paper for histrogram feature and glcm feature

Applied Soft Computing 13 (2013) 26682682

Contents lists available at SciVerse ScienceDirect

Applied Soft Computing

j ourna l ho me p age: www.elsev ier .co

Two fu imSOM-b

A. Ortiza . Lla Department ob Department o ainc Virgen de las

a r t i c l

Article history:Received 1 DeReceived in reAccepted 24 November 2012Available online 6 December 2012

Keywords:Image segmentationMRINeural networSelf-organizinFeature extracGenetic algori

tioninrate

demvariety of image segmentation approaches have been implemented before. Nevertheless, most of themuse a priori knowledge about the voxel classication, which prevents guring out other tissue classesdifferent from the classes the system was trained for. This paper presents two unsupervised approachesfor brain image segmentation. The rst one is based on the use of relevant information extracted from thewhole volume histogram which is processed by using self-organizing maps (SOM). This approach is faster

1. Introdu

Many cuuation and on the medmagnetic reits excellencharacter. Mprovide a vauation of thperformed time-consu

Generallbased on ththe human

CorresponE-mail add

1568-4946/$ http://dx.doi.oksg mapstionthms

and computationally more efcient than previously reported methods. The second method proposedconsists of four stages including MRI brain image acquisition, rst and second order feature extractionusing overlapping windows, evolutionary computing-based feature selection and nally, map units aregrouped by means of a novel SOM clustering algorithm. While the rst method is a fast procedure for thesegmentation of the whole volume and provides a way to model tissue classes, the second approach is amore robust scheme under noisy or bad intensity normalization conditions that provides better resultsusing high resolution images, outperforming the results provided by other algorithms in the state-of-the-art, in terms of the average overlap metric. The proposed algorithms have been successfully evaluatedusing the IBSR and IBSR 2.0 databases, as well as high-resolution MR images from the Nuclear MedicineDepartment of the Virgen de las Nieves Hospital, Granada, Spain (VNH), providing in any case goodsegmentation results.

2012 Elsevier B.V. All rights reserved.

ction

rrent problems in image-guided surgery, therapy eval-diagnostic tools strongly benet from the improvementical imaging systems at reduced cost [1]. In this way,sonance imaging (MRI) has been widely used due tot spatial resolution, tissue contrast and non-invasiveoreover, modern medical imaging systems [2] usuallyst amount of images to be analyzed. The study and eval-ese images are usually developed through visual ratingsby experts and other subjective procedures which areming and prone to error.y, MRI images are qualitatively analyzed by expertseir own experience and skills, but it is always limited byvision system which it is not able to distinguish among

ding author.ress: [email protected] (J.M. Grriz).

more than several tens of gray levels. However, as current MRI sys-tems can provide images up to 65,535 gray levels, there is muchmore information contained in a MRI than the human vision is ableto extract. This way, computer aided tools (CAD) play an importantrole for analyzing high resolution and high bit-depth MRI images,as they provide an important source of information for radiologistswhen diagnosing a disease or looking for a specic anomaly.

Segmentation of MR images consists in identifying the neuro-anatomical structures within medical images or splitting an imageinto its constituent parts [31]. Brain segmentation techniques, asa part of CAD systems, can be used to characterize neurologicaldiseases, such as dementia, multiple sclerosis, schizophrenia andeven the Alzheimers disease (AD) [3]. In the case of AD, there isno a well-known cause and it is very difcult to diagnose. Withthe improvements of MR imaging systems, the image processingtechniques as well as the discovery of new biomarkers, neurologi-cal disorders such as AD are expected to be diagnosed even beforethe manifestation of any cognitive symptoms [57,58]. Thus, seg-mentation of brain MRI enables nding common patterns in AD

see front matter 2012 Elsevier B.V. All rights reserved.rg/10.1016/j.asoc.2012.11.020lly-unsupervised methods for MR brainased strategies

, J.M. Grrizb,, J. Ramrezb, D. Salas-Gonzlezb, J.Mf Communication Engineering, University of Malaga, Malaga, Spainf Signal Theory, Networking and Communications, University of Granada, Granada, SpNieves Hospital, Granada, Spain

e i n f o

cember 2010vised form 17 August 2012

a b s t r a c t

Image segmentation consists in partiis especially interesting, since an accuidentify many brain disorders such asm/l ocate /asoc

age segmentation using

amas-Elvirac

g an image into different regions. MRI image segmentationsegmentation of the different brain tissues provides a way toentia, schizophrenia or even the Alzheimers disease. A large

A. Ortiz et al. / Applied Soft Computing 13 (2013) 26682682 2669

patients such as hippocampal volume or cortical gray matter den-sity reduction. Furthermore, these techniques could help to ndother causes of brain disorders or anomalies. In fact, the segmen-tation algorithms presented in this paper are part of a larger studyperformed early diagn

The devedifferent aning interestThese toolsclasses foun(GM) and csues or uidway the huon the MR i

There arcan be classniques. Manused for yebelonging tmentation, techniques.

The mosemiautom[8,9,16,22],machine (SHistogram-sists in deteorder to sepprevious traimages. Seguse the factsue [35]. Ththe peaks anbased segmrelative poshistogram [mentation ainformationinformationare more liferent MR ithresholds.

Other setechniques for segmenwitt, Laplacdifferent obfor active co

In regionrithm startsproperties ssearch for vgeometrica

Statisticthe groupinvoxels in aninto the samor learned iclass. Then contains grstatistical calgorithms [16] or Markas Fuzzy k-min the classi

Support vector classiers [40] are a new type of classiers basedon statistical learning theory which have been successfully appliedto image segmentation [20] due to its generalization ability. Othersegmentation techniques are based on articial neural network

ers [ent

ttersing ffectroup

abovefereeral f

but ]. In [e ste: (i) snallyKohosteped anethodMR i

mma

his wethohistoeferrypes e opBouhe Ser D

in th secows, aach

of m] in olecte

theectoroton a lpaceOM urouped by

be d. Thc clusing as deve acc

metedgervisecesalgorovera

papals ationsSectiby the authors on the use of tissue distribution for theosis of AD [57,58].lopment of effective tools for grouping and recognizingatomical tissues structures and uids, is a eld of grow-

with the improvement of the medical imaging systems. are usually trained to recognize the three basic tissued on a brain MR image: white matter (WM), gray mattererebrospinal uid (CSF). All of the non-recognized tis-s are classied as suspect to be pathological. In the sameman expert has to learn to recognize different regionsmage, the segmentation algorithms have to be trained.e a wide range of brain segmentation techniques. Theyied into manual, semiautomatic and automatic tech-ual techniques are the most common and have been

ars. They require a human expert to select the voxelso a specic object individually. In semiautomatic seg-the human expert is usually aided by image processing

st common image processing techniques used foratic segmentation are histogram-based techniques

statistical classiers, fuzzy classiers, support vectorVM) classiers, and neural network-based classiers.based techniques are based on thresholding, which con-rmining the thresholds of the voxel intensity values inarate the voxels belonging to each class. This requires aining process of the system using expert segmentationmentation techniques based on histogram thresholding

that the peaks on histogram can belong to a specic tis-us, the problem is reduced to classifying and modelingd valleys on the histogram. There are other histogram-entation techniques which also take into account theition of the peaks or other statistics calculated from the36,37]. Nevertheless, the histogram thresholding seg-pproaches usually do not take into account the spatial

contained on a MR image. On the other hand, spatial is essential since anatomical regions of the brain [18]kely to accommodate a given tissue. As a result, dif-mages could have similar histograms and then, similar

gmentation approaches are based on contour detection[10,11], using the boundaries among different tissuestation. Edge detection algorithms such as Sobel, Pre-ian or Canny lters [31] select the border voxels amongjects. These lters generally perform the preprocessingntour algorithms [12].-based techniques [13] once a voxel is marked, the algo-

to add more voxels surrounding it, preserving someuch as homogeneity or intensity level. Other algorithmsoxels belonging to the initial class following a specicl model [38].al classiers use some previous learned rules to performg. These are called clustering techniques which classify

unsupervised manner, since they group similar voxelse class. Thus, a similarity criterion has to be established

n order to determine whether a voxel belongs to a giventhe classier [4] will generate different classes whichoup of voxels with the same properties. Some of thelassiers are based on the expectation-maximization(EM) [1,14,15], maximum likelihood (ML) estimationov random elds [13,17]. K-means and its variants sucheans are widely used as they avoid abrupt transitions

cation process [19].

