A Hybrid Approach for DICOM Image Segmentation Using Fuzzy Techniques by IJFLS

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

A Hybrid Approach for DICOM Image Segmentation Using Fuzzy Techniques J. Umamaheswari1 and G.Radhamani2, 1 Research Scholar, Department of Computer Science, Dr.G.R.D. College of Science, Coimbatore,Tamilnadu,India. umamugesh@yahoo.com 2

Director, Department of Computer Science, Dr.G.R.D. College of Science, Coimbatore,Tamilnadu,India. radhamanig@hotmail.com

ABSTRACT This paper provides an hybrid method for segmentation using FCM thresholding with fuzzy levelset . FCM thresholding gives fine segmented results when compared to edge detection method. The optimization property of FCM is improved when it is combined with local thresholding. The application of Fuzzy levelset gives enhanced segmentation results. The experimental result proves that the hybrid method is efficient in statistical metrices that enhances the segmented results with fine regions.

KEYWORDS Medical Image segmentation, FCM, Local thresholding, Levelset, Fuzzy levelset, Adaptive thresholding.

1. INTRODUCTION Segmentation of images holds an important position in the area of image processing and widely used in medical applications which includes surgical planning, abnormality detection and treatment progress monitoring. The purpose of segmentation is to partition an image into distinct, semantically meaningful entities by defining boundaries between features and objects in an image based on some constraint, or homogeneity predicate. Computer aided detection of abnormal growth of tissues is primarily motivated by the necessity of achieving maximum possible accuracy. The various hybrid models for medical image segmentation is explained in [1,4]. There are many methods available using levelset segmentation [9,10,13,14]. Such algorithms employ fuzzy clustering, based on image intensity, for initial segmentation and employ levelset methods for object refinement by tracking boundary variation. The previous work on liver tumor segmentation [9] has based on fuzzy clustering. These methods approximately delineate a tumor boundary which not only relieves manual intervention, but also accelerates levelset optimization. Ho and Suri, on the other hand, proposed to regularize levelset evolution locally by fuzzy clustering, in order to deviate the problems of noises sensitivity and weak boundaries of medical images [10,13,14]. An optimized approach that uses a variational method of image segmentation is described to minimize energy by weighted Total Variation (TV) method is discussed in [2,3]. This model describes the Fuzzy C-means method (FCM) to obtain segmentation via fuzzy pixel classification. FCM allows pixels to fit in multiple classes with varying degrees of membership than hard classiDOI : 10.5121/ijfls.2012.2305

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

fication methods that normally makes pixel to fit in one class. This approach allows additional flexibility in many applications and has recently been used in processing of magnetic resonance image (MRI) and Computer Topography (CT) image. Threshold segmentation is widely used in many fields because of its simplicity and efficiency which is most frequently used for image segmentation. In our work the integration of FCM thresholding with fuzzy levelset is analyzed. The segmented results are proved to be efficient compare to other traditional method. The paper is organized as follows, section 2 discusses about the optimal method for DICOM image segmentation. Section 3 describes the experimentation and results. Finally the section 4 includes the conclusion and references.

2. OVERVIEW OF THE OPTIMAL APPROACH FOR DICOM IMAGE SEGMENTATION The optimal approach consists of FCM thresholding with fuzzy levelset process. The FCM algorithm that incorporates spatial information into the membership function is used for clustering, while a conventional FCM algorithm does not fully utilize the spatial information in the image. The advantages of the algorithm are its less sensitivity to noise and consider regions more homogeneous compared to other methods. So fuzzy levelset by Bing Nang Li [15] is used for the enhancement of the segmentation results. The optimal approach gives better results for DICOM image segmentation.

2.1 FCM Thresholding The fuzzy c means clustering method with thresholding approach is based on the principles of fuzzy algorithm. It consists of three components namely, Fuzzy clustering, C -Means and Thresholding

a. Fuzzy clustering: The goal of a clustering analysis is to divide a given set of image data or objects into a cluster, which represents subsets or a group. The partition should have two properties such as homogeneity and heterogeneity. The homogeneity cluster consists of similar data whereas the heterogeneity cluster contains different data. The membership functions do not reflect the actual data distribution in the input and the output spaces. They may not be suitable for fuzzy pattern recognition. To build membership functions from the data available, a clustering technique may be used to partition the data, and then produce membership functions from the resulting clustering. In our method C-means clustering is used. It is a simple unsupervised learning method which can be used for data grouping or classification when the number of the clusters is known. It consists of the following steps: Step 1: Choose the number of clusters K Step 2: Set initial centers of clusters C1, C2,…, C. Step 3: Classify each vector x l = [ x l1, x l 2,.... x l n ] T into the closest center ci using Euclidean distance measure: xi − ci = min xi − ci Step 4: Recompute the estimates for the cluster centers Let ci = [c l1, c l 2,....c ln ]

be computed by: im

∑x =

c. i

∈ cluster (i li

x lim

)

where N i is the number of vectors in the i-th cluster. 52

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

Step 5: If none of the cluster centers ( ci =1, 2,…, k) changes in step 4 stop process, otherwise go to step 3.

