The importance of the Expectation Maximization (EM) algorithm isincreasing day by day in order to solve Maximum A Posteriori (MAP) estimation problems and Gaussian Mixture Models (GMMs), which are parametric probability density functions, have become more popular in computerized applications due tothe EM algorithm. This article explains an automatic GMM based image segmentation method for histology cell images. For this purpose, the GMM parameters, which are recomputed iteratively starting with initial values, arecalculated by using the EM algorithm which classifies each pixel into the class withthe largest probability distribution using maximum likelihood. The accuracy of this segmentation algorithm depends on how much close the probabilistic model to the gray level distributions of the input images

Evgin Goceri

Epoka University

“1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.649Expectation Maximization And Gaussian Model BasedSegmentation on Histology SlidesEvgin GÖÇERİDepartment of Computer Engineering, Pamukkale University, Denizli-TURKEYEmail: egoceri@pau.edu.trABSTRACTThe importance of the Expectation Maximization (EM) algorithm isincreasing day by day in order to solve Maximum A Posteriori (MAP) estimationproblems and Gaussian Mixture Models (GMMs), which are parametric probabilitydensity functions, have become more popular in computerized applications due tothe EM algorithm. This article explains an automatic GMM based imagesegmentation method for histology cell images. For this purpose, the GMMparameters, which are recomputed iteratively starting with initial values, arecalculated by using the EM algorithm which classifies each pixel into the class withthe largest probability distribution using maximum likelihood. The accuracy of thissegmentation algorithm depends on how much close the probabilistic model to thegray level distributions of the input images.INTRODUCTIONMedical image segmentation is generally performed manually by experts,which is cumbersome, time consuming, tedious task due to the complex and unclearedge structures.  Therefore such a segmentation leads to high outcome variability.Also, not only variations in image shape and size, but also the usage of differentelectronic devices for imaging, overlapping signal intensities and several imagingartifacts cause the segmentation process to be a more challenging task.Although the advantages of semi-automatic segmentation algorithms, they arestill remain labor intensive and so the need for fully automatic segmentationtechniques which means without any user interaction is becoming more and moreimportant. Automated and accurate segmentation of medical images to separateanatomically meaningful partitions is needed. For instance, caudate nucleussegmentation in patients with specific neurologic diseases is of great interestbecause it can help in improving patient treatment and/or diagnose.“1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.650There are several image segmentation approaches in the literature such asregion growing method, watershed method, level set method, morphologicaloperations, active shape models, deformable models, artificial neural network andatlas based segmentation techniques. Also, different combinations of thesetechniques are applied to obtain accurate results on different images. For instance, in[1-3] k-means based segmentation methods are applied for cDNA microarray spots,brain and fingerprints. K-means method, which is an iterative and unsupervisedclassification technique, based on minimization of the sum of distance between datapoints and their cluster centers. Data points are assigned to their nearest centers andeach center is re-computed. Usually Euclidean distance is used to measure thedistance. Region-based segmentation techniques [4-6] attempt to segment an imageby identifying the various homogeneous regions that correspond to different objectsin an image. Unlike clustering methods, region-based methods explicitly considerspatial interactions between neighboring voxels. In its simplest form, regiongrowing methods usually start by locating some seeds representing distinct regionsin the image. The seeds are then grown until they eventually cover the entire image.The region growing process is therefore governed by a rule that describe the growthmechanism and a rule that check the homogeneity of the regions at each growthstep. In the split-and-merge technique [7], an image is first split into many smallregions during the splitting stage according to a rule, and then the regions aremerged if they are similar enough to produce the final segmentation. In addition tothese generally used techniques, a neural network based approach is proposed [8]for liver segmentation. Another neural network based method [9] uses radial basisfunctions for segmentation. A deformable model based approach is proposed in [10]for kidney segmentation. Probabilistic atlases are constructed and used for medicalimage segmentation [11]. Also, an active shape model based segmentation techniqueby using non-rigid image registration is explained [12].In this study, EM based image segmentation is explained and an applicationresult by using a histological image is presented.