraTS2012 aims mainly at validating various segmentationapproaches by evaluating and comparing 3D MRI brain tumor andedema segmentation algorithms. Segmenting brain tumors frommulti-modal imaging data is one of the most challenging tasksin medical image analysis due to their unpredictable appearance


and shape. Although many different segmentation approaches havebeen proposed in the literature during the past few years, it wouldbe so hard to compare the existing methods because the validationdatasets that could be used could differ widely in terms of input


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ata regarding specifically structural MRI contrasts; MRI perfusionr MRI diffusion data... Other difficulties could be related to the typef lesion as it could be primary or secondary tumors; solid lesionr infiltrated growing lesion, as well as the state of the pathologypre- or post-treatment). In order to surmount some difficultiesegarding the current state-of-the-art in automated brain tumoregmentation and assure possible comparisons between differentethods, a Multimodal Brain Tumor Segmentation (BraTS2012)

hallenge has been organized in conjunction with the MICCAI 2012onference. For this purpose, a large dataset of brain tumor MRIcans was hence available in which the tumor and edema regionsave been manually delineated. In fact, the ground-truth seg-entations for tumor and edema for training data as well as the

uantitative evaluation results were seriously studied.

.2. Training data sets

A publicly available set of training data could be downloadedrom Kitware/MIDAS [17] or from the Virtual Skeleton Database16]. The training data regroups real and simulated data. It consistsf multi-contrast MRI scans (T1, T2, FLAIR, and post-Gadolinium T1)f both low grade and high grade glioma patients with expert anno-ations for “active tumor” and for “edema”. The simulated imageslosely follow the conventions used for the real data, except thatheir names start with “SimBraTS”.

Each MRI modality is characterized by (i) the Repetition TimeTR), which represents the time between successive applications ofadiofrequency pulse sequences, and (ii) the Echo Time (TE), whichepresents the delay before the radiofrequency energy radiated byhe tissue in question is measured. The T1-weighted modality (T1)s characterized by a short TR and a short TE. This Provides betternatomic details. The T2-weighted modality (T2) is characterizedy a long TR and a short TE. It is more sensitive to water content and,s a result, more sensitive to pathology. The Fluid Attenuated Inver-ion Recovery (FLAIR) modality is characterized by a long TR and ahort TE. It removes the signal from the cerebrospinal fluid (CSF),hereby allowing a clearer visualization of the cerebral edema.he T1-weighted with gadolinium contrast agent (T1C) modalitys characterized by the enhancement of the malignant tumor dueo the contrast agent.

All MRI scans and ground truth segmentations are stored usingnsigned 16 bit and unsigned 8 bit integers, respectively. All vol-mes were linearly co-registered to the T1 contrast image, skulltripped, and interpolated to 1mm isotropic resolution. The MRIcans were distributed in the ITK and VTK compatible formatnd stored as signed 16-bit integers, but only positive valuesould be used. The manual segmentations (file names ending bytruth.mha”) have only three intensity levels: 1 for edema, 2 forctive tumor, and 0 for everything else.

The total number of training cases is 80, including:

25 High-Grade simulated images: SimBraTS HG. A number is fur-ther added to denote each of the cases, e.g., SimBraTS HG0001 forthe first case;25 Low-Grade simulated images: SimBraTS LG;20 Real High-Grade images: BraTS HG; and10 Real Low-Grade images: BraTS LG.

.3. Testing data sets

This testing data is similar to the training data, except that the


eference segmentations are not publicly available. Automated seg-entations should be uploaded directly to the evaluation page to

btain dice metric scores. The total number of testing data is 30 andould be referred as follows:

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• 10 High-grade simulated images: BraTS Challenge Sim HighGrade;

• 5 Low-grade simulated images: BraTS Challenge Sim Low Grade;• 11 Real high-grade images: BraTS Challenge High Grade; and• 4 Real low-grade images: BraTS Challenge Low Grade.

In summary, BraTS2012 is a very heterogeneous and diversifieddataset and, therefore, could be considered as a very realistic testingbenchmark.