classiAs m

as a paprocesmore evoxel gall thefrom r

Sevposed,[1,57in threniquesand, Fuzzy a two-removtion mto the

1.1. Su

In ttion mimage SOM, rprototpute thDaviesThus, tthe lowtissue

Thewindofrom emeans[32,55The seto traininput vber of pspace iinput seach Sto be gresenthave todenegenericlusterSOM) iuses th

Theknowlunsupeis not nas the of the

Thematerisubsecwork; 2127], such as self-organizing maps (SOM) [2326,28].ioned before, segmentation of MR images can be seenn classication and recognition problem. Thus, a pre-stage is necessary in order to make the segmentationive as well as a post-processing stage for ensuring theing algorithm is performed correctly. On the other hand,e segmentation methods use some a priori knowledgence images [5].ully-automated segmentation methods have been pro-most of them also use reference images for training5], an automatic segmentation framework which worksps is presented. It uses a combination of different tech-kull-stripping, (ii) intensity inhomogeneity correction, (iii) classication of the brain tissue by means of anens Competitive Learning algorithm (F-KCL). In [6]

algorithm is presented. In the rst step, the noise isd in the second step, an unsupervised image segmenta-

based on fuzzy C-means clustering algorithm is appliedmage in order to partition it into distinct regions.

ry and organization

ork, we present two different MR image segmenta-ds. The rst one uses information from the volumegram to compose feature vectors to be classied by aed as HFS-SOM method in the following. Then, SOMare clustered by a k-means algorithm. In order to com-timum k value for the best clustering performance, thelding index (DBI) [47] is computed for several trials.OM prototypes are grouped into k clusters providingBI, and each of these clusters corresponds to a differente image.nd method splits the acquired images into overlappingnd computes rst and second order statistical featureswindow. A feature selection process is performed byulti-objective optimization using a genetic algorithmrder to select the most discriminative set of features.d features compose the feature vectors used as inputs

SOM. During the training stage, the SOM projects thers into a two dimensional space and computes a num-types. These prototypes are a generalization of the inputower number of vectors, meaning the quantization the. SOM is a clustering algorithm itself, and it considersnit as a cluster [33]. Nevertheless, similar units haveed as voxels belonging to the same tissue can be rep-

similar prototypes [33]. This way, the SOM prototypesclustered and the borders between clusters have to bee computation of these borders can be addressed by atering algorithm such as k-means, or by a specic SOMlgorithm [46]. In this work, a specic algorithm (i.e. EGS-ised to improve the segmentation performance whichumulated entropy to cluster the SOM units.hods described in this paper do not use any a priori

about the voxel classication, and result in fully-ed methods for MRI image segmentation. In addition, itsary to indicate the number of tissue classes to be found,ithms compute this number maximizing the goodnessll clustering process.er is organized as follows: Section 2 presents thend methods used in this work. It is divided into four; Section 2.1 describes the image databases used in thison 2.2 shows the pre-processing stage which is common

2670 A. Ortiz et al. / Applied Soft Computing 13 (2013) 26682682

to the two segmentation approaches; Section 2.3 presents a fasterimplementation of the method which uses information extractedfrom the image histogram for segmentation of the whole vol-ume and; Section 2.4 shows a high resolution approach for imageslices. Sectithe evaluatand discussconclusions

2. Materia

This sectsegmentatito evaluate tation refer

2.1. Databa

In ordertion approasegmentatiInternet Brsachusetts provides ma set of maT1-weighteweighted vand processthe Massacroutines alrison metricsegmentatidatabase wto compareimages fromalgorithm. FMR images Nieves Hoevaluate th

2.2. Image

Once thperformed ground. Bra(i.e. skull anhave been dtor (BSE), BStrip (McStstructures aertheless imscalp/skull been extrac

In orderbuilt by detmultiplyingvoxels and ground in blosing voxedescribed b

2.3. Fast vo

Fig. 1 suthis paper: and (ii) the

the main characteristics of the proposed algorithms, regarding thetype of image features, the learning paradigm (i.e. supervised orunsupervised), and the feature selection method. In this Section,the HFS-SOM segmentation method which uses statistical features

ted fr

A histly, es th

nformid prelinging ], whan die us

ypes ion 22 volam fas thedivid

imat conond

tograpi), umbindoindo

mi,

SOM his wsingixtu

aks aativee the

spaese vagonion 3

SOMta maing t

arg

x(t), vect

U(tted. totyo upd

1) =

(t) orhoand types f the

e

(on 3 depicts the experimental results obtained fromion of the proposed methods using the IBSR databasees the main questions derived from them and. Finally,

are drawn in Section 4.

ls and methods

ion consists of three subsections which summarize theon methods and the image databases used in this workthe proposed methods, which include manual segmen-ences considered as the ground truth.

ses

to check the performance of our image segmenta-ch in comparison with other existing methods, manualon labeling of the processed databases is required.ain Segmentation Repository (IBSR) from the Mas-General Hospital [25] is suitable for this purpose, as itanually guided expert segmentation results along withgnetic resonance images. Thus, IBSR 1.0 provides 20d volumetric images and IBSR 2.0 set provides 18 T1-olumetric images that have been spatially normalizeded by the Center for Morphometric Analysis (CMA) athusetts General Hospital with the biaseld correctioneady applied. On the other hand, the overlap compar-

is provided for each volume for comparing differenton methods. Consequently, images from the IBSR 1.0ere used to compute the average overlap metric in order

to other previously proposed algorithms. In addition, IBSR 2.0 are also used to assess the performance of oururthermore, an image set consisting of high resolutionfrom the Nuclear Medicine Service of the Virgen de lasspital, Granada, Spain (VNH) are also used in order toe proposed segmentation algorithms.

preprocessing

e MR image has been acquired, a pre-processing isin order to remove noise and clean-up the image back-in tissue extraction from undesired structures removald scalp) can be done at this stage. Several algorithmseveloped for this purpose such as Brain Surface Extrac-rain Extraction tool (BET) [56], Minneapolis Consensusrip) or Hybrid Watershed Algorithm (HWA) [5]. Thesere already removed from the ISBR 1.0 database. Nev-ages provided by IBSR 2.0 are distributed without the

already removed. In the latter database, the brain hasted in the pre-processing stage using BET.

to remove background noise, we use a binary mask,ecting the greatest contiguous object in the image. After

the binary mask (which contains 0 at the background1 otherwise) by the original image, we get the back-lack. Moreover, the image is centered in order to avoidls when using the sliding window technique as furtherelow in this Section (see Fig. 1).

lume image segmentation by HFS-SOM

mmarizes the two segmentation methods proposed in(i) the fast volume segmentation algorithm (HFS-SOM)

EGS-SOM algorithm (EG-SOM). Table 1 summarizes

extrac

2.3.1. Firs

describvides ito avoin modimprov[4345Gaussiwork, wprototin SectIBSR 1histogrputed image on thesince icorresp

Hisities ((bin nbins wthat w(pi, bi,SOM.

