An Optimal Unsupervised Satellite image Segmentation Approach Based on Pearson System and k-means Clustering Algorithm Initialization

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1 International Journal of Inforation and Counication Engineering 5: 009 An Optial Unsupervised Satellite iage Segentation Approach Based on Pearson Syste and -eans Clustering Algorith Initialization Ahed Rei, ourad Zribi, Ahed Ben Haida and ohaed Benjelloun Abstract This paper presents an optial and unsupervised satellite iage segentation approach based on Pearson syste and -eans Clustering Algorith Initialization. Such ethod could be considered as original by the fact that it utilised K-eans clustering algorith for an optial initialisation of iage class nuber on one hand and it exploited Pearson syste for an optial statistical distributions affectation of each considered class on the other hand. Satellite iage exploitation reuires the use of different approaches, especially those founded on the unsupervised statistical segentation principle. Such approaches necessitate definition of several paraeters lie iage class nuber, class variables estiation and generalised ixture distributions. Use of statistical iages attributes assured convincing and prooting results under the condition of having an optial initialisation step with appropriated statistical distributions affectation. Pearson syste associated with a -eans clustering algorith and Stochastic Expectation-axiization SE algorith could be adapted to such proble. For each iage s class, Pearson syste attributes one distribution type according to different paraeters and especially the Sewness β and the urtosis β. The different adapted algoriths, K-eans clustering algorith, SE algorith and Pearson syste algorith, are then applied to satellite iage segentation proble. Efficiency of those cobined algoriths was firstly validated with the ean Quadratic Error QE evaluation, and secondly with visual inspection along several coparisons of these unsupervised iages segentation. Keywords Unsupervised classification, Pearson syste, Satellite iage, Segentation. I I. INTRODUCTION NCREASING use of satellite iages acuired periodically by satellites on different areas and for ultiple purposes aes it extreely interesting for various applications. Indeed, the recent construction of ulti spectral and hyper spectral iages would provide detailed data with inforation in both the spatial and spectral doains. This data shows A. Rei is with Unité de Recherche en Technologie de l Inforation etelectroniue édicale TIE, Ecole Nationale d Ingénieurs de Sfax (ENIS, BP W, 3038 Sfax, Tunisia, and Laboratoire d Analyse des Systèes du Littoral, (LASLEA 600, Université du Littoral Côte d Opale, France (e-ail: ahedrei@yahoo.fr..zribi is with Laboratoire d Analyse des Systèes du Littoral, (LASLEA 600, France (e-ail : ourad.zribi@lasl.univ-littoral.fr. A. B. Haida is the Director of the Unité de Recherche en Technologie de l Inforation et Electroniue édicale TIE, (ENIS, BP W, 3038 Sfax, Tunisia (e-ail : Ahed.Benhaida@enis.rnu.tn. great proise for reote sensing applications ranging fro environental and agricultural to national security interests. Aong satellite iage processing, nuerous algoriths using different approaches have been proposed during the past few years. These approaches include local edge detection [, 4], deforable curves [, 5], orphological region-based approaches [3, 6, 7], global optiization approaches on energy functions and stochastic odel-based ethods [8, 9]. Soe intensity-based ethods such as thresholding and histogra-based finite ixture odels are forulated easily and uicly. However they often fail to segent objects with low contrast or noisy iages with varying bacgrounds. It is noted that these ethods don t use the spatial orphological iages inforation [0]. On the other hand, soe other ethods such as orphological segentation, region growing and deforable curves, ainly focus on spatial inforation such as local structures or regions. Unfortunately, the ajority of these techniues are not suitable for satellite iage segentation since such type of iage presents a non hoogenous texture []. In this context, it would be iportant to develop unsupervised statistical segentation ethods capable of analysing and classifying these types of iages adeuately. There has been recently considerable interest in stochastic odel-based iage segentation techniues because of their efficiency. In such techniues, an iage would be separated into a set of disjoint regions with each region associated with one of a finite nubers of classes that would be characterized by distinct paraeters. In fact, there are two different statistic iage segentation approaches: the supervised approach and the unsupervised approach. In the supervised approach, it is usually assued that training data are available for the iage classes; therefore, the paraeters can be estiated fro the training data before segentation. But, this is rather unrealistic in any practical situations. Zribi [] says that, for unsupervised techniues, the objective is to estiate the paraeters and segent the iage siultaneously. 38