2.4. Evaluation metric and top-ranked methods

We performed quantitative evaluations using the well-knownDice Metric (DM) [18] by computing the affinities between ground-truth segmentations provided with BraTS2012 dataset and theobtained results. DM takes values within the interval [1], where1 indicates a perfect match and 0 a complete mismatch. For thetesting data, the ground-truth segmentations were not publiclyavailable. However, automated segmentations should be uploadeddirectly to the evaluation page to obtain dice metric score [17].

The challenge training data results highlight four top-rankedmethods [5,4,12,19]. The authors of [5] presented an automaticalgorithm based on learning a model of intensity for each patientin order to determine the initial probabilities. They used a classi-fication forest (CF) with spatially non-local features to representthe data, and estimated tissue classes by providing the CF withinitial probabilities. The study in [4] presented a fully automatedalgorithm using random forest classification with hierarchical con-ditional random field regularization in an energy minimizationscheme. The method presented in [12] built on the discriminativerandom decision forest framework to provide a voxel-wise proba-bilistic classification of the volume. The authors in [19] presenteda semi-automatic method, where the user should draw manuallya diameter to define the foreground region and a box limiting thebackground region [19]. The method computes tumor and back-ground strengths, and use a level set surface to delineate the tumor.All the results obtained on the BraTS2012 dataset were made avail-able on the challenge website. In the rest of this paper, we will referto the algorithms in [4,5,12,19] as Bauer et al., Zikic et al., Geremiaet al. and Hamamci et al., respectively. These methods will be usedin our comparisons to demonstrate the performance of the pro-posed method on the training dataset. For the testing data, we usedthe online tool provided by the Virtual Skeleton Database.

2.5. Notations

Because we use multi-modal MRI, we need to denote eachmodality. We will use notation Ii, where i ∈ (T1, T2, T1C, FLAIR). IT1denotes the T1 modality, IT2 the T2 modality, IT1C the T1C modal-ity and IFLAIR the FLAIR modality. The ground-truth segmentationof each case will be denoted by GT added to the case type andnumber, e.g., GTHG0001 (Fig. 1). Before describing the segmenta-tion processes, let us first consider the following definitions andnotations:

• SRT1 is the segmentation result obtained for T1 modality imageIT1;

• SRT2 is the segmentation result obtained for T2 modality imageIT2;

• SRT1C is the segmentation result obtained for T1C modality image


• SRFLAIR is the segmentation result obtained for FLAIR modalityimage IFLAIR.

• ISumFLAIRT1C is the summation of SRT1C and image IFLAIR as shown in

Fig. 2 and could be defined by:


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Fig. 1. BraTS HG000l from the BraTS

SumFLAIRT1C = SRT1C + IFLAIR (1)

‘+’ represents the normalized summation process.We can also define:

ISumT1T1Cis the summation of SRT1C and image IT1

ISumT2T1Cis the summation of SRT1C and image IT2

ISumT1CT2 is the summation of SRT2 and image IT1C

ISumT1T2is the summation of SRT2 and image IT1

ISumFLAIRT2 is the summation of SRT2 and image IFLAIR

. Graph cut distribution matching

In this section, we describe the different steps of our approachor brain tumor and edema segmentation, which is based on distri-ution matching and is tested and validated using BraTS2012. Firstf all, we present a complete and convivial flow chart that describeshe process; See Fig. 3.

.1. Flowchart of the proposed multimodal brain tumor/edemaegmentation algorithm

As depicted in Fig. 3, the MRI modalities are used as follows:he T1C modality is used for high grade tumor segmentation, the2 for low grade tumor segmentation and the FLAIR modality fordema segmentation. The latter could involve both high and lowrade tumor and would necessitate one preprocessing stage.

The tumor region presents different gray level intensities com-ared to the normal brain tissue. Therefore, we can define twoifferent parts: �I , which represents the normal part (Fig. 4) and


I, which represents the searched tumor region. From the normalart, we estimate a non-parametric model distribution of intensityI. Such a model would be then a prior that contains all the statis-

ical information about the image within the normal regions in the

Fig. 2. Illustration of the s

ataset (same patient, axial slice 88).

considered brain image. The main step of the algorithm consists offinding within the suspected tumor region RI a sub-region whoseintensity distribution most closely matches the learned model,i.e. MI. We extract then the normal part from the infected one,and therefore the targeted tumor region. We state the problemas the optimization of an energy function containing (1) an inten-sity distribution matching prior that measures a global similaritybetween non-parametric distributions, and (2) a smoothness priorthat avoids the occurrence of small, isolated regions in the solution.

