SURVEY ON MEDICAL IMAGE SEGMENTATION USING ENHANCED K-MEANS AND KERNELIZED FUZZY C- MEANS

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1 SURVEY ON MEDICAL IMAGE SEGMENTATION USING ENHANCED K-MEANS AND KERNELIZED FUZZY C- MEANS Gunwanti S. Mahajan & Kanhan S. Bhagat. Dept of E &TC, J. T. Mahajan C.o.E Faizpur, India ABSTRACT Diagnosti imaging is an invaluable tool in mediine. Magneti resonane imaging (MRI), omputed tomography (CT), digital mammography provide an effetive means for noninvasively mapping the anatomy of a subjet. With the inreasing size and number of medial images, the use of omputers in failitating their proessing and analyses has beome neessary. More reently lustering is an effetive tool in segmenting medial images for further treatment plan. In order to solve the problems of lustering performane affeted by initial enters of lusters, a new tehnique is introdues a speialised enter initialization method for exeuting the proposed algorithms in segmenting medial images. Clustering is the proess of organizing data objets into a set of disjoint lasses alled lusters. The objetive of this paper is to make survey of enhaned k-means and Kernelized fuzzy -means for a segmentation of brain magneti resonane images. KEYWORDS: Enhane k-means, Kernelized fuzzy - means, Magneti resonane imaging, entre initialisation, lustering algorithm. I. INTRODUCTION Segmentation is an important step in the analysis of medial images for omputer-aided diagnosis and therapy [1]. Medial image segmentation separates the image into distint lasses suh as brain tumours, and neroti tissues, et. It provides an appropriate therapy presription by quantifying tissue volumes and deteting tumours, and neroti tissues. As a result, this tehnique is urrently a ruial diagnosti imaging tehnique for early detetion of abnormal hanges in tissues and organs. Many image proessing tehniques have been proposed for brain MRI segmentation inluding thresholding, region growing, and lustering [2],[3]. However, these tehniques based on pixel attributes lead to inauray with segmentation beause medial images are limited spatial resolution, poor ontrast, noise, and non-uniform intensity variation. Clustering is the proess of organizing data objets into a set of disjoint lasses alled lusters. Clustering aims to analyze and organize data into groups based on their similarity. Clustering is an example of unsupervised lassifiation. Classifiation refers to a proedure that assigns data objets to a set of lasses [4]. Unsupervised means that lustering does not depends on predefined lasses and training examples while lassifying the data objets. Cluster analysis seeks to partition a given data set into groups based on speified features so that the data points within a group are more similar to eah other than the points in different groups. Therefore, a luster is a olletion of objets that are similar among themselves and dissimilar to the objets belonging to other lusters. Fuzzy -means of unsupervised lustering tehniques whih used on established outstanding results in automated segmenting medial images in a robust manner. Fuzzy -means lustering is suessfully applied in many real world problems suh as astronomy, geology, medial imaging, target reognition, and image segmentation [4]. Among them, fuzzy -means segmentation method has onsiderable benefits, beause they ould retain muh more information from the original image than hard segmentation methods. But as we know that the lustering depends on hoie of initial luster 2531 Vol. 6, Issue 6, pp

2 entre hene we have used the luster entre initialisation algorithm in order to mprove the performane of k-means and fuzzy C-means in addition with Kernelized fuzzy -means and Enhaned k means. In this work mainly onfined K-means, Fuzzy -means, Kernelized fuzzy -means, and Enhaned k means. The rest of this paper is organized as follows: Setion II literature survey desribes different segmentation methods for MRI images. Setions III, IV give onlusion and future work respetively. II. LITERATURE SURVEY Numerous methods are available in medial image segmentation. These methods are hosen based on the speifi appliations and imaging modalities. Imaging artifats suh as noise, partial volume effets, and motion an also have signifiant onsequenes on the performane of segmentation algorithms. Some of these methods with their idiosynrasies are thresholding Method Classifiers,Markov Random Field Models,Artifiial Neural Networks, Atlas-Guided Approahes, Deformable Models Clustering Analysis, Fuzzy C-Means,Clustering K-means lustering [5] K-Means Clustering K-means is one of the simplest unsupervised learning algorithms that solve the well known lustering problem. The proedure follows a simple and easy way to lassify a given data set through a ertain number of lusters (assume k lusters) fixed a priori. The main idea is to define k entroids, one for eah