Improved Fuzzy C-Mean Algorithm for Medical Image S egmentation

Improved Fuzzy C-Mean Algorithm for Medical Image S egmentation

Piyush Valvi

PG Student, V.T.Patel Department of Electronics and Communication Engineering, Changa, Gujarat, India

Brijesh Shah Associate Professor, C.S.Patel Institute of

Technology, CHARUSAT,

Changa, Gujara t, India

Satish Shah Professor, M.S. University,

Baroda, Gujarat, India

Abstract

Image segmentation is a very important part of image processing. This paper presents an image segmentation approach using improved fuzzy c-mean (FCM) algorithm. The improved fuzzy c-mean algorithm is formulated by modifying the distance measurement of the standard fuzzy c-mean algorithm. The original Euclidean distance in the fuzzy c-mean algorithm is replaced by correlation distance, and thus the corresponding algorithm is derived and called as the improved fuzzy c-mean algorithm, which is shown to be more robust than original fuzzy c-mean algorithm. Experimental results on both synthetic and real MR- images show that the proposed algorithms have better performance when noise and other artifacts are present than the standard algorithms.

1. Introduction

   Image segmentation is a challenging task in image analysis. A large variety of methods of have been proposed in several years. The fuzzy c-mean technique that has been successfully applied to analysis, clustering designs in the fie ld of astronomy, geology, med ical image, target recognition, image segmentation. An image can be acted in d iffe rent feature spaces, and fuzzy c-mean method classifies by grouping the similar data points in the feature space into clusters.

   Image segmentation plays important role in medica l image. In the field of medica l diagnosis an extensive diversity of imag ing techniques is presently available, such as radiography, computed tomography (CT) and magnetic resonance imag ing (MRI) [1],[2]. In the recent times, magnetic resonance image is the most effectively used for diagnostic image e xa minat ion for brain diagnostic image e xa mination for brain d iseases such as tumor. Even through original fuzzy c-mean algorith m yie lds good results for segmenting noise free images, it fa il to segment image corrupted by noise,

   outliers and other imaging art ifacts.

   Medical image segmentation is an essential step for most successive image ana lysis task. This paper presents an image segmentation approach using improved fuzzy c -mean a lgorith m [3], [4].

2. Clustering

   The process of grouping a set of physical or abstract objects into classes of simila r objects is called clustering. A cluster is a collection of data objects that are similar to one another within the same cluster and are dissimilar to the objects in other clusters.

   There are two p roperties in clustering:

   • Ho mogeneity inside clusters: the data, which belongs to one cluster, should be as similar as possible.

   • Heterogeneity between the clusters: the data, which belongs to different clusters, should be as different as possible.

   By definition,

   "cluster analysis is the art of finding groups in data", or "clustering is the classification of similar objects into different groups, or more precisely, the partitioning of a data into subsets (clusters), so that the data in each subset (ideally) share some co mmon tra it – often proximity according to some defined distance measure"[5]. Clustering is an important task of research. Clustering is the unsupervised data min ing technique, which partitions the input space into K regions depending on some similarity/dissimilarity metric where the value of K may or may not be known a priori. The main objective of any clustering technique is to produce a K n partition matrix U(X) of the given data set X, consisting of n patterns,

   X x1, x2 , xn .

   N m

3. Improved fuzzy c-mean algorithm

   Fuzzy c-mean (FCM ) algorithm, also known as

   i 1 ij xi

   v j N m , j

   1,, C 4

   fuzzy ISODATA, was introduced by Bezdek [6] as an e xtension to Dunn's algorithm [7]. The fuzzy c-mean based algorithms are the most commonly used fuzzy clustering algorith ms in practice .

   i 1 ij

   Step 3: Ca lculate the new d istance by correlation:

   Let

   X x , x

   1 2

   ,, xN

   , where xi

   n present a

   cov

   x, y

   given set of feature data. the objective of fuzzy c-mean algorith m is to minimize the fuzzy c-mean cost function formulated as

   dij

   x, y

   corr x, y 5

   x y

   C N m 2

   Step 4: Update the fuzzy partit ion matrix U:

   J U,V

   j 1i 1 ij

   xi v j

   1

   If dij 0

   (indicating that xi v j )

   V v1, v2 ,, vc are the cluster centers.