3.2. Brain tumor segmentation formulation: high/low grade

For high or low grade brain tumor segmentation, image I couldbe one of the following inputs:

I ∈ {IT1C, ISumT1CT2 , ISumT1C

T1 , ISumT1CFLAIR} for high gradet umor (2)

I ∈ {IT2, ISumT2T1C, ISumT2

T1, ISumT2FLAIR} for low grade tumor (3)

let I : �I ⊂ DI ⊂ Rn(n ∈ {2, 3}) → ZI be an image function

defined from a fixed domain �I to the space ZI of intensity val-ues. DI is the whole domain of image I. �I would be a subset ofthe whole image domain containing the tumor. Fig. 4 shows a typ-ical T1C example in which the blue line is used to divide the wholeimage domain DI into two parts. In this example, �I correspondsto the right-hand part of the image and represents the suspiciouspathological part (i.e., the part that contains the suspected tumor).

�I = DI \ �I denotes the complement of �I within DI, whichrepresents the normal part (i.e., not including the tumor region).MI(z) would be the kernel density estimate for the gray level dis-


tribution of image I within �I .

∀z ∈ ZI MI(z) =∑

p∈�IK(z)

A(�I)(4)

ummation process.


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ig. 3. Flowchart of the multimodal brain tumor/edema segmentation algorithm.

where A(�I) denotes the area (or volume) of �I (i.e., the numberf pixels/voxels within the region), and K(z) is a kernel function,


ypically Gaussian:

(z) = 1√2��2

exp

(− (z − �)2

2�2

), (5)

ig. 4. Illustration example for High Grade brain segmentation example (BraTS2012ataset). (For interpretation of the references to color in text, the reader is referredo the web version of this article.)

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where � is the kernel width and � is the expected value.MI is a prior model, which contains all the statistical informa-

tion about image I within the normal regions. The main step of thealgorithm consists of finding within �I (i.e., the abnormal part) aregion RI whose intensity distribution most closely matches modelMI (Refer to Fig. 4 for a typical example). We obtain therefore thenormal part, which represents the non-tumor region in �I. Thisyields the searched tumor region: �I \ RI. We state the problem asthe minimization of a discrete cost function with respect to a binarylabeling LI : �I →

{0, 1

}, which defines a variable partition of the

image domain: RI ={

p ∈ �I |LI(p) = 1}

, corresponding to the nor-

mal part, and RI = {p ∈ �I/LI = 0} = �I \ RI , corresponding to thetumor region. The optimal labeling is obtained by minimizing aglobal cost function containing a non-linear distribution matchingconstraint based on the Bhattacharyya measure and a smoothnessconstraint. To introduce the cost function, let us first introduce thefollowing notations for any binary labeling LI : �I →

{0, 1

}:

• PRIis the Kernel Density Estimate (KDE) of the distribution of

image data I within RI region.

∀z ∈ ZI PRI(z) =

∑p∈RI

K(z)

A(RI)(6)

where A(RI) denotes the area (or volume) of RI.• BZ(f, g) is the Bhattacharyya coefficient, which measures the

amount of overlap between two distributions f and g defined overa set of values ZI:

BZ(f, g) =∑z∈ZI

√f (z)g(z) (7)

The algorithm consists of finding an optimal labeling LoptI that

minimizes the following cost function:

LoptI = argmin

LI :�I→{0,1}FI(LI), (8)

with

FI(LI) = −BZ(PRI, MI)︸︷︷︸

Distribution matching

+ �S(LI)︸︷︷︸Smoothness

(9)

S(LI) is a smoothness prior, which regularizes the segmentationboundary [6]:

S(LI) =∑

{p,q}∈N

rp,qıLI (p) /= LI (q) (10)

with

ıx /= y ={

1 if x /= y

0 if x = y,and rp,q = 1

‖p − q‖ (11)