luster[5]. These entroids should be plaed in a unning way beause of different loation auses different result. So, the better hoie is to plae them as muh as possible far away from eah other. The next step is to take eah point belonging to a given data set and assoiate it to the nearest entroids. When no point is pending, the first step is ompleted and an early groupage is done. At this point we need to re-alulate k new entroids as baryenters of the lusters resulting from the previous step. After we have these k new entroids, a new binding has to be done between the same data set points and the nearest new entroid. A loop has been generated. As a result of this loop we may notie that the k entroids hange their loation step by step until no more hanges are done. In other words entroids do not move any more [5]. Finally, this algorithm aims at minimizing an objetive funtion, in this ase a squared error funtion. The objetive funtion is given as k n J w (U, V) = x j v i 2 i=1 j=1 (2.1.1) Where x j v i is a hosen distane measure between a data point X j and the luster entre V i, is an indiator of the distane of the n data points from their respetive luster enters. A novel initialization algorithm of luster entres for K-means algorithm has been proposed by S. Deelers et al[7]. The algorithm was based on the data partitioning algorithm used for olour quantization. A given data set was partitioned into k lusters in suh a way that the sum of the total lustering errors for all lusters was redued as muh as possible while inter distanes between lusters are maintained to be as large as possible[7] 2.2 Fuzzy C-means Clustering Fuzzy -means (FCM) is a method of lustering whih allows one piee of data to belong to two or more lusters[8]. The traditional FCM algorithm has been used with some suess in image segmentation. The FCM algorithm is an iterative algorithm of lustering tehnique that produes optimal partitions, entres V= {v 1, v 2,, v } whih are exemplars, and radii whih defines these partitions. Let unlabelled data set X={x 1, x 2,, x n} be the pixel intensity where n is the number of image pixels to determine their memberships. The FCM algorithm tries to partition the data set X into lusters [8]. The standard FCM objetive funtion is defined as follows J m (U, V) = n U m ik x k v i 2 i=1 k=1 (2.2.1) Where x k v i 2 represents the distane between the pixel x k and entroid v i, along with i=1 onstraint U ik = 1, and the degree of fuzzifiation m 1. A data point x k belongs to a speifi luster v i that is given by the membership value U ik of the data point to that luster. Loal minimization of the objetive funtion J m(u,v) is aomplished by repeatedly adjusting the values of U kj and v i aording to the following equations[3] Vol. 6, Issue 6, pp

3 U ik = V i = 1 1 m 1 ( x k v i 2 j=1 2) x k v j n k=0 U ik m X k n U m k=0 ik (2.2.2) (2.2.3) Starting with an initial guess for eah luster entre, the FCM onverges to a solution for V i representing the loal minimum or a saddle point of the ost funtion. Convergene an be deteted by omparing the hanges in the membership funtion or the luster entre at two suessive iteration steps.[8]. Keh-Shih Chuang etal[8] proposed spatial FCM that inorporates the spatial information into the membership funtion to improve the segmentation results. The membership funtions of the neighbours entred on a pixel in the spatial domain are enumerated to obtain the luster distribution statistis. These statistis are transformed into a weighting funtion and inorporated into the membership funtion. This neighbouring effet redues the number of spurious blobs and biases the solution toward pieewise homogeneous labelling. The new method was tested on MRI images and evaluated by using various luster validity funtions. Preliminary results showed that the effet of noise in segmentation was onsiderably less with the new algorithm than with the onventional FCM. 2.3 Kernelized fuzzy C-means The standard FCM objetive funtion for partitioning a dataset {X k } N k=1 into lusters is given by J m (U, V) = n U m ik x k v i 2 i=1 k=1 (2.3.1) Where {V i } C i=1 are the enters or prototypes of the lusters and the array {U ik} =U represents a partition matrix satisfying N U {u ik [0, 1] i=1 u ik = 1, k and 0 < k=1 u ik < N, i } (2.3.2) The parameter m is a weighting exponent on eah fuzzy membership and determines the amount of fuzziness of the resulting lassifiation. In image lustering, the most ommonly used feature is the gray-level value, or intensity of image pixel [14]. Thus the FCM objetive funtion is minimized when high membership values are assigned to pixels whose intensities are lose to the entroid of its partiular lass, and low membership values are assigned when the point is far from the entroid[14]. From the disussion, we know every algorithm that only uses inner produts an impliitly be exeuted in the feature spae F. This trik an also be