2.3.2. In t

types uusing mthe pecrimin

Oncfeaturetion, th2D hexin Sect

Thethe daaccord

U(t) =

wheretotypevectoris updathe proare als

i(t +

whereneighbfactor protothood o

hui(t) =om the volumetric image histogram is presented.

togram computationthe volume image histogram is computed, whiche probability of occurrence of voxel intensities and pro-ation regarding different tissues. A common approach

ocessing the large number of voxels in a MR consists the intensity values as a nite number of prototypes,the computational effectiveness. This is addressed inere the voxel intensities are modeled by a mixture of

stributions [43,44] or -stable distributions [45]. In thise a SOM to model intensity values by a nite number ofcorresponding to the number of map units, as described.3.2. Fig. 2a shows the rendered brain surface from theume using SPM8 [41] and Fig. 2b shows the computedor the whole volume. The probability of each bin is com-

frequency of occurrence of that intensity in the volumeed by the total number of different intensities presentge. Finally, the 1st bin is removed from the histogramtains all the background voxels. Thus, only informationing to the brain is stored.m data including the intensity occurrence probabil-the relative position regarding the intensity valueer, bi), the mean of the probability values over a 3-w centered on the bin i (mi) and the variance ofw (2

i) are used to compose the feature vectors F =

2i), pi, mi, 2i R, bi Z, which are the inputs of the

modelingork, voxel intensities are modeled by the SOM proto-

the information contained in the histogram instead ofres of probability density functions. This aims to modelnd valleys of the image histogram as they retain dis-

information for voxel classication. volume image histogram has been computed and thece has been composed as shown in the preceding sec-ectors are used as inputs for training a SOM [33] with aal grid since it tted better the feature space as shown.

algorithm can be summarized as follows. Let X Rdnifold. The winning unit is computed in each iterationo:

mini{x(t) i(t)} (1)

x X, is the input vector at time t and i(t) is the pro-or associated to the unit i. The unit closer to the input) is referred as winning unit and the associated prototypeTo complete the adaptive learning process on the SOM,pes of the units in the neighborhood of the winning unitated according to:

i(t) + (t)hUi(t)(x(t) i(t)) (2)

is the exponential decay learning factor and hUi(t) is theod function associated to the unit i. Both, the learninghe neighborhood function diminish with time and theadaptation process becomes slower as the neighbor-

unit i contains less number of units.

(ruri2/2(t)2))

(3)

AshokHighlight


Fig. 1. Block diagram of the segmentation method process.

Table 1Comparison of the proposed methods.

Method Based on Learning algorithm Feature selection Main characteristic

HFS-SOM Image histogram Unsupervised Computational cost and precision tradeoffEGS-SOM Statistical image descriptors Unsupervised GA Resolution/noise immunity

Eq. (3) sthe positiobetween thneighborhoeach iteratiwinning unhand, (t) ceach iterati

(t) = 0e(

In the SOhedron. In othree dimenput layer) ilocated clostance). Thisspace are acluster the

Initializainto accounThe prototyto a width tprincipal cothat the rsally to the

ed pre ops tra

the r the

the arianing. Toidsinings. Ad onam.

the c qualans oant trminld (i.e am

eservans oerroata v

errohows the neighborhood function, where ri representsn on the output space and rU ri is the distancee winning unit and the unit i on the output space. Theod is dened by a Gaussian function which shrinks inon as shown in Eq. (4). In this competitive process, theit is named the Best Matching Unit (BMU). On the otherontrols the reduction of the Gaussian neighborhood inon according to a time constant 1.

t/1) (4)

M, each prototype i is the centroid of its Voronoi poly-ther words, SOM projects the prototypes into a two orsional space (depending on the dimension of the out-

n such a way that the most similar the prototypes areer in the output space (in terms of the Euclidean dis-

way, the prototypes and their location on the output valuable source of information which can be used toSOM [45].tion of the SOM prototypes is performed linearly, takingt the eigenvalues and eigenvectors of the training data.pes are arranged into hexagonal lattices (correspondinghat is proportional to the standard deviation of the rstmponent) [33,34]. This initialization method impliest dimension of the prototypes is arranged proportion-rst principal component and the second dimension is

arrangonce thwork iduring

Aftetors ofunity vwhitenmap avthe trafeaturegroupehistogrputing

Theby meimportto detemanifodistancogy prby mezation each dlogicalFig. 2. Rendered brain surface extracted from IBSR 12 volume (aoportionally to the second principal component. Thus,timal number of map units has been estimated, the net-ined linearly. All the above calculations are performedmap initialization process.

map is initialized, it is trained using the feature vec-reduced feature space normalized for zero mean andce. This normalization procedure is also known as datahe normalization of the vectors used for training the

one dimension to have more inuence than others on process due to the different nature of the extracted

s a result of the training process, a set of prototypes the SOM layer models the features of the volume imageIndeed, a classication process is accomplished by com-losest prototype for each voxel.ity of the map determines the representation of the dataf the prototypes computed during training. Then, it iso measure of the goodness of the trained map in ordere (i) the distance between the prototypes and the datae. the prototypes generalizes the input data) and (ii) theong similar prototypes in the output space (i.e. topol-ation). The quality of the trained map can be evaluatedf two measures. These two measures are the quanti-r (te), which determines the average distance betweenector and its Best Matching Unit (BMU) and the topo-r (qe), which measures the proportion of data vectors) and computed histogram (b).


Fig. 3. Similarfor IBSR 12 vo

for which quantizatioand (6) resp

te = 1N

Ni=1

u

qe =N

i=1xi

In Eq. (5)and the sec(6) the quanon the inputo the best values of tepreservatiois to say, thtopological

2.3.3. SOM The outp

number of which modtering algorHowever, stered as beSOM prototThis way, kthe prototy

The DBIresults, is coof the clustSOM units. and the numferent sizessize of the ed as the result after 3 clusters (k

DBI is usAn image cCSF) shouldare expectevalidity indmanually se

The clusspecic clasof voxels, thvoxel is lab

on the MRI). Fig. 4 shows several slices of the segmented IBSR 12volume following the described method.

S-SOM segmentation

aimsing

shows th

sectam i

a set

Featuhis sted toe of ulatiize pctors is ationlassi

thenseq

the tion

statand she grond

differder

winw is mtainindo

ted fiffereenss. Thfeatu. Thiss f =us a

the otheher

i afteppedder f

ity ity coloring graph (a) and k-means clustering of the SOM (b). Resultslume.

rst and second BMUs are not adjacent units. Both, then error and the topological error are dened by Eqs. (5)ectively.

(xi) (5)

bxi (6)

, N is the total number of data vectors, u(xi) is 1 if the rstond BMU for xi are non-adjacent and 0 otherwise. In Eq.tization error is dened where xi is the i-th data vectort space and b i is the weight (prototype) associatedmatching unit for the data vector xi. Therefore, lowerand qe implies better data representation and topologyn, which is equivalent to better clustering result. Thate lower values on the quantization error (qe) and the

error (te) the better the goodness of the SOM [33,42].

clustering and voxel classicationut layer of a trained SOM is composed by a reducedprototypes (the number of units on the output layer)el the input data manifold. Although SOM is a clus-ithm itself, it considers each unit as a single cluster.imilar units represent similar data and must be clus-longing to a group. Thus, it is necessary to cluster theypes in order to dene the borders between clusters.-means algorithm is used to cluster the SOM, groupingpes into k different classes.

[47], which gives lower values for better clusteringmputed for different k values to provide a measurementering validity. Fig. 3a shows the similarity graph for theIn this gure, the most similar units have similar colorsber of activations of each unit is represented with dif-

(the higher the number of activations, the greater theunit). This way, cluster borders can be visually identi-smaller units. In addition, Fig. 3b shows the clusteringcomputing the clusters with the k-means algorithm for

2.4. EG

Theprocescess issame ain thishistogrputing

2.4.1. At t

extracpurposby calcrecognture vefeatureinformgood cclassifyand, corole inmenta

Theorder from tthe secamong

In olappedwindoels coneach wextracby a da D-dimfeatureof the servedvector

Let whereOn the[1,G], wimage overlarst or

Intens = 3).ed to determine the k value for the k-means algorithm.ontaining only the three basic tissues (WM, GM and

provide the lowest DBI for k = 3. More than 3 classesd to be found in the image when a lower value of theex is given for k > 3. Nevertheless, the k-value can belected as the number of expected tissues.ters on the SOM group the units so that they belong to as. As each of these units will be the BMU of a specic sete clusters dene different voxel classes. This way, eacheled as belonging to a class (i.e. a tissue or uid present

Mean =

Variance

Howevedependencprovide texbe taken in of this method is to achieve higher resolution images byindividual slices from a volume. The segmentation pro-n in Fig. 1, where the initial pre-processing stage is the

e one described in Section 2.2. The method describedion is also based on SOM for voxel classication, butnformation from the image volume is replaced by com-

of discriminative features.