   1

   6

   ij 2

   U ij N C is a fu zzy partit ion matrix, in which each me mber ij indicates the degree of me mbership

   between the data vector xi and the cluster J. the values of matrix U should satisfy the following conditions

   C dij m 1

   k 1 d jk

   Else

   ij 0,1 , i

   C

   1,, N , j

   1,, C

   1. ij 1

      j 1 ij

      1, i

      1,, N

   2. Step 5:

   The exponent m 1,

   is the weighting e xponent,

   If the termination crite ria have been met, stop

   which determines the fuzziness of the clusters. The most commonly used distance norm is the Euclidean

   distance dij xi v j , although Babuska suggests that other distance norm could produce better results [8]. The Euclidean distance in improved fuzzy c-mean

   algorith m is replaced by the correlation distance. And

   this imp roved fuzzy c -mean algorithm is to be more robust than the original fuzzy c -mean a lgorith m.

   Minimization of the cost function J(U,V) is a

   nonlinear optimization proble m, which can be minimized with the following iterative a lgorith m:

   Step 1: Init ialize the me mbership matrix U with

   random values so that the conditions (2) and (3) are satisfied. Choose appropriate e xponent m and the termination criteria.

   Step 2: Ca lculate the cluster centers V according to the equation:

   Else go to Step 2

   A suitable termination crite rion could b e to calculate the cost function (Eq. 1) and to see whether it is below a certain tolerance value or if its improve ment compared to the previous iteration is below a certain threshold [9]. Also the ma ximu m number of iterat ion cycles can be used as a termination criterion.

   Expe riments are conducted on real images to e xa mine the performance of the proposed improved fuzzy c-mean technique in segmenting the MR-images.

4. Experime ntal results

   The proposed improved fuzzy c-mean algorith m is imple mented using MATLAB and tested on real images to explore the segmentation accuracy of the proposed approach.

   The proposed approach of image segmentation using improved fuzzy c-means algorith m eliminates the effect of noise greatly. Th is in turn increased the segmentation accuracy of the proposed image segmentation technique.

   1. (e) (i)

   2. (f) (j)

   3. (g) (k)

   4. (h) (l)

      Fig. (a) to (d) original images, (e) to (h) is segmented images using fuzzy c-mean algorithm of original images (a) to (d) respectively, (i) to (l) is segmented images using improved fuzzy c-mean algorithm of original images (a) to (d)

      respectively

5. Conclusion

   Fuzzy c-mean a lgorith m is one of a traditional clustering method and has been generally useful for med ical image segmentation. On the other hand conventional fuzzy c-mean algorithm at all times suffers from noise in the images. Even through the original fuzzy c-mean algorith m yie lds good results for segmenting noise free images, it fails to segment

   images corrupted by noise, outliers and other imag ing artifact. in the proposed improved fu zzy c-mean algorith m, a re incorporated to control the trade-off between them. The algorith m is formu lated by modifying the distance measurements of the standard fuzzy c-mean algorith m to allow the labeling of a pixe l to be influenced by other pixels and to control the noise effect during segmentation. The experimental results suggested that the proposed algorithm performed well than other fuzzy c-mean e xtension, segmentation algorith m.

6. References

1. D. L. Pham, C. Y. Xu, and J. L. Prince, A survey of current methods in medical image segmentation, Annual Review on Biomedical Engineering, vol. 2, pp. 31537, 2000 [Technical report version, JHU/ECE 99- 01, Johns Hopkins University].

2. Liew AW-C, and H. Yan, Current methods in the

   automatic tissue segmentation of 3D magnetic resonance brain images, Current M edical Imaging Reviews, vol. 2, no. 1, pp.91103, 2006.

3. S. C. Chen, D. Q. Zhang, Robust image se gmentation using FCM with spatial constraints based on new kernel- induced distance measure, IEEE Transactions Systems M an Cybernet, vol. 34, no. 4, pp. 1907-1916, 2004.

4. Ruspini, E. (1969). Numerical methods for fuzzy clustering. Information Science 2, 319-350.

5. Amiya halder, Soumajit pramanik, Arindam kar,

   "Dynamic image segmentation using fuzzy c-mean based genetic algorithm", International journal of computer applications(0975-8887),volume 28-

   No.6,Augast 2011

6. Bezdek, J.C. (1981). Pattern Recognition with Fu77y Objective Function Algorithrns. Plenum, New York.

7. J.C. Dunn, "A Fuzzy Relative of the ISODATA Process

   and its Use in Detecting Compact, Well Separated Clusters", Journal of Cybernetics, Vol. 3, No. 3, pp. 32- 57, 1974.

8. R. Babuska, Fuzzy M odelling for Control, Kluwer Academic Publishers, The Netherlands, 1998.

9. J.-S. Jang, C.-T. Sun and E. M izutani, Neuro-Fuzzy and

Soft Computing, Prentice-Hall, USA, 1997.