2 International Journal of Inforation and Counication Engineering 5: 009 ost of the proposed solutions to the unsupervised segentation proble could be classified into two broad categories: one is a two-step procedure estiating the paraeters for each class and then using a relaxation schee to do segentation. The other is an iterative procedure which starts with initial paraeters and alternatively segents the iage based on current paraeters and estiates paraeters based on current segentation as if they were correct. In the first category, clustering algoriths are usually adopted to estiate the classes paraeters. In the second category, paraeters are estiated in each iteration using the current segentation as if they were correct, and the estiated paraeters are used in the next segentation as if they were true paraeters. Although these techniues have deonstrated substantial success for satellite iagery, they have soe liitations. Indeed, ost of the statistical iage segentation techniues need a anual initial input such as the classes nuber. eanwhile, these ethods are often sensitive to these initial conditions. oreover, all these ethods cannot segent correctly the entire iage if the initialization step is not optial and if the distribution of every iage classes is not nown. We propose in this paper an unsupervised satellite iage segentation approach with an optial initialisation step based on Pearson syste, in order to assure a better representation and definition of each iage's classes. We explore also in this wor two odels paraeters estiation, the E odel and the SE odel, and we propose a coparison between these odels [3]. We focus particularly on the ixture of distribution proble. In this context, we review the available theoretical results on the convergence of these algoriths and on the behaviour of SE. Then we show that, for soe particular ixture situations, the SE algorith is alost always preferable than the E algorith. The SE algorith could be used as an efficient data exploratory tool for locating significant axia of the lielihood function. In the real data case, we show that the SE stationary distribution provides a contrasted view of the log-lielihood by ephasizing sensible axia. II. STATISTICAL SATELLITE IAGE CLASSIFICATION : THE UNSUPERVISED APPROACH Segentation of a satellite iage into differently textured regions classes is a difficult proble. Usually, one does not now a priori what types of textures exist in a satellite iage, how any textures there are, and what regions have certain textures [4]. The onitoring tas can be accoplished by supervised classification techniues, which have proven to be effective categorisation tools [5]. Unfortunately, these techniues reuire the availability of a suitable training set (classes nubers for exaple for each new iage of the considered area to be classified. However, in real applications, it is not possible to rely on suitable ground truth inforation for each of the available iages of the analysed site. Conseuently, not all the satellite iages acuired on the investigated area at different ties can be used for updating the related land-cover aps. In this context, it would be iportant to develop classification ethods capable of analysing the iages of the considered site for which no training data would be available, thus increasing the effectiveness of onitoring systes based on the use of reote-sensing iages. Recently, researchers faced this proble by proposing an unsupervised retraining techniue for axiu-lielihood (L classifiers capable of producing accurate land-cover aps even for iages for which ground-truth inforation is not available [6]. This techniue allows the unsupervised paraeters updating of an already trained classifier on the basis of the distribution of the new iage to be classified. 