re extractiontage, some signicant features from the MR image are

be subjected to selection and classication. The mainthe feature extraction is to reduce the original data setng some properties that can be used to classify and toatterns included in the input images. As a result, a fea-

which dimension is equal to the number of extractedobtained. These features should retain the essential

and should be different enough among classes for acation performance. Moreover, the features used to

voxels on each image may depend on the specic imageuently, the feature extraction process plays a decisive

classication performance and thus, in the overall seg-process.istical features used in this work are classied into rstecond order features. First order features are deriveday level of a specic voxel and its neighborhood andorder features are derived from the spatial relationshiprent voxels.

to extract features from the image, a sliding and over-dow of size x y is moved along the image. As thisoved voxel-wise, we obtain as many windows as vox-

ed in the image. Then, a feature set is computed fromw and referred to the central voxel. The feature set

rom each window describes each voxel in the imagent feature vector. Thus, the feature vectors belong toional feature space, where D is the number of extractedis procedure is slower than the one that uses the meanres for each window, however image resolution is pre-

way, the original image is converted into a set of feature [f1,f2, ..., fD] belonging to the feature space F R24.ssume we have an image of dimension M N voxels,intensity is a function i(x,y) being x,y space variables.r hand, the function i(x,y) can only take discrete valuese G = max(i(x,y)) is the maximum intensity level in ther quantization. Let also assume we split the image into

windows of size x y. Then we dene the followingeatures:

I = i(x, y) (7)

1xy

xx=1

yy=1

i(x, y) (8)

2 = 1(xy 1)

xx=1

yy=1

(i(x, y) ) (9)

r, these features do not take into account the spatiale among the voxels in a window. Therefore, they do nottural information. Spatial relationship among voxels can

to account using:


Fig. 4. Segmen 0 (d). B(For interpreta b vers

a) Textural ods suchsum and[29] procompute

The mbeing anposed indiscrimi

The Goccurrincan be m

pxy (i, j)

At theability m[31] (see

The seentropy,sum avemomentshade, dtion for tthis pape

b) Moment under sccation computeto classiincludedway thaselectedselected

Once tthe featuof vectorfeatures.containe

2.4.2. FeatuThe orig

to be reducthe set of ifeature spacof a genetic

The GA uzation and tas lower vamize the goprocess). Oof features

secorovidy funf 5 feent

s. feaeratizatioplishted timple ovees ofg alghm [3he imtion n ord

avaiindiction lectiostic uon ofed croan fu

tneremeor (tens wtive he fu

.5

e pen

FQT +

p is tring

featn thien, td antation results for IBSR2 volume #12, axial plane, slice 130 (a), 140 (b), 150 (c) and 16tion of the references to color in this gure legend, the reader is referred to the we

features. They can be computed using different meth- as Gray-Level Co-Occurrence Matrix (GLCM) or through

difference histograms of each window. Haralick et al.posed the use of 14 features for image classication,d using the GLCM structure.ost signicant features depend on the specic imagealyzed. Thus, we computed all the textural features pro-

[29,36] and, afterwards, the most signicant and mostnative features will be selected.LCM structure represents the distribution of co-g gray values at a given offset. For an image Im, the GLCMathematically dened as:

=n

p1=0

mp2=0

{1 if Im(P1, P2) = i and Im(P1 + x, P2 + y) = j

0 otherwise

same time, px(i) is the i-th entry in the marginal prob-atrix. This matrix is computed by means of

Gj=1p(i, j)

Appendix A for further details).t of second order features we have used are energy,

contrast, angular second moment (ASM), mean,rage, autocorrelation, correlation, inverse difference, maximum probability, cluster prominence, clusterissimilarity and variance. The mathematical formula-hese features is detailed in the Appendix at the end ofr.invariants. In [29,30], a set of parameters invariantaling and rotation are introduced for image classi-and recognition. In our case, the moment invariantsd from each window centered on each voxel are usedfy different tissues on the MR image. Thus, we have

seven moment invariants dened in [29]. In the samet rst and second orders explained above have to be, the most discriminative moment invariants will be.he above features have been computed, we constructre vector. This feature set is contained in RD and consistss of dimension D, where D is the number of extracted

In our case, D = 24, and therefore, the feature space isd in R24.

re selectioninal set of features calculated on the previous step, hased in order to select the most discriminative ones formages considered. In this work, the dimension of the

order, time ppenaltmum oor momproces

Theeach itquantiaccompresendone saveragaveragtraininalgorit

In tpopulamask ithe 24

As populaThe sestochatributiscatterGaussi

Themeasucal errfunctiotiobjecThen, t

FQT = 0

and th

Fp =

wheremask s

Thecated iand thevolvee is reduced using evolutionary computation by means algorithm (GA).sed for feature selection tries to minimize the quanti-opological errors of the SOM described in Section 2.3.2,lues of quantization and topological errors tend to opti-odness of the SOM (i.e. a better quality of the clusteringn the other hand, we have noticed that less numberusually provides lower error values but keeping rst

GA iterationnumber of converged (verges to aconverges ness functioby the GA error in therown, orange and green correspond to WM, GM and CSF respectively.ion of this article.)

nd order and moment invariant features at the samees better segmentation results. Therefore, we used action to prioritize those solutions which have a mini-atures and at least one per type (rst order, second order

invariants), imposing a constraint in the optimization

ture selection process requires training a SOM inon as the evaluation of the tness function uses then error and topological error. This training process ised by a batch training algorithm which the data set iso the SOM as a whole, and vector weight updating isy by replacing the prototype vectors with a weightedr the samples. Thus, new weight vectors are weighted

the data vectors [33,34]. This method, known as batchorithm is considerably faster than the sequential training3].plementation of the feature selection algorithm, the

is encoded using a binary vector which acts as a featureer to select at least ve features (at least, 5 bits from

lable in the vector should be set to 1).ated in [32] GAs should perform better for moderatesizes, although it depends on the specic application.n algorithm used consists of a modied version of theniform selection [31] which provides a uniform dis-

the population. The crossover is implemented throughssover technique [32], and the mutation operator uses anction for p-distribution which shrinks in each iteration.ss function shown in Eq. (10) uses equally weightednts of the quantization error (qe) and the topologi-). This method, consisting in assigning weights to thehich can be minimized at the same time is usual in mul-optimization problems [32] with compatible objectives.nction to be minimized is:

qe + 0.5 te (10)

alty function modies the tness value according to:

FQTp n (11)

the penalty factor and n is the number of bits on the.ure selection process is summarized in Fig. 5. As indi-s gure, the SOM is trained using the initial populationhe map quality is computed. This initial population isd the SOM is initialized and trained again (i.e. a new

) until the stop conditions are reached: the maximumallowed generations is reached, or the algorithm hasi.e. the map quality is no longer improved, and GA con-

stable value for the tness function). The algorithmin less than 200 generations using the proposed t-n. Indeed, after 200 generations, the solution proposedis the same during a number of trials. Moreover, the

tness function for 50 runs is always below 3%, and


Initial

populationSOM training

Map Quality

evaluation

GA Iteration

Maximum number

of generations or

GA convergence?yes

no

Selected

Features

Fig. 5. Feature selection process.

the optimization mechanism is robust enough to guarantee therepeatability of the optimized feature sets.

Fig. 6 presents the evolution of the tness function averagedover 50 runs, showing that GA is able to escape from local minima.

2.4.3. EGS-SOnce the

use the vectice is usedexplained in

As in theto zero mewith a randselection of

The traintors, providto the neargroup vectopoint, the vcould be shdifferent reit would mity among vthe clustersout a clear bresults baseclustering afor SOM clucalculated iground voxcorrespond

map units are calculated and the voxels associated are assigned toan image segment as shown in Fig. 7.

Other procedure devised in this work in order to improve theresolution of the clustering method consists in using the featurevectors asso

ent ahe pally,

ed in prooces

witproceed on

theing i

y) =

q. (12culatplanHm. T

) =

1 = OM clustering dimension of the feature space has been reduced, wetors of this space for training a SOM. A hexagonal lat-

on the SOM layer and the map size is determined as Section 2.3.