N is some neighborhood system containing all pairs {p, q} neigh-boring elements in �I. The smoothness prior (or regularization)avoids the occurrence of small, isolated regions in the solution. �is a positive constant that balances the relative contribution of thedistribution matching term and the regularization term. Lopt

I givesan optimal boundary-smooth region, Ropt

I = {p ∈ �I/LoptI (p) = 1},

whose intensity distribution most closely matches MI. This optimalregion would be expected to correspond to the non-tumor regionor non-edema region in �I. Therefore, the tumor (or edema) regionwould be finally computed from Lopt

I as follows:

opt opt


SRI = �I \ RI = {p ∈ �I/LI (p) = 0} (12)

The distribution matching term in (9) is a higher-order (non-linear)functional, which is difficult to optimize [20,21]. It has an ana-lytical form that cannot be directly amenable to fast optimizers




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Brain edema segmentation is an additional step within ourdeveloped system, where we could clearly differentiate the tumorregion from the edema region, an output highly demanded in clin-

Fig. 5. Edema

uch as graph cuts [22] or convex-relaxation techniques [23]. In theegmentation literature, such non-linear terms are commonly opti-ized via standard gradient-descent procedures, e.g., active curves

nd level sets [24,25], which result in computationally intensivelgorithms [26]. In this work, we use the recent bound optimizationesult in [26]. Rather than optimizing directly the initial functionali.e. the Bhattacharyya coefficient in our case), one can solve aequence of easier sub-problems, each corresponding to a boundf the functional.

A(u, ui) is an auxiliary function of a cost function FI(u) if it satisfieshe following conditions:

I(u) ≤ A(u, ui), i > 1 (13)

I(u) = A(u, u) ∀u ∈{

0, 1}

(14)

e optimize iteratively a sequence of instrumental functions,enoted A(u, ui), i ≥ 1 in which i represents the iteration numbernd whose optimization is easier than FI(u):

i+1 = argminu∈{0,1}

A(u, ui), i≥1 (15)

sing the equality and inequality conditions in the definition ofuxiliary function, one can easily show that the obtained sequence


f solutions yields a decreasing sequence of the original functionI(u):

I(ui) = A(ui, ui)≥A(ui+1, ui)≥FI(ui+1) (16)

ocessing step.

Furthermore, the original function is lower bounded and, therefore,the sequence of solutions converges to a minimum of FI(ui).

The authors of [26] derived an auxiliary functional of theBhattacharyya measure. They further showed that such auxiliaryfunctional is amenable to fast graph-cut optimization using theBoykov–Kolmogorov algorithm [22]. The bound-optimization pro-cess in [26] converges within a few iterations (typically less than5).

In this work, we use the auxiliary functional in [26] and theBoykov-Kolmogorov algorithm [22]. Further details on this auxil-iary functional and bound optimization can be found in [26]. Also,the graph-cut algorithm of Boykov and Kolmogorov [22] is wellestablished in the computer vision literature. Therefore, we omitthe details of graph cut optimization here.

3.3. Brain edema segmentation


ical practices. According to the conceived algorithm, one coulddesign the same segmentation process but beginning with a pre-processing step necessary for FLAIR modality so as to clarify theedema shape.


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.3.1. PreprocessingTo segment the brain edema, we proceeded to the following

reprocessing steps on IfinalFLAIR so as to create a new image (refer to

ig. 5 for the details of creating image IfinalFLAIR):

We create an intermediate image IinterFLAIR defined by

IinterFLAIR = SRT1C + IFLAIR (17)

Let IsymVFLAIR be the image obtained from IFLAIR by vertical symmetry

and IsymHFLAIR the image obtained from IFLAIR by horizontal symmetry.