used in lustering, as shown in support vetor lustering and kernel (fuzzy) -means algorithm[5]s. A ommon ground of these algorithms is to represent the lustering entre as a linearly-ombined sum of all Φ (xk), i.e. the lustering entres lie in feature spae. In this setion, we onstrut a novel Kernelized FCM algorithm with objetive funtion as following n J m (U, V) = U m ik φ(x k ) φ(v i ) 2 i=1 k=1 (2.3.3) Where Φ is an impliit nonlinear map as desribed previously. Unlike, Φ(V i) here is not expressed as a linearly-ombined sum of all Φ(X k) anymore, a so-alled dual representation, but still reviewed as an mapped point (image) of i v in the original spae, then with the kernel substitution trik, we have ɸ(x k ) ɸ(x k ) 2 = (ɸ(x k ) ɸ(x k )) T (ɸ(x k ) ɸ(x k )) =ɸ(x k ) T ɸ(x k ) ɸ(v i ) T ɸ(x k ) ɸ(x k ) T ɸ(v i ) + ɸ(v i ) T ɸ(v i ) =K (x k, x k ) + K(v i, v i ) 2K(x k, v i ) (2.3.4) Below we onfine ourselves to the Gaussian RBF kernel, so K(x, x) = 1. From Eq. (2.3.4), Eq.9(2.3.3) an be simplified to N J m = 2 i=1 k=1 u m tk (1 K(x k, v i ) (2.3.5) Formally, the above optimization problem omes in the form min U,{v i } i=1 J m, (2.3.6) In a similar way to the standard FCM algorithm, the objetive funtion Jm an be minimized under the onstraint of U. Speifially, taking the first derivatives of Jm with respet to uik and vi, and zeroing them respetively, two neessary but not suffiient onditions for Jm to be at its loal extreme will be obtained as the following 2533 Vol. 6, Issue 6, pp

4 u tk = (1 K(x k,v i )) 1/(m 1) (1 K(x k,v j )) 1/(m 1) j=1 (2.3.7) V i = k=1 u tk n m K(x k,v i )x k n k=1 u m tk K(x k,v i ) (2.3.8) E.A. Zanaty etal had presented [9] alternative Kernelized FCM algorithms (KFCM) that ould improve magneti resonane imaging (MRI) segmentation. Then they implemented the KFCM method with onsidering some spatial onstraints on the objetive funtion. The algorithms inorporate spatial information into the membership funtion and the validity proedure for lustering. We use the intra-luster distane measure, whih is simply the median distane between a point and its luster entre. The number of the luster inreases automatially aording the value of intraluster, for example when a luster is obtained, it uses this luster to evaluate intra-luster of the next luster as input to the KFCM and so on, stop only when intra-luster is smaller than a presribe value. The most important aspet of the proposed algorithms is atually to work automatially. Alterative is to improve automati image segmentation[9] 2.4 Enhaned K-means Although K-means is simple and an be used for a wide variety of data types, it is quite sensitive to initial positions of luster entres. The final luster entroids may not be optimal ones as the algorithm an onverge to loal optimal solutions. An empty luster an be obtained if no points are alloated to the luster during the assignment step. Therefore, it is quite important for K-means to have good initial luster entres. The algorithms for initializing the luster entres for K-means have been proposed a new luster entre initialization algorithm. Hene the enhaned k-means algorithm will be as follows. 1. Read the input image. 2. Deide the number luster and initialize the luster entre obtained from luster entre initialization algorithm. 3. Partitioning the input data points into k lusters by assigning eah data point to the losest luster entroid using the seleted distane measure, 4. Computing a luster assignment matrix U. 5. Re-omputing the entroids. 6. If luster entroids or the assignment matrix does not hange from the previous iteration, stop; otherwise go to step 2. In Researh of Shreyansh Ojha it has proven that the Enhaned k-means algorithm is better than the onventional K-Means Clustering Algorithm for olour image segmentation, the validity measure of nearly all the images has been better than the onventional K-Means lustering algorithm, the onventional K-means algorithm uses user defined number of luster whih use to ause noisy image, but in the proposed algorithm, it uses the method for determining the number of optimal luster. It also removes the problem of empty lusters problem from onventional K-Means lustering algorithm where there was issue that if no pixel is assigned to a luster then that luster remains empty.[10] III. CONCLUSION Medial image segmentation is fasinating and very important as well. Fuzzy C-Means, K-Means and,kernelized Fuzzy C-Means,Enhaned K-means lustering algorithms have been onsidered so far they have been seen effetive in the image segmentation. They are easy to use unlike some other methods in existene. But there are still limitations that like k-means segmenting with predetermined number of lusters Fuzzy C-means generating an overlapping results and not being able to segment oloured images until they are onverted into grey sale.to improve the performane of k-means and fuzzy C-means, Kernelized fuzzy -means luster entre initialisation algorithm is used in Enhaned K means algorithm. IV. FUTURE WORK In general the lustering algorithm hooses the initial entres in random manner. In future a new entre initialization algorithm for measuring the initial entres of lustering algorithms is used. This algorithm is based on maximum measure of the distane funtion whih is found for luster entre 2534 Vol. 6, Issue 6, pp