HFS-SOM algorithm the feature vectors are normalizedan and unit variance [33,34]. The vectors are selectedom permutation distribution in order to weight up the

background vectors.ing stage performs a classication of the feature vec-

ing a map in which different units have been associatedest feature vector. Thus, different regions on the maprs from the feature space with similar features. At thisoxels whose vectors are associated to each map regionown together in an image as we have as many tissues asgions found during the classication stage. Neverthelessix different tissues into one image due to the similar-oxels belonging to different partitions. In other words,

on the map have to be redened in order to gureorder among different segments. This way, we presentd on two approaches. On the one hand, a 2-neighborpproach is used. This approach consists of three stepsstering calculation. In the rst step, a hit histogram isn order to remove the map units with more hits. As back-els are included in the classication process, these units

to the background. Then, the 2-neighbors to the other

suremNext, tand nincludto eachThis prdealingtering includculatescluster

Hd(x,

In Efor calimage called

Hm(x, y

whereFig. 6. Example of evolution of the tness function.ciated to each prototype to compute a similarity mea-mong the vectors belonging to the rest of prototypes.rototypes are sorted in ascending order of the contrast,

the feature vectors associated to each prototype are a cluster. Each time a new group of voxels belongingtotype is added to a cluster, the entropy is calculated.s is repeated until a threshold on the entropy is reached,h the lowest DBI, as it maximizes the quality of the clus-ss. Therefore, all voxels belonging to the feature vectors

a cluster form an image segment. This procedure cal- direction of the EGS-SOM from each map unit and thes delimited using the opposite direction.

Wxi=1

Wyj=1

P(x,y)d

(i, j) log(P(x,y)d

(i, j)) (12)

), and d are the direction and the distance respectivelying the GLCM [29], and (x,y) are the coordinates in ae. The mean entropy computed for all the directions ishus,

4

k=1Hkd(x, y) (13)

0 o , 2 = 45o , 3 = 90

o , 4 = 135o , and d = 1.Fig. 7. 2-Neighbor clustering approach.


Subimage-i

Contrast

Calculation

Sort

subimages by

ascending

contrast

Add

subimage-i to

segment s

Compute

entropy

H(i)

Add

subimage-

(i+k) to

segment s

Compute

entropy

H(i+k)

Add

subimage-

(i+k+1)

segment s

Compute

entropy

H(i+k+1)

H(i+k)>H(i+k+1)

H(i+k)


Fig. 10. EGS-SOM accumulation trajectory example. (For interpretation of the ref-erences to color in the text, the reader is referred to the web version of this article.)

intensity normalized, but scalp and skull are not already removedfrom the image. This way, it is necessary to use the BET tool toextract the brain and to remove undesirable structures. We alsoused images with a higher resolution (512 512 512 voxels) pro-vided by VNH. These images contain the scalp and skull, and weused them

As in andepends onmap is usuIn fact, it of units muestimation map units =samples. This calculateof the autoimportant is the initiaof the SOMing the eig

Table 2Genetic algorithm parameters.

GA parameter Value

Encoding type Binary vectorPopulation size 30Crossover probability 0.8Mutation probability 0.03Selection algorithm Modied stochastic uniform selection [32,55]Crossover algorithm Scattered crossover [32,55]Mutation algorithm Gaussian with p-distribution [32,55]

the orientation of the eigenvectors corresponding to the twolargest eigenvalues provides the directions in which the train-ing data exhibits the most variance. Nevertheless, the map sizehas to be experimentally ne-tuned in order to improve the per-formance of the classication algorithm. The optimal map sizefor the analyzed images was 8 8 units for both, EGS-SOM andHFS-SOM segmentation methods and the SOM was trained using5000 iterations.

In the case of the EGS-SOM method, a sliding window of 7 7voxels is used as it has been determined to be larger enough tocapture textural features without losing resolution (i.e. while largerwindow sizes tend to loose resolution, smaller ones lose texturalinformation).

Regarding the feature selection process involved in the EGS-SOM method, the GA set-up parameters are shown in Table 2.

Fig. 11 depicts the image formation from the subimages byadding the voxels associated to each prototype, when the EGS-SOM

hm is applied to a high resolution MR image from VNH. Inn, thnit obott

to tttomold wto tharizond

perim

13ae 100

Fig. 11. Subimas they come to test our algorithms.y SOM-based system, the classication performance

the map size. This way, the number of units on theally set a priori in order to avoid map under-sizing.is not recommended to use a map with a numberch less than the training samples [33,34]. An initialof the number of map units is given by the formula

5 d1/2 [33,34], where d is the number of traininge ratio between the two dimensions of the map sized as the ratio between the two largest eigenvalues-correlation matrix of the training data [34]. Anotherissue which determines the performance of the SOMlization of the map. In this work linear initialization

weights is used [34]. This is addressed by comput-envectors and eigenvalues of the training data, since

algoritadditioeach utop to spondsand bothreshadded the bincorresp

3.2. Ex

Fig.volumages and accumulated entropy. Figures are top to bottom and left to right in increasing ee resulting subimages when voxels corresponding ton the cluster are added to the tissue, are shown fromom and left to right. Thus, top most left image corre-he less entropy when only a subimage has been added

most right corresponds to the accumulated entropyhen subimages 1, 34, 39, 49, 19, 3, 16 and 35 have beene tissue as indicated in Fig. 10. This way, Fig. 12 showsed version of Fig. 11 when subimage 35 is added. Thiss to WM.

ental results and discussion

and b shows the segmentation results for the IBSR 23 using the HFS-SOM algorithm and the EGS-SOMntropy order. The indicated subimage is added to the segment.


Table 3Mean and standard deviation of the Tanimotos performance index for the segmentation methods on Fig. 14.

Segmentation algorithm Ref. WM index GM index CSF index

Manual (4 brains averaged over 2 experts) [35] 0.832 * 0.876 * *EGS-SOM 0.70 0.04 0.70 0.04 0.22 0.08Constrained GMM (CGMM) [50] 0.68 0.04 0.66 0.06 0.20 0.06MPM-MAP [17] 0.66 0.10 0.68 0.10 *HFS-SOM 0.60 0.1 0.60 0.15 0.1 0.05Adaptive MAP (amap) [35,51] 0.57 0.13 0.58 0.17 0.07 0.03Biased MAP (bmap) [35,51] 0.56 0.17 0.58 0.21 0.07 0.03Maximum a posteriori probability (map) [35,52] 0.47 0.11 0.57 0.20 0.07 0.03Tree-structure k-means (tskmeans) [35,53] 0.48 012 0.58 0.19 0.05 0.02Maximum likelihood (mlc) [35,54] 0.54 0.16 0.57 0.20 0.06 0.03* Data not available in the source.

Fig. 12. Binarized WM segment (from Fig. 10, when subimage 35 is added to thesegment).

algorithm, respectively. In these images, WM, GM and CSF areshown for sExpert segm

Visual cground trutfast volumeand Table 3segmentatimentation oway, althou

a faster segmentation method which outperforms parametric orsupervised methods such as MAP based methods.

The performance of the presented segmentation techniqueshave been evaluated by computing the average overlap ratethrough the Tanimotos index, as it has been widely used by otherauthors to compare the segmentation performance of their propo-sals [35,4850,17,5154]. Tanimotos index can be dened as:

T(S1, S2) =S1 S2S1 S2 (16)

where S1 is the segmentation set and S2 is the ground truth.Fig. 14a shows the segmentation results for the IBSR 2.0 volume

12 using the HFS-SOM algorithm, where each row corresponds toa tissue and each image column corresponds to a different slice. Inthe same way, Fig. 14b shows the same slices of Fig. 13b but the

ntati the s

IBSR impse ono guthan nts ce on

Fig. 13. Segmand 160 on thelices 120, 130, 140, 150, 160 and 170 on the axial plane.entation from IBSR database is shown in Fig. 13c.

omparison between automatic segmentation and theh points up that the EGS-SOM method outperforms the

segmentation method. This fact is also stated in Fig. 15 where the Tanimotos index is shown for different

on algorithms. However, while HFS-SOM performs seg-f the whole volume, EGS-SOM works slice-by-slice. Thisgh EGS-SOM provides a higher resolution, HFS-SOM is

segmeshowsby the

It isdatabaods alslower segmethan thentation of the IBSR volume 100 23, using the HFS-SOM algorithm (a) and the EGS-SOM axial plane are shown on each column. First column corresponds to WM, second columon is performed using the EGS-SOM method. Fig. 14cegmentation performed by expert radiologists provided

database (ground truth).ortant to highlight that expert segmentations of IBSRly include internal CSF spaces. Nevertheless, our meth-re out sulcal CSF. This way, Tanitomos index for CSF arefor WM or GM, as can be seen in Table 3, since the CSFomputed by our algorithms may be considerably largeres found on expert segmentations since the IBSR ground algorithm (b). Ground Truth is show in (c). Slices 120, 130, 140, 150n to GM and third column to CSF.