We create a new image ImultFLAIR defined by:

ImultFLAIR = SRT1C · IsymV

FLAIR

if the tumor is within one hemisphere

ImultFLAIR = SRT1C · IsymH

FLAIR

if the tumor is shared by the two hemispheres

(18)

Finally, we define IfinalFLAIR as follows:

IfinalFLAIR = Imult

FLAIR + IinterFLAIR (19)

.3.2. SegmentationWe used the same distribution matching process to obtain an

ptimal region EedemaFLAIR . Finally, edema segmentations for high grade

nd/or low grade tumors could be obtained as follows:

demaHGFLAIR = Redema

FLAIR · SRT1C (20)

demaLGFLAIR = Redema

FLAIR · SRT2 (21)

In the end of this edema segmentation process, we have to definehese following images in order to segment brain edema in thether image modalities (IT1C, IT1 and IT2):

ISumFLAIRT1 = SRfinal

FLAIR + IT1

ISumFLAIRT1C = SRfinal + IT1C (22)


FLAIR

ISumFLAIRT2 = SRfinal

FLAIR + IT2

here SRfinalFLAIR is the tumor segmentation result obtained in Ifinal

FLAIR.

ig. 7. Tumor and edema segmentation (SimBraTS HG000l) (a) tumor (blue curve) segmdema ground truth (green curve) on the IT1C; (b) tumor (blue curve) segmentation, edemruth (green curve) on the IT2 image; (c) tumor (blue curve) segmentation, edema (red cgreen curve) on the IFLAIR image; (d) tumor (blue curve) segmentation, edema (red curve)urve) on the IT1 image. (For interpretation of the references to color in this figure legend

Fig. 6. An example for High Grade edema segmentation (BraTS2012 dataset).

Then, we use the same distribution matching process with thefollowing image inputs:

I =

⎧⎪⎨⎪⎩

ISumFLAIRT1C for segmenting the T1C modality;

ISumFLAIRT1 for segmenting the T1 modality;

ISumFLAIRT2 for segmenting the T2 modality.

(23)

4. Segmentation methodology implementation

In this section, we report quantitative evaluations of the pro-posed methodology over the publicly available training data setfrom the Multimodal Brain Tumor Segmentation 2012 challenge(BraTS 2012). Also, we report comparisons with the top rankedmethods in the challenge [5,4,12,19]. This section would be fur-ther supported by several visual illustrations, which would depicttypical examples of the obtained results using the different typesof images in the data set. We also give plots that would detail theobtained performance for each case in the data set. The Mean DiceMetric “MDM” was chosen as a measure of such performance (seeSection 2.4). The implementation results for the training data wouldbe presented first followed by the implementation for the testingdata and this would be followed by discussions on these exper-imental results. As an important and valuable procedure for eachimplementation (training as well as testing datasets), we had optedfor the simulated cases first, followed by the real cases (Fig. 6).

4.1. Tumor and edema segmentation: training data


4.1.1. Simulated training dataWe present several segmented MRI images as visual examples,

along with a detailed performance evaluation in term of DM mea-sure obtained for the training data. Fig. 7 depicts the segmentation

entation, edema (red curve) segmentation, tumor ground truth (yellow curve) anda (red curve) segmentation, tumor ground truth (yellow curve) and edema groundurve) segmentation, tumor ground truth (yellow curve) and edema ground truth

segmentation, tumor ground truth (yellow curve) and edema ground truth (green, the reader is referred to the web version of this article.)




Fig. 8. Tumor and edema segmentation with the (SimBraTS LG 0023) (a) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellowcurve) and edema ground truth (green curve) on the IT2 image; (b) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellow curve) andedema ground truth (green curve) on the IT1 image; (c) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellow curve) and edemaground truth (green curve) on the IT1C image; (d) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellow curve) and edema groundtruth (green curve) on the IFLAIR image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Ft

orobt

ma

Fig. 10. Dice Metrics for the SimBraTS LG data.

Faegt

ig. 9. Dice Metrics for the SimBraTS HG data. (For interpretation of the referenceso color in text, the reader is referred to the web version of this article.)