3 4 Bands Iage Data Set (4 band par pixel Pixel Grey Land Cover Signatures Value Signature (based on training areas Copare Urban River 9 Forest Fig. Iportant steps in supervised classification F F F F F F F F F R F F F F F F F R R U U U U F F R R U U U U F F R R U U U U F F R R U U U U F F F R U U U U F F F F R F F F F Classify A. Unsupervised and supervised classification principle Classification principle could be described as follows: any individual pixel or spatially grouped sets of pixels representing soe feature, class, or aterial is characterized by a (generally sall range of digital nubers for each band onitored by the reote sensor. The digital nubers values (deterined by the radiance averaged over each spectral interval are considered to be clustered sets of data in D plotting space. These are analyzed statistically to deterine their degree of uniueness in this spectral response space and soe atheatical function(s is/are chosen to discriinate the resulting clusters. Two ethods for unsupervised and supervised classification are coonly used [5]: 39

3 International Journal of Inforation and Counication Engineering 5: 009 UNSUPERVISED CLASSIFICATION NO SEPARTE DATA INTO GROUPS WITH CLUSTERING CLASSIFY DATA INTO GROUPS ASSIGN NAE TO EACH GROUP SATIFACTORY? YES SUPERVISED CLASSIFICATION NO FOR IAGES OF DATA CHOOSE TRAINING PIXELS FOR EACH CATEGORY CALCULATE STATISTICAL DESCRIPTORS SATIFACTORY? YES YES CLASSIFY DATA INTO CATEGORIES DEFINED Fig. Unsupervised and supervised classification principle. In supervised classification the interpreter nows beforehand what classes are present and where each is in one or ore locations within the scene. These are located on the iage, areas containing exaples of the class are circuscribed (aing the training sites, and the statistical analysis is perfored on the ultiband data for each such class (see Fig.. Instead of clusters then, one has class groupings with appropriate discriinant functions (it is possible that ore than one class will have siilar spectral values but unliely when ore than three bands are used because different classes/aterials seldo have siilar responses over a wide range of wavelengths. All pixels in the iage lying outside training sites are then copared with the class discriinants, with each being assigned to the class it is closest to this aes a ap of established classes. In unsupervised classification, every individual pixel is copared to each discrete cluster to see which one it is closest to. A ap of all pixels in the iage, classified as to which cluster each pixel is ost liely to belong, is produced (in blac and white or ore coonly in colors assigned to each cluster. This, then, ust be interpreted by the user as to what the color patterns ay ean in ters of classes, which are actually present in the real world scene; this reuires soe nowledge of the scene's feature/class/aterial content fro general experience or personal failiarity with the area iaged. The ai of the unsupervised classification ethods is to find partitions of individuals set according to proxiity criteria s of their attribute vectors in the representation space. The objective is in fact to group ultiband spectral response patterns into clusters that are statistically separable. Thus, a sall range of digital nubers (DNs say three bands, can establish one cluster that is set apart fro a specified range cobination for another cluster (and so forth. Separation depends on the paraeters we choose to differentiate. However, the unsupervised classification ethods are used to do blind classification and so to achieve segentation without priori nowledge of the iage, but soe iportant paraeters lie the class nubers ust be fixed. Indeed, the ajority of unsupervised classification algoriths need an initialization step on which paraeters lie the class nubers ust be nown. It exists different techniues for the estiation of this paraeter. We are going to present in this paper our initialization and estiation techniues used for this ai, and we try to describe the different steps of our statistical satellite iage segentation algorith. B. Unsupervised Satellite Iage Segentation Approach The approach that we are going to evoe, thereafter, is in fact an optial unsupervised segentation ethod based on the adoption of the Pearson syste [7], which is going to guarantee an optial adjustent of the ixture densities. Our approach involves four steps described as follows: a A first step of initialisation and definition of iage classes by the use of the -eans algorith in order to provide an optial classes nuber, and to assure a better convergence of these different iages attributes. b A second step perits the set of distribution failies for every classes of our