b. C-means algorithm: The criterion function used for the clustering process is: J (v ) =

∑ Σk k =1

where

∈

c xk−vi

is the sample mean or the center of samples of cluster i, and v={v1,v2,…,vc}.

Clusters are not completely disjoint and the data could be classified as belonging to one cluster almost as well to another. Therefore, the separation of the clusters becomes a fuzzy notion, and representation of the data can be more accurately handled by fuzzy clustering methods. It is necessary to describe the data in terms of fuzzy clusters. The criterion function used for fuzzy Cmeans clustering is c

∑ ∑ u

J (v ) =

i=1

k =1

m ik

xk−vi

where:

x ,...... x − ‘n’ data sample vectors; v ,......v − ‘c’ denotes cluster centers (centroids); u =u cxm matrix, where uik is the i-th membership value of the k-th input sample xk, and the 1

membership values satisfy the following conditions: 0 ≤

∑ U

i=1

0 <

< 1 ; i = 1 , . . . . . . .c ; k = 1 , . . . . . . , n ;

= 1 ; k = 1 , . . . . .n ;

∑ U k −1

< 1 ; i = 1 , . . . . . .c ;

m ∈ [1, ∞ ) is an exponent weight factor c. Thresholding Local threshold method is used to automatically perform histogram shape-based image thresholding or, the reduction of a graylevel image to a binary image. The algorithm assumes that the image to be threshold contains two classes of pixels or bi-modal histogram (e.g. foreground and background) then calculates the optimum threshold separating those two classes so that their combined spread is minimal. Through FCM method the segmented part cannot be seen visibly. Here FCM is used based on local thresholding. The segmentation image is made visible through optimized method.

2.2 Fuzzy Levelset for Image Segmentation This approach is based on the active [5-8] fuzzy model with the integration of adaptive region information to obtain a robust segmentation model. The level set method was first introduced by Osher and Sethian [17]. The level set method is a numerical and theoretical tool for propagating interfaces. Both FCM algorithms and level set methods are general-purpose computational mod53

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

els that can be applied to problems of any dimension. However, when applied to medical image segmentation, it helps to consider the specific circumstances for better performance. A new fuzzy level set algorithm is thereby proposed for automated medical image segmentation [15]. It begins with spatial fuzzy clustering, whose results are utilized to initiate level set segmentation, estimate controlling parameters and regularize level set evolution. It employs an FCM with spatial restrictions to determine the approximate contours of interest in a medical image. Benefitting from the flexible initialization as in levelset, the enhanced level set function can accommodate FCM results directly for evolution. Suppose the component of interest in an FCM results, the level set function φ of the closed front C is defined as follows, [16]  ( x, y ) = ± d

(( x, y ) ,C )

Where d((x, y),C) is the distance from point (x, y) to the contour C, and the sign plus or minus are chosen if the point (x, y) is inside or outside of interface C. The interface is now represented implicitly as the zero level set (or contour) of this scalar function C =

{ ( x , y )  ( x , y )}

Such an implicit representation has numerous advantages over a parametrical approach. The level set evolution equation is given by

∂

( x, y ) ∂t

 k (  ( x , y ) )   x , y ( ) ( )   ( I ( x , y )−  c



) − ( I ( x, y )−  0) 2

    

Where μ0 and μ1 are the mean of the image intensity within two subsets inside or outside the contours respectively. The final segmented image can be represented as a set of piece-wise constants.