btained on the third case of SimBraTS HG, and Fig. 8 shows theesult of case 23 in SimBraTS LG. The blue curve illustrates thebtained tumor boundary, the red curve corresponds to the edemaoundary, the yellow curve involves the tumor ground truth and


he green curve corresponds to the edema ground truth boundary.For the methodology performance, we evaluated the DM

easure for the simulated cases involving 25 SimBraTS HG as wells 25 SimBraTS LG pathologies from the training dataset. Fig. 9

ig. 11. Tumor and Edema Segmentation (BraTS HG0003 Case) (a) tumor (blue curve) send edema ground truth (green curve) on the IT1C image; (b) tumor (blue curve) segmedema ground truth (green curve) on the IT2 image; (c) tumor (blue curve) segmentationround truth (green curve) on the IFLAIR image; (d) tumor (blue curve) segmentation, edemruth (green curve) on the IT1 image. (For interpretation of the references to color in this

illustrates the mean Dice Metrics as functions of the case numberfor high grade tumor (blue) and edema (red). Fig. 10 illustratesthe Dice Metrics for the low grade cases. The proposed algorithmscored a mean Dice Metric measure for complete tumor and edemasegmentation higher than 0.86 for the simulated high grade cases


and higher than 0.84 for the simulated low grade cases.

gmentation, edema (red curve) segmentation, tumor ground truth (yellow curve)ntation, edema (red curve) segmentation, tumor ground truth (yellow curve) and, edema (red curve) segmentation, tumor ground truth (yellow curve) and edemaa (red curve) segmentation, tumor ground truth (yellow curve) and edema ground

figure legend, the reader is referred to the web version of this article.)



I. Njeh et al. / Computerized Medical Imaging and Graphics xxx (2014) xxx–xxx 9

Fig. 12. Tumor and edema segmentation (BraTSL G000l case) (a) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellow curve) andedema ground truth (green curve)on the IT2 image; (b) tumor (blue curve) segmentation, edema (red curve) segmentation, tumor ground truth (yellow curve) and edemag edema (red curve) segmentation, tumor ground truth (yellow curve) and edema groundt (red curve) segmentation, tumor ground truth (yellow curve) and edema ground truth( is figure legend, the reader is referred to the web version of this article.)

4

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Fig. 14. Dice metrics for the BraTS LG data.

Table 1Overall DM quantitative evaluations (simulated training data).

Mean dice SIMBRATS HG SIMBRATS LG

Tumor Edema Tumor Edema

Zikic et al. [5] 0.9 0.65 0.71 0.55

round truth (green curve) on the IT1 image; (c) tumor (blue curve) segmentation,

ruth (green curve) on the IT1C image; (d) tumor (blue curve) segmentation, edemagreen curve) on the IFLAIR image. (For interpretation of the references to color in th

.1.2. Real training dataWe present several segmented MRI images as visual examples,

long with a detailed performance evaluation in term of DM meas-res. Fig. 11 depicts the segmentation obtained on the first case ofraTS HG, and Fig. 12 depicts the result of the first case in BraTS LG.he blue curve illustrates the obtained tumor boundary whereashe red curve corresponds to the edema boundary. The yellow curvenvolves the tumor ground truth and the green curve correspondso the edema ground truth.

For the methodology performance, we evaluated the DM mea-ure for the 20 BraTS HG real cases as well as for the 10 BraTS LGeal cases from the training dataset. Fig. 13 illustrates the meanice metrics as functions of the case number for high grade tumor

blue) and edema (red). Fig. 14 illustrates the Dice metrics for theow grade cases.

For complete tumor and edema segmentation, the proposedlgorithm scored a mean Dice Metric measure higher than 0.89 forimulated high grade cases and higher than 0.88 for simulated lowrade cases.

.1.3. RecapitulationTables 1 and 2 report the results of our algorithm and the

ethods in [5,4,12,19] respectively on simulated and real train-


ng data. The mean Dice Metrics in Tables 1 and 2 demonstrate aery competitive performance of the proposed algorithm, whichutperformed all top-ranked methods on both synthetic and realraining data. For instance, within the set of real data, the proposed

ig. 13. Dice metrics for the BraTS HG data. (For interpretation of the references toolor in text, the reader is referred to the web version of this article.)

Bauer et al. [4] 0.9 0.68 0.74 0.54Geremia et al. [12] – – – –Hamamci et al. [19] 0.8 0.43 0.55 0.14Proposed method 0.95 0.84 0.91 0.86

Bold value are used to highlight the results.

algorithm scored a mean Dice metric (DM) higher than 0.80 for allcases (edema/tumor and low grade/high grade), whereas the best


performance attained before by the competing algorithms is DM= 0.73.