5 detetion proess. The future implementation will be fousing on omparison of different parameters like silhouette sore, mean square error, peak signal to noise ratio of these four algorithms K means, fuzzy mean, Kernelized fuzzy means, and Enhaned k means. REFERENCES [1]. S. Shen, W. Sandham, M. Granat, and A. Sterr, MRI fuzzy segmentation of brain tissue using neighborhood attration with neural-network optimization, IEEE Transations on Information Tehnology in Biomediine, vol. 9, no. 3, pp , 2005 [2]. R. Gonzalez, and R. Woods, Digital image proessing, 2 nd ed., Prentie hall, Upper Saddle River, New Jersey, 2001 [3]. K. S. Fu and J. K. Mu, A Survey on Image Segmentation, Pattern Reognition, vol. 13, pp. 3-16, 1981 [4]. A Generalized Spatial Fuzzy C-Means Algorithm for Medial Image Segmentation Huynh Van Lun and Jong-Myon Kim, Member, IEEE, Korea, August 20-24, [5]. Fuzzy k--means Clustering Algorithm for Medial Image Segmentation, Ajala Funmilola A, Oke O.A, Adedeji T.O, Alade O.M, Adewusi E.A,Department of Computer Siene and Engineering, LAUTECH Ogbomoso, Oyo state, Nigeria. Journal of Information Engineering and Appliations ISSN (print) ISSN (online)vol 2, No.6, 2012 [6]. S. Deelers, and S. Auwatanamongkol, Enhaning K-Means Algorithm with Initial Cluster Centres Derived from Data Partitioning along the Data Axis with the Highest Variane, International Journal of Eletrial and Computer Engineering 2: [7]. Fuzzy -means lustering with spatial information for image segmentation, Keh-Shih Chuang a, Hong- Long Tzeng a,b, Sharon Chen a, Jay Wu a,b, Tzong-Jer Chen. [8]. A Kernelized Fuzzy C-means Algorithm for Automati magneti Resonane Image Segmentation, E.A. Zanaty,Sultan Aljahdali,Narayan Debnath. [9]. Enhaned K-Means Clustering Algorithm for Color Image Segmentation, Thesis submitted by Shreyansh Ojha at Shool Of Mathematis Andomputer Appliations, Thapar University Patiala [10]. N. Hema, R.Bhavani, Enhaning K-means and Kernelized Fuzzy C-means Clustering with Cluster Center Initialization in Segmenting MRI brain images, 2011 IEEE [11]. Vinod D, S Shrivastava, R. C. Jain, Clustering Of Image Data Set Using K-Means And Fuzzy K- Means Algorithms, 2010 International Conferene on Computational Intelligene and Communiation Networks. [12]. Martin Tabakov, A Fuzzy Clustering Tehnique for Medial Image Segmentation, International Symposium on Evolving Fuzzy Systems, [13]. D-Q ZHANG, S-C CHEN, Kernel-Based Fuzzy Clustering Inorporating Spatial Constraints For Image Segmentation, Proeedings of the Seond International Conferene on Mahine Learning and Cybernetis, [14]. J.M. Pena,J.A. Lozano, An Empirial Comparison of Four Initialization Methods for the K-Means algorithm, Pattern Reognition Letters 20 (1999) [15]. Stephen L. Chiu, Fuzzy Model Identifiation Based on Cluster Estimation, Journal of Intelligent and Fuzzy Systems 2 (1994) [16]. learning. html# kernel_methods. [17]. Shehroz S.Khan, Amir Ahmad, Cluster enter initialization algorithm for K-means lustering, Pattern Reognition Letters 25 (2004) [18]. S.R. Kannan, S. Ramathilagam, Robust kernel FCM in segmentation of breast medial images, Elsevier Expert Systems with Appliations 38 (2011) [19]. Image Segmentation using k-means lustering, EM and Normalized CutsSuman Tatiraju Department of EECS, Avi Mehta Department of EECS. [20]. Kernel-based fuzzy and possibilisti -means lustering, Dao-Qiang Zhang and Song-Can Chen, Department of Computer Siene Nanjing University of Aeronautis and Astronautis Nanjing, , People s Republi of China. [21]. T. Kanungo, D. M. Mount, N. Netanyahu, C. Piatko, R. Silverman, k-means lustering algorithm: Analysis and implementation, IEEE Conf. Computer Vision and Pattern Reognition, pp Vol. 6, Issue 6, pp

6 AUTHORS BIOGRAPHY Gunwanti Subhash Mahajan was born in Bhalod, India, in Year She reeived the Bahelor in Eletronis and Teleommuniation degree from the University of Pune, in Year She is urrently pursuing the Master degree with the Department of Eletronis And Teleommuniation Engineering, Faizpur. Her researh interests inlude Image proessing and information theory. Kanhan S. Bhagat was born in Jalgaon, India, in Year He reeived the Bahelor in Eletronis and Teleommuniation degree from the University of Marathwada, Aurangabad, in Year 1997 and the Master in Eletronis and Teleommuniation degree from the University of Amravati, in Year 2010, both in Eletronis and Teleommuniation engineering. His researh interest inlude Image proessing Vol. 6, Issue 6, pp