iage, based on the Pearson syste. c A third step of estiation and optiization of the different classes distribution paraeters. d And finally, a bayesien segentation step in order to define the different regions of interest in the iage. III. ODELLING AND CLASSIFICATION ALGORITH A. Initialisation step: K-eans clustering algorith The K-eans is an unsupervised classification algorith based on a clustering techniue [8] through which one set of data (observations is divided into different groups ('clusters', while introducing a siilarity criteria, eleents of a sae group are ost siilar possible. The objective of this algorith is to regroup pixels in K distinct regions (classes; K being fixed by the user. The K-eans techniue s taes pixels intensities as a basis. One randoly assigns each pixel to a class and one reiterates as follows: Centers of various groups (class would be recalculated and each pixel would be again affected to the group according to its nearest center. Convergence would be reached when all centers would be fixed. Principle: For one space referred to as V, observations consists of vectors v i (i,,. K-eans algorith consists in finding a partition of V noted G{G, G,, G K }, whose subsets would be called clusters, and each group would be represented by a vector C called centroïd. Let C{C,, C K } are the whole of the centroïds, also called alphabet or partition dictionary. One introduces a distance easureent d(v i,c between the i th saple and the th centroïd. 40

4 International Journal of Inforation and Counication Engineering 5: 009 The K-eans algorith proceeds in an iterative way starting fro an initial alphabet C [0]. With every iteration [], every saple, represented by a vector v i, is an associated closest centroïde C, and a new partition G [] is thus found. Total distance, relatively to every iteration, could be forulated as follows: D in( d( v j, c with,,k ( [ ] [ ] j For each group, (noting Q the nuber of vectors associated with the th group, the new centroïds are found by iniizing the distance: [ ] [ ] D( G [ ] d( v j, c Q [ v ] j G ( T ( ( x μ x μ f ( x i φ e (4 p (π The Gaussian ixture odel [9] is an onipresent statistical odel for density estiation, pattern recognition, and function approxiation thans to its benefits fro analytical tractability, asyptotic properties, and universal approxiate capability for continuous density functions. The associated paraeters can be estiated in an approxiate axiu a posteriori (AP estiation or the axiu lielihood estiation. The AP or L estiation can be obtained by the expectation axiization (E algorith or its ore recent stochastic version (SE [0]. [ ] [ ] 0 ( G i.e.: (3 c First Gaussian Gaussian ixture In our application, we will consider the Euclidean distance d as a etric distance. 0. Feature space X X X X X X X X X X K-eans Classification X X X X X X X X X X X V ο ο ο 0.08 f(x Second Gaussian ThirdGaussian Forth Gaussian Fifth Gaussian Gaussian ixture Fig. 3 K-eans classification principle B. odelling and classification step In our statistical iage segentation algorith, we suppose the existence of two rando fields: for the S set of pixels, we consider two sets of rando variables X(X s s S, and Y(Y s s S called rando fields. Each X s taes its value in a finite set of classes Ω { ω,,ω }, and each Y s taes its value in IR. The proble of segentation (classification is then that of estiating the unobserved realisation Xx of the field X fro the observed realisation Y y of the field Y, where y (y s ss is the digital iage to be segented. The proble is then solved by the use of Gaussian ixture odel and a Bayesian strategy which is "the best" in the sense of soe criterion. Gaussian ixtures: The Gaussian ixtures are usually used in classification because they correspond often with the variable distribution law. In the Gaussian case, the φ represents the averages of th class, noted μ, and Σ is the atrix of covariance. The density of ultivariate probability in an X conditionally to -φ is written as : x Fig. 4 ixture of five Gaussian distribution. Through this exaple, we can notice that the Gaussian ixture density perits to coe as close as possible to the histogra of the iage test. However, a few errors of approxiations exist again in different classes. To iniize these errors, it is indispensable to estiate and to optiize the different paraeters of the Gaussian ixture density. To reedy this proble, we are going to use the axiu lielihood estiator thereafter associated to the E and SE algorith, and we are going to justify and to approve this choice through the calculation of the ean uadratic error easured, between the ixture density and the one of the iage test. C. Gaussian ixtures estiation Consider a ixture odel with > coponents n inr for n : n p( x π p( x x R, (5 4