Table 2Overall DM quantitative evaluations (real training data).

Mean dice BRATS HG BRATS LG

Tumor Edema Tumor Edema

Zikic et al. [5] 0.71 0.7 0.62 0.44Bauer et al. [4] 0.62 0.61 0.49 0.35Geremia et al. [12] 0.68 0.56 0.52 .0.29Hamamci et al. [19] 0.73 0.56 0.71 0.38Proposed method 0.89 0.84 0.86 0.82

Bold value are used to highlight the results.




Fig. 15. Tumor and edema segmentation (BraTS Challenge Sim High Grade of case 168) (a) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT1C

image; (b) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT2 image; (c) tumor (blue curve) segmentation and edema (red curve) segmentationon the IFLAIR image; (d) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT1 image. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 16. Tumor and edema segmentation (BraTS Challenge Sim Low Grade of case 155) (a) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT1C

i the Io gmenl

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We present several segmented MRI images as visual examples,along with a detailed performance evaluation in term of the DMmeasures obtained for the real testing data. Fig. 19 depicts the seg-mentation obtained on the third case of BraTS Challenge High Grade

mage; (b) tumor (blue curve) segmentation and edema (red curve) segmentation onn the IFLAIR image; (d) tumor (blue curve) segmentation and edema (red curve) seegend, the reader is referred to the web version of this article.)

.2. Tumor and edema segmentation: testing data

In this part, we present quantitative evaluations of the proposedlgorithm over the testing dataset from the MICCAI Multimodalrain Tumor Segmentation 2012 live challenge. We report alsoomparisons with several other methods competing over the chal-enge data. This section is further supported by several visualllustrations, which depict typical examples of the obtained resultssing the different types of testing images. We also give plots thatetail the obtained performance for each case in the data set. Wesed the mean Dice Metric as a measure of performance. Such aeasure is computed with the online Virtual Skeleton Database

valuation tool.

.2.1. Simulated testing dataWe present several segmented MRI images as visual exam-

les, along with a detailed performance evaluation in term of thebtained DM measures. Fig. 15 depicts the segmentation obtainedn case 168 of BraTS Challenge Sim High Grade, and Fig. 16 showshe result of case 5 in BraTS Challenge Sim Low Grade. The blueurve illustrates the obtained tumor boundary and the red curveorresponds to the edema boundary.

For the methodology performance, we evaluated the DM mea-ure for the 10 BraTS Challenge Sim High Grade as well as for the


BraTS Challenge Sim Low Grade from the testing dataset. Fig. 17llustrates the Dice metrics as functions of the case number for highrade tumor (blue) and edema (red). Fig. 18 plots the Dice metricsor the low grade cases.

T2 image; (c) tumor (blue curve) segmentation and edema (red curve) segmentationtation on the IT1 image. (For interpretation of the references to color in this figure

For complete tumor and edema segmentation, the proposedalgorithm scored a mean Dice Metric measure higher than 0.91 forsimulated high grade cases and higher than 0.84 for simulated lowgrade cases.

4.2.2. Real testing data


Fig. 17. Dice metrics for the BraTS Challenge Sim Low Grade data. (For interpretationof the references to color in text, the reader is referred to the web version of thisarticle.)



I. Njeh et al. / Computerized Medical Imaging and Graphics xxx (2014) xxx–xxx 11

0lb

sCD(gp0c

Fig. 21. Dice metrics for the BraTS Challenge High Grade data. (For interpretationof the references to color in text, the reader is referred to the web version of this

Fiol

F(It

Fig. 18. Dice metrics for the BraTS Challenge Sim High Grade data.

119, and Fig. 20 shows the result of the first case in BraTS Chal-enge Low Grade0109. The blue curve depicts the obtained tumoroundary and the red curve corresponds to the edema boundary.