Fig. 14. Segm140 and 150 o

Fig. 15. Tanimalgorithms.

truth is use(16).

In Tabletation methTable 3 shothe IBSR 1.0the results no similarl

Table 4Mean and stantation method

Segmentatio

EGS-SOM R-FCMNL-FCMFCM HFS-SOMentation of the IBSR 2.0 volume 12, using the HFS-SOM algorithm (a) and the EGS-SOM n the axial plane are shown on each column. First column corresponds to WM, second co

oto performance index calculated through images from the IBSR database. Tanimotos

d in the Tanimotos index computation as shown in Eq.

3, a quantitative comparison among different segmen-ods through the Tanimotos index is provided from [35].ws the average Tanimotos index over the images on

database. In this table, while values of 1.0 means thatare very similar, values are near 0.0 when they sharey. Standard deviation for each method is included in

dard deviation of the Tanimotos performance index for the segmen-s on Fig. 15.

n algorithm Ref. WM index GM index

0.76 0.04 0.73 0.05[48] 0.75 0.05 0.65 0.05[49] 0.74 0.05 0.72 0.05[48] 0.72 0.05 0.74 0.05

0.60 0.08 0.60 0.09

order to procalculated o

Fig. 15a IBSR 1.0 impresents thsegmentati

Table 4 on the IBSR

Table 5Sensitivity and

Tissue

White matteGray matterCerebrospinalgorithm (b). Ground Truth is show in (c). Slices 100, 110, 120, 130,lumn to GM and third column to CSF.

index for WM (a) and GM (b) are shown for different segmentation

vide the statistical deviation of the index, as it has beenver all the images on the IBSR 1.0 database.shows the mean Tanimotos index calculated over theages for different segmentation algorithms, and Fig. 15be Tanimotos index over the IBSR 2.0 images for the twoon algorithms presented in this paper.shows the Tanimotos index averaged over the images

2.0 database. Segmentation methods such as Fuzzy

specicity values achieved by EGS-SOM and HFS-SOM algorithms.

EGS-SOM HFS-SOM

Sensitivity Specicity Sensitivity Specicity

r 81.7% 95.7% 77.5% 81.5% 76.6% 96.4% 70.7% 80.3%al uid 80.8% 99.8% 66.1% 85.4%


Fig. 16. Tanimoto performance index calculated through images from the IBSR2 database. Tanimotos index for WM (a) and GM (b) are shown for different segmentationalgorithms.

Fig. 17. Segmented tissues of the 128:30:166 slice from the IBSR 100 23 volume, axial plane. (a) 2-Nearest neighbor clustering approach, (b) k-means, (c) EGS-SOM algorithm,(d) ground truth.


Fig. 18. High resolution MR image from anonymous patient (VNH). Slice from axialplane.

C-Means (FCM) [48], Robust FCM (R-FCM) [48] or Non-Local FCM[49] have been applied to the IBSR 2.0 images providing good resultsas shown in Table 4 and Fig. 16.

HFS-SOM is an unsupervised and automatic method which doesnot need anit performsOn the othods have behigher overEGS-SOM iparameters

As showyields similimages. Nemethods wIBSR 1.0 imbetter resu(specially, tlapping win

Althougapproachesin terms of values for e

In order rithms, Fig.(axial plane

As showWM, whileway, clusteterms of itsbor approathe performSOM (Fig. 1As commennot includetation methaddressed u

We useddatabase asTable 4.

Images from IBSR have been used to evaluate the segmentationalgorithms. These images come with a resolution of 256 63 256(IBSR 1.0) and 256 128 256 (IBSR 2.0). In the following, theEGS-SOM algorithm is tested on a high resolution VHN database.Although expert segmentation references are not available forthese high resolution images, the results obtained (Fig. 19) whichcorresponds to the segmentation of the image in Fig. 18, clearlyshow the benets of the proposed method, nevertheless it was notpossible to calculate hits and false positive ratios in this case.

As stated in our experiments, the results obtained depend onthe image resolution. The method used for calculating the clus-ters has been proved to be more effective when the window size issmall beside the image size. On the other hand, using small windowsizes is not effective for texture calculation. In images with a lowerresolution, the window size should be decreased in order to havehigher image sizewindow size ratio. Nevertheless, smaller win-dow sizes do not capture the textural features of the image, and it

ssary. Mor pretain

clus

o unsganizformo clarotot

k-me intilityeter.nd at wapose

do nrage

ompaoes nlizathisto

ord addiscrissie

as weing mved

ions FS-S

deofy parameter to be set up. Moreover, as shown in Fig. 15, better than other parametric or supervised methods.er hand, as improved supervised or parametric meth-en used to segment the IBSR 2.0 database they provideslap ratio values than the HFS-SOM method. Althoughs also a fully-unsupervised method, it requires some

regarding the feature selection and clustering stages.n in Fig. 16, segmentation using the EGS-SOM methodar results than other existing methods for normalizedvertheless, the presented methods outperform otherith images containing intensity inhomogeneities as theages. In the case of the EGS-SOM method, it provideslts with high resolution images due to the featureshe second order ones) are best captured using the over-dow.h Tanimotos index is used to compare with other, it does not provide an overall performance metric (i.e.error). This way, we provide sensitivity and specicityach tissue in Table 5.to compare the results obtained with the different algo-

17 shows the segmentation results for the slice 166) of the 100 23 IBSR volume.n in Fig. 17, all the methods tend to better delineate

GM and CSF delineation depends on the method. Thisring the SOM using k-means (Fig. 17a) fails with GM in

similarity with the ground truth. The 2-nearest neigh-ch (Fig. 17b) gures out GM better than k-means butance with WM is lower. On the other hand, the EGS-7c) provides a good trade-off among the three tissues.ted before in this paper, IBSR expert segmentations do

internal CSF spaces. This way, assessment of segmen-ods which delineates sulcal CSF cannot be completelysing the IBSR references (ground truth) for CSF.

the expert manual segmentation provided by the IBSR a reference for calculating the overlap metric shown in

is neceolutionto othenot con

4. Con

Twself-oruses inorder tSOM pby thetize thprobabparamcient ain a fasthe prowhichthe avebeen cSOM dgeneraimage seconddow. Inmost dthe clamizedclusterhas proconditThus, Hthe traFig. 19. Segmented tissues with our unsupervised method of a 512 512 voxels slice f to achieve a trade off between window size and res-reover, the HFS-SOM method provides similar resultsviously segmentation algorithms when the image does

severe inhomogeneities.

ions

upervised MR image segmentation methods based oning maps were presented in this paper. The rst methodation computed from the whole volume histogram inssify the voxels using SOM (HFS-SOM). Moreover, theypes, which generalize the input vectors, are clusteredeans algorithm. SOM prototypes generalize and quan-ensities present on the MRI, taking into account the

of each voxel intensity. This process does not need any On the other hand, HFS-SOM is computationally ef-llows the segmentation of the whole volume at oncey. The evaluation experiments carried out showed thatd HFS-SOM method provides good results with imagesot contain severe intensity inhomogeneities. Although

overlap ratio is lower for the HFS-SOM method, it hasred with supervised or parametric methods, while HFS-ot require any parameter to be selected, exploiting theion properties of the SOM. EGS-SOM does not use thegram to compose the feature vectors, but the rst ander computed from the image using an overlapping win-ition, evolutionary computing is used for selecting theminative set of features leveraging the performance ofr. As a result, the number of units on the map is also opti-ll as the classication process. On the other hand, a mapethod has been devised based on the EGS-SOM which

to be robust under noisy or bad intensity normalizationand provides good results with high resolution images.OM or EGS-SOM methods can be used depending on

f between computational cost and precision.

rom anonymous patient. WM (a), GM (b) and CSF (c).