5 International Journal of Inforation and Counication Engineering 5: 009 where ( 0 π,,,, are the ixing proportions subject to π. For the Gaussian ixture, each coponent density p( x is a noral probability distribution. p ( x where x ; Θ as (t T ( x μ ( x μ. e n det( θ (6 (π where T denotes the transpose operation. Here we encapsulate these paraeters into a paraeter vector, writing the paraeters of each coponent as θ ( μ,, to get Θ π, π,, π, θ θ, θ. Then, E. (5 can be rewritten as (,, p( x Θ π p( xθ (7 If we new the coponent fro which x cae, then it would be siple to deterine the paraeters Θ. Siilarly, if we new the paraeters Θ, we could deterine the coponent that would be ost liely to have produced x. The difficulty is that we now neither. However, algorith lie E, or SE could be introduced to deal with this difficulty through the concept of issing data. E algorith: The E algorith is a highly successful tool especially in statistics, but it has also found an array of different applications. One of the ore coon applications within the statistics literature is for the fitting of linear ixed odels or generalized linear ixed odels []. Another very coon application is for the estiation of ixture odels. We will show thereafter, the principle of this algorith. Given a set of saples X{x, x,, x K }, the coplete data set S(X;Y consists of the saple set X and a set Y of variables indicating fro which coponent of the ixtures the saple cae. We describe, below how to estiate the paraeters of the Gaussian ixtures with the E algorith. The usual E algorith consists of an E-step and an - (t step. Suppose that Θ denotes the estiation of Θ obtained after the tth iteration of the algorith. Then at the (t + th iteration, the E-step coputes the expected coplete data log-lielihood function : K { log p( x } ( t ( t Q( ΘΘ π θ x ; Θ, (8 x ; Θ is a posterior probability and is coputed ( t π p( x θ ( t ( t l π l p( x ( t ( t θ l (9 And the -step finds the (t + th estiation of (t axiizing Q( Θ Θ ( t + ( t+ ( + Θ t by K ( t π x ; Θ, (0 ( t x x Θ t + ; ( μ ( ( t x ; Θ x ; Θ ( t ( t+ ( t+ T {( x μ ( x μ } ( t x ; Θ ( SE algorith: The SE algorith is a stochastic alternative and an iproveent of the E algorith, obtained by the addition of a stochastic coponent. Indeed, in order to prevent a possible stabilization of E algorith in the neighbourhood of the axiu lielihood, a siulation phase (stochastic, step S is added between the estiation phase (step E and the axiization phase (step with an ai of aing it less sensitive to the local inia. Indeed, the SE algorith contains priarily three stages (Estiation, Siulation, and axiisation, thus allowing to optiize the proble of the classes nuber in the classification procedures while decreasing this one starting fro a raised value K ax. The classes having few pixels are eliinated before a restarting. In fact the principal idea of this algorith is to insert a stochastic step between the step E and the step. To every iteration one draws in each point x i the ultinoial rando variable e n (x i (e n (x i ;,K with ult (; zˆi,..., z ˆiK paraeters, were: t ˆ ( ˆt t π f xi φ zˆ i (3 K t ˆ ( ˆt π f x φ i The ultinoial distribution (ultk characterizes the phenoena where, (a rando pulling, K distinct and copleentary events can occur, each one with a probability p i subjected to the condition: p i. i The probability that event i occurs xi 0 ties during N independent tests is given by this function: n! xi f ( x p, n pi x!. x!... x! i The e n n n n (x i define a P ( P,..., P K, were n n P x / zˆ ( x { } i i The step is based then on these sub-saples for the estiation of the axiu lielihood: t+ t+ t+ θ (( π, μ, Σ,...,( π, μ, Σ. K 4