2.3 Fuzzy Thresholding and Fuzzy Levelset Method While applying normal thresholding to the edges, the region of the image is not segmented properly and hence the excess regions are removed by applying FCM method. An FCM algorithm which is the general-purpose computational model is applied to DICOM CT image segmentation, for the better results. An image can be represented in various feature spaces, and the FCM algorithm classifies the image by grouping similar data points in the feature space into clusters. The resultant image obtained by FCM consists of less spatial information. So to improve that and to separate the segmented part from the spatial region, the local thresholding is applied. The image obtained by fuzzy thresholding consist of some deblurred edges and some incorrect segmented part. To improve the segmentation the fuzzy levelset method is used. The levelset function will automatically slow the evolution down and will become totally dependent on the smoothing term. Since a conservative levelset evolution is adopted here, it stabilizes automatically. For robust segmentation a comparatively large iteration of evolution is adopted. The levelset evolution is applied in order to avoid insufficient or excessive segmentation.

3. EXPERIMENTATION AND RESULTS: DICOM medical images are taken as test images for evaluating results. Here an average of ten images is taken for evaluation. The algorithm is tested in MATLAB. The reconstruction of an im54

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

age has the dimensions of 256 pixel intensity. The DICOM CT images in this contain a wide variety of subject matters and textures. Most of the images used are brain images with normal and abnormal images. The results are estimated statistically based on The Energy, Entropy and Mutual Information (MI) To test the accuracy of the segmentation algorithms, four steps are followed. i) First, a DICOM CT image is taken as test input. ii) Second, the different segmentation method is applied to a DICOM image. iii)Third, the performance evaluation is obtained based on the statistical measures like Energy, Entropy and MI.

a. Energy: The gray level energy indicates how the gray levels are distributed. It is formulated as,

E ( x) = â&#x2C6;&#x2018;i =1 p( x) x

where E(x) represents the gray level energy with 256 bins and p(i) refers to the probability distribution functions, which contains the histogram counts. The larger energy value corresponds to the lower number of gray levels, which means simple. The smaller energy corresponds to the higher number of gray levels, which means complex. The following table 1 shows the different parametric evaluation for segmentation algorithm. Table 1. Parametric Evaluation for Different Segmentation algorithms

Method Adaptive threshold Edge Fuzzy Threshold Fuzzy Levelset HM

Energy 0.6719 0.8987 0.6932 0.6934 0.90E-01

Entropy 0.5097 0.2087 0.4851 0.4952 1.48E-00

MI 0.2003 0.0671 7.38E-01 6.24E-01 1.43E+00

b) Entropy: Suppose that two discrete probability distributions of the images have the probability functions of p and q, the relative entropy of p with respect to q is then defined as the summation of all possible states of the system, which is formulated as,

d = â&#x2C6;&#x2018;i =1 p (i ) log 2 k

p (i ) q (i )

The following figure 1 shows the energy value for segmentation algorithm. The hybrid method gives high energy value compare to other methods.

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

Fig. 1 Energy Value of Different Segmentation Algorithm

Fig. 2 Entropy Value for Different Segmentation Algorithm

The above figure 2 shows the entropy value for segmentation algorithm. The hybrid method gives less entropy value compared to other methods. c) Mutual Information (MI) The notion of the mutual information can be applied as another objective metric. The mutual information acts as a symmetric function, which is formulated as, I ( X ,Y ) =

∑

( X , Y ) log

P 2

= −

∑

( X ) log

P ( X ) +

∑

x .y

( X ,Y )

( X )P

(Y )

( X , Y ) log

P 2

( X ,Y )

( X )P yY )

= H ( X , ) − H ( X |Y )

where I(X; Y) represents the mutual information; H(X) and H(X|Y) are entropy and conditional entropy values. It is interpreted as the information that Y can tell about X and the measure of reduction in uncertainty of X due to the existence of Y. At the same time, it also shows the relationship of the joint and product distributions. The following figure 4 shows the MI value for segmentation algorithm. The hybrid method gives high MI value compared to other methods. 56

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

Fig.3. MI Value for Different Segmentation Algorithm

(a) Input Image

(d) Fuzzy Threshold

(b) Adaptive Threshold

(e) Fuzzy Level Set

(f) Hybrid Method

Fig. 5 Image Results for Different Segmentation Algorithm

The above figure 5 shows the image results for different segmentation algorithm. The hybrid method gives the suitable segmented results with fine regions.

4. CONCLUSION In this paper an optimal method for DICOM CT image segmentation is explored with the integration of FCM thresholding with fuzzy levelset for medical image processing FCM thresholding gives fine segmented results when compared to Otsu method. The optimization property of FCM is improved when it is combined with local thresholding. The application of Fuzzy levelset gives enhanced segmentation results. The experimentation results based on the statistical metrices proves that the optimal approach enhances the segmented results with fine regions.

International Journal of Fuzzy Logic Systems (IJFLS) Vol.2, No.3, July 2012

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