The experiments performed using the IBSR database as well ashigh resolution images from VNH provide good results. Indeed, theresults shown in Section 3 has been compared with the segmenta-tions provided by the IBSR database obtaining about 78% for graymatter andsegmentatidevised in tother algorinumber of sured out aucould be ide

Experimfrom VNH yever, as exquantitativesible.

It is worover real brour algorith

Segmentdisorders ormentation study perfothe early diHFS-SOM mby EGS-SOMslices to buisication.

Acknowled

This woTEC2008-02de Innovacithe Excellen7103.

Appendix A

The mattioned in Se

Energy E =

Entropy H

Contrast C

Homogenei

Sum averag

Autocorrela

Maximal corre

Correlation Cor =G1

i=1G1

j=0 ijp(i, j) xyxy

(A.8)

r secG1G1

um p

pro

sha

ilarit

ce V

ation

corral de

=Gi=

k) =

y, xe parnce cray G1i=0G1i=0

j) =Gk

he to y cow.

nces

apur,gnetic

Webss, Inc.KambntatioE Traniad, Aroachrnatioogeswntatiouisitiang,

ges: acessin about 81% for white matter of hits from the manualons. Moreover, the clustering method for the SOMhis work provides better results for this application thanthms such as k-means or Fuzzy k-means. As a result, theegments or different tissues found in a MR image is g-tomatically making possible to nd out tissues whichntied with pathology.ents performed using high resolution real brain scansield good results, especially for CSF delineation. How-pert segmentation is not provided for these images,

assessment through the Tanimotos index is not pos-

th noting that all the experiments have been performedain scans. Thus, all the images used on this work to testm contain noise due to the acquisition process.ation techniques could help to nd causes of brain

anomalies such as Alzheimers disease. In fact, the seg-algorithms presented in this paper are part of a largerrmed by the authors on the use of tissue distribution foragnosis of AD. This way, generalization provided by theethod as well as precise tissue distribution generated

segmentation may be applied over the most relevantld AD brain models allowing further NORMAL/AD clas-

gments

rk was partly supported by the MICINN under113 and TEC2012-34306 projects and the Consejeran, Ciencia y Empresa (Junta de Andaluca, Spain) underce Projects P07-TIC-02566, P09-TIC-4530 and P11-TIC-

. Textural features

hematical formulation for the textural features men-ction 2.3.2 is detailed as follows:G1

i=0

G1j=0

p2(i, j) (A.1)

= G1i=0

G1j=0

p(i, j) log(p(i, j)) (A.2)

=G1i=1

G1j=0

(i j)2p(i, j) (A.3)

ty Hom =G1i=1

G1j=0

p(i, j)

1 + (i j)2(A.4)

e Sav =2G2i=0

ipx+y(i) (A.5)

tion Ac =G1i=1

G1j=0

(ij)p(i, j) (A.6)

lation coefcient Mcor =

2nd largest eigenvalue ofQ (A.7)

Angula

Maxim

Cluster

Cluster

Dissim

Varian

Not

p(i,j)spati

px(i)

px+y(

x, of thvariathe G

2i

=

i =

Q (i,

G is t x

wind

Refere

[1] T. Kma

[2] J.G.Son

[3] M. meIEE

[4] A. RappInte

[5] T. LmeAcq

[6] Y. WimaProond moment ASM =i=1 j=0

p(i, j)2 (A.9)

robability MP = maxi,jp(i, j) (A.10)

minence CP =G1i=1

G1j=0

(i + j x y)4p(i, j) (A.11)

de CS =G1i=1

G1j=0

(i + j x y)3p(i, j) (A.12)

y Dis =G1i=1

G1j=0

i jp(i, j) (A.13)

ar =G1i=1

G1j=0

(1 )2p(i, j) (A.14)

:

esponds to the (i,j)-th entry in the normalized gray levelpendence matrix.1

0

p(i, j); py(j) =G1j=0

p(i, j)

G1i=0

G1j=0

p(i, j), i + j = k, k = 1, 2..., 2 (G 1)

, y, are respectively the means and standard deviationstial probability density functions px and py. In the case ofalculation, represents the mean of the values within

Level Co-occurrence Matrix.G1j=0

(i i)2; 2j =G1i=0

G1j=0

(j j)2

G1

j=0ip(i, j)

1

=0

p(i,k)p(j,k)px(i)py(k)

tal number of intensity levels.orresponds to the number of voxels on the overlapped

W. Grimson, I. Wells, R. Kikinis, Segmentation of brain tissue from resonance images, Medical Image Analysis 1 (2) (1996) 109127.ter, Medical Instrumentation. Application and Design, John Wiley &, New York, 1998.er, R. Shinghal, D. Collins, G. Francis, A. Evans, Model-based 3D seg-n of multiple sclerosis lesions in magnetic resonance brain images,sactions on Medical Imaging 14 (3) (1995) 442453.. Atwan, H. El-Bakry, R. Mostafa, H. Elminir, N. Mastorakis, A new

for segmentation of MR brain image, in: Proceedings of the WSEASnal Conference on Environment, Medicine and Health Sciences, 2010.ari, M. Karnan, Hybrid self-organizing map for improved imple-

n of brain MRI segmentation, in: International Conference on Signalon and Processing, 2010.

T. Adali, Quantication and segmentation of brain tissues from MR probabilistic neural network approach, IEEE Transactions on Imageg 7 (8) (1998) 11651180.


[7] K. Lim, A. Pfefferbaum, Segmentation of MR brain images into cerebrospinaluid spaces, white and gray matter, Journal of Computer Assisted Tomography13 (4) (1989) 588593.

[8] C. Hsu, L. Hsiao, Yang, C. Wang, C. Chen, Automatic threshold level set modelapplied on MRI image segmentation of brain tissue, Applied Mathematics andInformation Sciences (2013) 589598.

[9] D. Kennedy, P. Filipek, V. Caviness, Anatomic segmentation and volumetric cal-culations in nuclear magnetic resonance imaging, IEEE Transactions on MedicalImaging 8 (1) (1989) 17.

[10] M. Brummer, R. Mersereau, R. Eisner, R. Lewine, Automatic detection of braincontours in MRI data sets, Lecture Notes in Computer Science 511 (1991)188204.

[11] M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, InternationalJournal on Computer Vision 1 (1988) 321331.

[12] A. Yuille, S. Zhu, Region competition: unifying snakes, region growing andBayes/MDL for multiband image segmentation, IEEE Transactions on PatternAnalysis and Machine Intelligence 18 (9) (1996) 883900.

[13] W. Wells, W. Grimson, R. Kikinis, F. Jolesz, Adaptive segmentation of MRI data,IEEE Transactions on Medical Imaging 15 (4) (1996) 429442.

[14] Y. Tsai, I. Chiang, Y. Lee, C. Liao, K. Wang, Automatic MRI meningioma seg-mentation using estimation maximization, in: Proceedings of the 27th IEEEEngineering in Medicine and Biology Annual Conference, 2005.

[15] J. Xie, H. Tsui, Image segmentation based on maximum-likelihood estimationand optimum entropy distribution (MLE-OED), Pattern Recognition Letters 25(2005) 11

[16] S. Smith, Markov rTransacti

[17] N. MohammentatioProcessin

[18] A. Ballin, brain struNotes on

[19] G. Liyuansegmenta

[20] C. Parra, and patteConferenDecembe

[21] P. Sahoo,Compute

[22] Z. Yang, J.Organizin

[23] I. Gler, self-organProcessin

[24] S. Ong, N.a two-sta279289.

[25] J. Alirezaimages u45 (4) (19

[26] W. Sun, Swork, Ne

[27] L. Fan, D. network,Engineer

[28] Y. Jiang, Kthe 9th InGranular

[29] R.M. Haracation, IE

[30] M. Hu, ViInformati

[31] M. Nixson2008.

[32] S. Sivanandam, S. Deepa, Introduction to Genetic Algorithms, Springer-Verlag,2008.