6 International Journal of Inforation and Counication Engineering 5: ixture density witht E ixture density witht SE ixture density without estiation syste. For,,3,4 let us consider the oents of Y defined by: [ ] μ Ε Y (5 [ Y E( Y ] μ Ε ( for (6 0.0 f(x and two paraeters (β, β defined by: β ( μ3 ( μ 3 μ 4 β (7 ( μ x Fig. 5 The histogra of an iage test, associated to the Gaussian ixture density before and after the use of E and SE algorith. The QE easured respectively between the iage density (histogra and the one of Gaussian ixture without estiation is eual to E-009, and the one of Gaussian ixture after the use of E is eual to E-00, and after the use SE is eual to E-00. One notices therefore that the evaluation of Gaussian ixture paraeters by E and SE, iniize the ean uadratic error, peritting a better representation of the iage test density. However, one sees on Figure 5 that soe classes don't have the shape (probability density of a Gaussian, and that it would be discriinating to change the type of distribution. Indeed, instead of representing every class by a Gaussian law, we are going to try to insert new distributions (beta law, gaa law, in the ixture, and we are going to validate and to approve our choice by the calculation of the QE easured between the Gaussian ixture and the ixture of several Pearson distributions. β is called Sewness and β Kurtosis. On the one hand, the coefficients a, c 0, c, c are related to μ, μ, β, β by the following forula : c 0 ˆ ˆ ˆ (4β 3β c 0 ˆ β 0 ˆ β 8 ˆ β ˆ 3β 6 c 0 ˆ β 0 ˆ β 8 ( β β + μ + ( β + 3 a 0 ˆ β 0 ˆ β 8 On the other hand, given: ˆ β ˆ ˆ ( β ˆ β 0 ˆ β 8 β( β + 3 ( 4β 3β ( β 3β 6 β μ (8 λ, (9 4 The eight failies are illustrated in the Pearson's graph given in Figure 6. IV. CLASSES DISTRIBUTION OPTIIZATION AND BAYESIAN SEGENTATION A. Pearson s Syste A distribution density f on IR belongs to Pearson's syste if it satisfies: df ( x ( x + a dx c0 + cx + c x f ( x (4 4 The variation of the paraeters a, c 0, c, c provides distributions of different shape and, for each shape, defines the paraeters fixing a given distribution. Let Y be a real rando variable whose distribution belongs to Pearson's Fig. 6 the eight failies of Pearson's syste function of (β, β. 43

7 International Journal of Inforation and Counication Engineering 5: 009 The ai of this syste is to estiate all paraeters defining the coponents of the distribution ixture as the shape of the arginal distributions of classes. We ost therefore calculate the oents: μ, μ, μ 3, μ 4, which can be estiated fro epirical oents, fro which we deduce the estiated values of β, β by (7. Then, we estiate the faily using (9. Once the faily is estiated, values of a, c 0, c, c, given by (8 can be used to solve the paraeters defining the corresponding densities. And finally, one ust estiate the different paraeters of each faily by the SE algorith. B. Bayesian segentation The ai of the Bayesian segentation approach is to calculate the distribution of Y, and the odel paraeters if unnown, given X, that is: Knowing that: X / ωi. ωi ω i X (0 X P X ω X / ω ( ( i i i With: P (ω i X: a posterior probability. X ω i : adherence probability to a class. P (ω i : a prior probability. Original Iage Original Iage Segentation result Fig.7 Unsupervised segentation of the boat iage. The second test iage is a spot satellite iage representing the city of Cairo with a,5 resolution. The initialisation paraeters for this iage are: K ax 5, iteration N br 50. The QE easured respectively between iage density (histogra and the one of Gaussian ixture with K-eans initialization is eual to 4.605E-00, and the one with histogra thresholding is eual to.04569e-009. Segentation result The rule used for the probabilistic and Bayesian decision, for the choice of the class to which a pixel belongs, is the axiu a posteriori: { p( x C I, I } x Ci if p( x Ci I,, I P ax (, p V. EXPERIENTAL RESULTS In this section, we apply the proposed above approach to soe test iages. We also ae a coparison between the ean Quadratic Error (QE found with the use of -eans initiation step, and QE found with the use of histogra thresholding step. The first test iage is a natural iage representing a boat. The initialisation paraeters for this iage are: K ax 0, iteration N br 50. The QE easured respectively between iage density (histogra and the one of Gaussian ixture with K-eans initialization is eual to 3.375E-00, and the one with histogra thresholding is eual to 4.737E-009 Fig. 8 Unsupervised segentation of a Spot5,5 iage, representing the city of Cairo EGYPT. The third iage test is a spot iage representing the city of Rotterda with a 0 resolution. The initialisation paraeters for this iage are: K ax 0, iteration N br 50. The QE easured respectively between this iage density (histogra and the one of Gaussian ixture with K-eans initialization is eual to 3.643E-00, and the one with histogra thresholding is eual to E