“1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.651IMAGE SEGMENTATION USING EXPECTATION MAXIMIZATION ANDGAUSSIAN MODELGMMs are known as a weighted sum of Gaussians. When we know the mean,covariance and prior probability values then we can define a multivariate Gaussianprobability density function. Because, the probability distribution of each voxel canbe represented as a mixture of probability distributions with coefficients, which canbe taken as prior probabilities. The parameters of GMMs can be estimated by usingEM algorithm [13,14] that interleaves probability density function estimation foreach tissue class.Assume that the intensities in an image be denoted as a one-dimensionalarray. that have J pixels, where is the intensity ofvoxel j. Assume that we have K tissue types in the image, and voxel j can be belongto a tissue type, which can be represented as . In the GMM, it isassumed that each tissue type k has an intensity in the image. In other words, theprobability density function (1) is represented with voxel j of tissue type , whichhas intensity , can be written as,(1)where refers to a zero-mean Gaussian distribution with covariance andrepresents the set of model parameters.To simplify the explanation, let all the pixel labels represent by grouping ina label .  It is assumed that the label of each pixel isdrawn independently from the labels of the other pixels by using a priori knownprobability , which can be represented as,(2)The probability density function for image Y with the given the modelparameters is then written as,{ , 1, 2,3,..... }jY y j J  jy{1, 2,3..... }jl Kkjljy ( | , ) l jjj j j lp y l G y   (.)G  , , 1, 2,3....k k k K   jl{ , 1, 2,3,..... }jL l j J  jlk( )jljp L ( | ) ( | , ) ( )Lp Y p Y L p L  “1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.652with (3)(3) shows a mixture model that models the histogram of gray values of an image asa sum of Gaussian distributions, each distribution is weighted with its given priorprobabilityThe goal of an image segmentation process is to reconstruct the tissue labels Lusing the image Y. When we have the estimated parameters of the model, then eachpixel can be assigned to the tissue type which best fits to its gray level value.However, the obtained results mainly depend on the model parameters. The iterativeEM algorithm is used to estimate the maximum likelihood parameters(4)by filling in the unknown tissue labels L and using the current estimated parametervalues, This algorithm recalculates the parameters that maximizes the likelihood.Therefore, the algorithm consists of two steps:Expectation step  calculates that(5)Maximization step performs the recalculation by(6)and by using m the iteration number. It has been proved that the likelihoodis increased at each iteration for EM algorithms [15].The expectation step statistically classifies the voxels by using the estimationof the Gaussian distribution parameters that( | )jjp y ( | ) ( | , ).j j kkp y p y l k    k^^arg max log ( | )p Y  ( 1) ( 1)( | ) log ( , | ) | ,m mLE p Y L Y       ( ) ( 1)arg max ( | )m m   log ( | )p Y “1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.653(7)and the maximization step estimates the Gaussian distribution parameters based onthe classification as,(8)(9)According to a given convergence criteria, equation (7) gives the finalclassification results.APPLICATION ON HISTOLOGICAL IMAGESAn example application of the EM based segmentation method is performedby using a thyroid image as shown in Figure 1.a. The grayscale image is obtained(Figure 1.b) before application of the EM algorithm. The result image is shown(Figure 1.c) using different colors for each region in the original image.( 1)( 1)( 1)( | , )( | , ) ( | , )jjmj j lmj mj j lkp y lp l Yp y l k  ( 1) ( 1)( )( 1)( | , )( | , )m mj jjmk mjjp l k Y yp l k Y   ( 1) ( 1) ( ) ( 1) ( )( )( 1)( | , )( )( )( | , )m m m m m tj j k j kjmk mjjp l k Y y yp l k Y        “1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.654(a) Original image                      (b) Grayscale image                   (c) SegmentedimageFigure 1.  EM based histological image segmentationCONCLUSIONSThe advantage of the automated segmentation method is to achieve theprocess without any user supervision. Semi-automated or automated segmentationmethods generate more agreeable results.EM based probabilistic segmentation approaches for histological images giveacceptable results. The accuracy of this segmentation algorithm depends on howmuch close the probabilistic model to the gray level distributions of the inputimages.“1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011)”in Collabaration between EPOKA University and “Aleksandër Moisiu” University of Durrëson June  2-4 2011, Tirana-Durres, ALBANIA.655REFERENCES[1] Yijun, H. and Guirong, W. (2009) Segmentation of cDNA microarray spotsusing k-means clustering algorithm and mathematical morphology. WASEInternational Conference on Information Engineering (ICIE 2009), Shanxi,China[2] Juang, L. H. and Wu, M. N. (2010) MRI brain lesion image detection basedon color-converted k-means clustering segmentation. Measurement 43,941–949[3]  Yang, G., Zhou, G. T., Yin, Y. and Yang, X. 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Expectation Maximization And Gaussian Model Based Segmentation on Histology Slides

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Expectation Maximization And Gaussian Model Based Segmentation on Histology Slides

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