[33] T. Kohonen, Self-Organizing Maps, Springer, 2001.[34] E. Alhoniemi, J. Himberg, J. Parhankagas, J. Vesanta, SOM Toolbox for Matlab

v2.0, , 2005.[35] Internet Brain Database Repository. Massachusetts General Hospital, Center for

Morphometric Analysis, ,2010.

[36] R. Momenan, D. Hommer, R. Rawlings, U. Ruttimann, M. Kerich, D. Rio,Intensity-adaptative segmentation of Single-Echo T1-weigthed magnetic res-onance images, Human Brain Mapping 5 (3) (2002) 194205.

[37] N. Kovacevic, N. Lobaugh, M. Bronskill, B. Levine, A. Feinstein, S. Black, A robustmethod for extraction and automatic segmentation of brain images, NeuroIm-age 17 (3) (2002) 10871100.

[38] J. Brinkley, S. Bradley, J. Sundsten, C. Rosse, Hierarchical geometric networks asa representation for spatial structural knowledge, in: Proceedings of the 16thAnnual Symposium on Computer Applications in Medical Care, 1992.

[40] V. Vapnik, Statistical Learning Theory, Wiley, New York, 1998.[41] London Institute of Neurology, UCL, Statistical Parametric Mapping (SPM),

.[42] E. Arsuaga, F. Daz, Topology preservation in SOM, International Journal of

Mathematical and Computer Sciences 1 (1) (2005) 1922.[43] J. Ashburner, K.J. Friston, Unied segmentation, NeuroImage 26 (3) (2005)

839851.shburner, K.J. Friston, Image segmentation, in: R. Frackowiak, K. Friston, C.h, R. Din Funalas-Gntatioernatiasdemelf-or09) 54. Davitern A. Phance 752aldairal fuzzputereens

rk fordical I

Rajapgle-ch

(1997Berthodom . Clark. Tha

gnetic Bezdeng patKonakorithm100in Excienceearch/. Gorrge claing 11lvarez. Chapone331141.M. Brady, Y. Zhang, Segmentation of brain images through a hiddenandom eld model and the expectation-maximization algorithm, IEEEons on Medical Imaging 20 (1) (2001).ed, M. Ahmed, A. Farag, Modied fuzzy c-mean in medical image seg-

n, in: IEEE International Conference on Acoustics, Speech and Signalg, 1999.M. Galun, M. Gomori, R. Basri, A. Brandt, Atlas guided identication ofctures by combining 3D segmentation and SVM classication, LectureComputer Science 1491 (2006) 209216, MICCAI., C. Wanhua, X. Haixiang, Performance evaluation of SVM in imagetion, in: Proceedings of the ICSP 2008 International Conference, 2008.K. Iftekharuddin, R. Kozma, Automated brain tumor segmentationrn recognition using AAN, in: Proceedings of the 2nd Internationalce on Computational Intelligence, Robotics and Autonomous Systems.r 2003.

S. Soltani, A. Wong, Y. Chen, A survey of thresholding techniques,r Vision, Graphics, and Image Processing 41 (2) (2010) 233260.

Laaksonen, Interactive Retrieval in Facial Image Database Using Self-g Maps, MVA, 2005.A. Demirhan, R. Karakis, Interpretation of MR images usingizing maps and knowledge-based expert systems, Digital Signalg 19 (2009) 668677.

Yeo, K. Lee, Y. Venkatesh, D. Cao, Segmentation of color images usingge self-organizing network, Image and Vision Computing 20 (2002)

ie, M. Jernigan, C. Nahmias, Automatic segmentation of cerebral MRsing articial neural networks, IEEE Transactions on Nuclear Science98) 21742182.egmentation method of MRI using fuzzy Gaussian basis neural net-ural Information Processing 8 (2) (2005) 1924.Tian, A brain MR images segmentation method based on SOM neural

in: IEEE International Conference on Bioinformatics and Biomedicaling, 2007.. Chen, Z. Zhou, SOM based image segmentation, in: Proceedings ofternational Conference on Rough Sets, Fuzzy Sets, Data Mining, andComputing, 2003.lick, K. Shanmugam, I. Dinstein, Textural features for image classi-EE Transactions on Systems and Cybernet 6 (1973) 610621.sual pattern recognition by moments invariants, IRE Transactions onon Theory IT-8 (1962) 179187., A. Aguado, Feature Extraction and Image Processing, Academic Press,

[44] J. AFritBra

[45] D. SmeInt

[46] K. Tof s(20

[47] D.LPat

[48] D.Lona737

[49] B. ClocCom

[50] H. GwoMe

[51] J.C.sin(2)

[52] M. ran

[53] L.PR.WMa

[54] J.C.usi

[55] A. alg992

[56] Brarosres

[57] J.Mimaput

[58] I. AR.Mcomolan, K. Friston, C. Price, S. Zeki, A. Ashburner, W. Penny (Eds.), Humanction, 2nd ed., Academic Press, 2003.onzalez, M. Schlgl, J.M. Grriz, J. Ramrez, E.W. Lang, Bayesian seg-

n of magnetic resonance images using the -stable distribution, in:onal Conference on Hybrid Articial Intelligence Systems, HAIS, 2011.ir, E. Mernyi, Exploiting data topology in visualization and clustering

ganizing maps, IEEE Transactions on Neural Networks 20 (April (4))9562.

es, D.W. Bouldin, A cluster separation measure, IEEE Transactions onnalysis and Machine Intelligence 1 (4) (1979) 224227.m, J.L. Prince, Adaptative fuzzy segmentation of magnetic res-images, IEEE Transactions on Medical Imaging 18 (9) (1999).ou, F. Rousseau, N. Passat, P. Habas, C. Studholme, C. Heinrich, A non-y segmentation method: application to brain MRI, Lecture Notes inr Science 5702/2009 (2009) 606613.pan, A. Ruf, J. Goldberger, Constrained Gaussian mixture model frame-

automatic segmentation of MR brain images, IEEE Transactions onmaging 25 (9) (2006) 12331245.akse, J.N. Giedd, J.L. Rapoport, Statistical approach to segmentation ofannel cerebral MR images, IEEE Transactions on Medical Imaging 16) 176186.d, Z. Kato, S. Yu, J. Zerubia, Bayesian image classication using Markovelds, Image and Vision Computing 14 (1996) 195285.e, R.P. Veltuizen, M.A. Camacho, J.J. Heine, M. Vaidyanathan, L.O. Hall,tcher, M.L. Silbiger, MRI segmentation: methods and applications,

Resonance Imaging 13 (3) (1995) 343368.k, L.O. Ifall, L.P. Clarke, Review of MR image segmentation techniquestern recognition, Medical Physics 20 (4) (1993) 10331048., D.W. Coit, A.E. Smith, Multi-objective optimization using genetics: a tutorial, Reliability Engineering and System Safety 91 (2006)

7.traction tool (BET). FMRIB Centre. Nufeld Department of Neu-s. University of Oxford, .iz, F. Segovia, J. Ramrez, A. Lassl, D. Salas-Gonzalez, GMM based spectssication for the diagnosis of Alzheimers disease, Applied Soft Com-

(2011) 23132325., J.M. Gorriz, M.M. Lpez, J. Ramrez, D. Salas-Gonzlez, F. Segovia,ves, C. Garcia, Computer aided diagnosis of Alzheimers disease usingnt based SVM, Applied Soft Computing 11 (2011) 23762382.

Two fully-unsupervised methods for MR brain image segmentation using SOM-based strategies1 Introduction1.1 Summary and organization

2 Materials and methods2.1 Databases2.2 Image preprocessing2.3 Fast volume image segmentation by HFS-SOM2.3.1 A histogram computation2.3.2 SOM modeling2.3.3 SOM clustering and voxel classification

2.4 EGS-SOM segmentation2.4.1 Feature extraction2.4.2 Feature selection2.4.3 EGS-SOM clustering

3 Results and discussion3.1 Experimental setup3.2 Experimental results and discussion

4 ConclusionsAcknowledgmentsAppendix A Textural featuresReferences

paper for histrogram feature and glcm feature

Documents