8 International Journal of Inforation and Counication Engineering 5: 009 Original Iage Segentation result (regions in the iage. Finally, it provides significantly better results than the existing unsupervised segentation approaches. REFERENCES Fig. 9 Unsupervised segentation of a Spot4-0 iage, representing the city of Rotterda NETHERLAND. The forth iage test is a spot iage representing the city of El Keela with a resolution eual to 5. The initialisation paraeters for this iage are: K ax 0, iteration nubers 50. The QE easured respectively between this iage density (histogra and the one of Gaussian ixture with K- eans initialization is eual to 3.463E-00, and the one with histogra thresholding is eual to.3369e-009. Original Iage Segentation result Fig. 0 Unsupervised segentation of a Spot 5 5 iage, representing the city of El Keela OROCCO. VI. CONCLUSION Classifying satellite iages is a challenging proble as these iages often contain different textured regions or varying bacgrounds, and are often subjected to illuination changes or environental effects. We proposed in this article one convivial solution to the optiization of unsupervised satellite iage segentation, in which a ethod based on K-eans techniue and Pearson syste is used in order to optiize segentation results. A ixture Gaussian odel and SE classification algoriths are also developed for Bayesien iage satellite segentation. Our proposed ethod showed a high perforance in satellite iage classification since other distributions could be used for an optial odelling. Such ethod is not sensitive to the selection of paraeter values, and does not reuire any prior nowledge about the nuber of class [] S. Li, T. Fevens, A. Krzyża and S. Li, Autoatic clinical iage segentation using pathological odelling PCA and SV, Engineering Applications of Artificial Intelligence, Volue 9, pp , June 006. [] A. Schwaighofer, V. Tresp, P. ayer, A.K. Scheel and G. uller, The RA scanner: prediction of rheuatoid joint inflaation based on laser iaging, IEEE Trans. Bioed. Iaging 50, pp [3] Y. Zheng, H. Li and D. Doerann, achine printed text and handwriting identification in noisy docuent iages, IEEE Trans. Pattern Anal. ach. Intell. 6, pp , 004. [4] W.Y. anjunath, A fraewor of boundary detection and iage segentation, IEEE Conference on Coputer Vision and Pattern Recognition, San Juan, Puerto Rico, pp , 005. [5] C.Y. and L.P. Jerry, Snaes, shapes, and gradient vector flow, IEEE Trans. Iage Process. 73, pp , 998. [6] S.C. and Y. Alan, Region copetition: Unifying snaes, region growing, and Bayes/DL for ultiband iage segentation, IEEE Trans. Pattern Anal. ach. Intell. 89, pp , 996. [7] G.-P. and G. Chuang, Extensive partition operators, gray-level connected operators, and region erging/classification segentation algoriths: Theoretical lins, IEEE Trans. Iage Process. 09, pp , 00. [8] K.S. and K.U. Jayara, Optiu iage thresholding via class uncertainty and region hoogeneity, IEEE Trans. Pattern Recog. ach. Intell. 37, pp , 00. [9] J.P, Stochastic relaxation on partitions with connected coponents and its application to iage segentation, IEEE Trans. Pattern Anal. ach. Intell. 06, pp , 998. [0] J. Xie, and H. T. Tsui, Iage segentation based on axiulielihood estiation and optiu entropy-distribution(le OED, Pattern Recognition Letters, Volue 5, Issue 0, pp. 33 4, July 004. [] Y. Deng, and B.S. anjunath, Unsupervised segentation of color texture regions in iages and video, IEEE Trans. Pattern Anal. ach. Intell. 38, pp , 00. []. Zribi and F. Ghorbel, An unsupervised and non-paraetric Bayesian classifier, Pattern Recognition Letters 4, pp. 97, 003. [3] A. Rei,. Zribi, A. Ben Haida and,. Benjelloun, Unsupervised Bayesian Iage Segentation Using Adaptive E Algorith based on Pearson ssyste, Vol. V, WSCI 006, Florida, USA, pp , 006. [4] T.R. Reed, J..H. Du Buf, A review of recent texture segentation, feature extraction techniues, CVGIP Iage Understanding 57, pp , 993. [5] J.A. Richards, Reote Sensing Digital Iage Analysis, second ed., Springer-Verlag, New Yor, 993. [6] L.Bruzzone, D.Fernandez Prieto, Unsupervised retraining of a axiu-liehood classifier for the analysis of ultiteporal reotesensing iages, IEEE Transactions on Geoscience and Reote Sensing 39 (00 pp [7] A. Rei,. Zribi,. Benjelloun and A. ben Haida, A -eans Clustering Algorith Initialization for Unsupervised Statistical Satellite Iage Segentation, IEEE-International Conference on E- Learning in Industrial Electronics, Haaet Tunisia, 006. [8] H. Frigui and R. Krishnapura; Clustering by copetitive aggloeration, Pattern Recogntion, Vol. 30, No.7, pp.09 9, 997. [9] G. clachlan, D. Peel, Finite ixture odels, Wiley, New Yor, 000. [0] G. clachlan, T. Krishnan, The E Algorith and Extensions, Wiley, New Yor, 997. [] cculloch, C. E, axiu lielihood algoriths for generalized linear ixed odels, Journal of the Aerican Statistical Association, pp. 6 70,