For the methodology performance, we evaluated the DM mea-ure for the 11 BraTS Challenge High Grade as well as for the 4 BraTShallenge Low Grade from the testing dataset. Fig. 21 illustrates theice metrics as functions of the case number for high grade tumor

blue) and edema (red). Fig. 22 plots the Dice metrics for the low


rade cases. For complete tumor and edema segmentation, the pro-osed algorithm scored a mean Dice Metric measure higher than.9 for real high grade cases and higher than 0.64 for real low gradeases.

ig. 19. Tumor and edema segmentation (BraTS Challenge High Grade 0119 case) (a) tumage; (b) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT

n the IFLAIR image; (d) tumor (blue curve) segmentation and edema (red curve) segmenegend, the reader is referred to the web version of this article.)

ig. 20. Tumor and edema segmentation (BraTS Challenge Low Grade 0109 case) (a) tumob) tumor (blue curve) segmentation and edema (red curve) segmentation on the IT2 imagFLAIR image; (d) tumor (blue curve) segmentation and edema (red curve) segmentation ohe reader is referred to the web version of this article.)

article.)

4.2.3. RecapitulationTable 3 reports the results of our algorithm and the other com-

petitors. The final results can be found at the Virtual SkeletonDatabase BraTS 2012. We used both real (BraTS Challenge High


Grade and BraTS Challenge Low Grade) and simulated (BraTS Chal-lenge Sim High Grade and BraTS Challenge Sim Low Grade) datafrom the BraTS2012 testing dataset. The mean Dice metrics in

mor (blue curve) segmentation and edema (red curve) segmentation on the IT1C

2 image; (c) tumor (blue curve) segmentation and edema (red curve) segmentationtation on the IT1 image. (For interpretation of the references to color in this figure

r (blue curve) segmentation and edema (red curve) segmentation on the IT1C image;e; (c) tumor (blue curve) segmentation and edema (red curve) segmentation on then the IT1 image. (For interpretation of the references to color in this figure legend,


ARTICLE ING ModelCMIG-1319; No. of Pages 12

12 I. Njeh et al. / Computerized Medical Imagi

Fig. 22. Dice metrics for the BraTs Challenge Low Grade data.

Table 3Quantitative evaluations and comparisons on testing data.

Dice mean Real cases Simulated cases

Subbana et al. [27] 0.75 –Zikic et al. [5] 0.75 0.91Hamamci et al. [19] 0.72 –Menze et al. [28] 0.69 –Zhao et al. [29] 0.76 –Bauer et al. [4] 0.66 0.87Geremia et al. [12] 0.62 0.83Shin et al. [30] 0.3 0.34Proposed method 0.77 0.88

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old value are used to highlight the results.

able 3 demonstrate a very competitive performance of the pro-osed algorithm.

. Conclusion

The major difficulty for brain tumor and edema segmentationrocess in medical image analysis is due to their unpredictableppearance and shape. Some of the earlier MRI brain tumor anddema segmentations did not rigorously test their segmentationethods on common databases such as BraTS2012. Most of theethods reported in the literature need a heavy and external

raining and, therefore, are time consuming and dependent of apecific choice of training data. An accurate and efficient method-logy was developed and validated. Our algorithm provides anutomatic segmentation of both brain tumor and its edema usingultimodal MRI scans (T1,T1C,T2 and FLAIR). This methodologyas carefully conceived and was based on a graph cut distributionatching methodology that yielded a competitive performance.

ased on distribution matching criteria, the proposed algorithmemoves the need an external learning from a large, manually-egmented training set, unlike most of the existing methods.he main purpose behind this research was of course to makerogress for clinical actions especially those necessitating sev-ral debates and clarifications. Clinical decisions and guidelinesould be hence so more exact when such regions of interest are

xtracted. Besides, such a convivial clinical aided tool could save lot of time during clinical practices with more accuracy andbjectivity.

Our results obtained over MRI scans from the BraTS2012 data


ets show that the proposed segmentation process, developed foroth brain tumor and edema, promise to serve as an efficient andonvivial clinical tool. Future research will involve several improve-ents regarding image quality or image artifacts that could affect

[

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PRESSng and Graphics xxx (2014) xxx–xxx

sometimes gray levels. Besides, in some low grade glioma, theregions of interest undergo low contrasts, which could affect thesegmentation results. The latter difficulty deserves further atten-tion.

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3D multimodal MRI brain glioma tumor and edema segmentation: A graph cut distribution matching approach