Integration of Spatial Fuzzy Clustering with Level Set for Efficient Image Segmentation

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1 Integration of Spatial Fuzzy Clustering with Level Set for Efficient Image Segmentation N. UmaDevi 1,R.Poongodi 2 1 Research Supervisor, Head, Department of Computer Science and Information Technology, Sri Jayendra Saraswathy MahaVidyalayaCollege of Arts and Science, Coimbatore-5, India. umadevigayathri@rediffmail.com 2 ResearchScholar, Sri Jayendra Saraswathy Maha VidyalayaCollege of Arts and Science, Coimbatore-5, India. poongodi.ct@gmail.com Abstract:Image segmentation plays a crucial role in numerous biomedical imaging applications, assisting technicians or health care professionals during the diagnosis of various diseases.a new fuzzy level set algorithm is proposed in this paper to facilitate medical image segmentation which is able to directly evolve from the initial segmentation of spatial fuzzy clustering. The Spatial induced fuzzy c-means using pixel classification and level set methods are utilizing dynamic variational boundaries for image segmentation. The controlling parameters of level set evolution are also estimated from the results of clustering. The fuzzy level set algorithm is enhanced with locally regularized evolution. Such improvements facilitate level set manipulation and lead to more robust segmentation. Performance evaluation of the proposed algorithm was carried on medical images from different modalities. Keywords: Fuzzy clustering, Level set, Gradient..1. INTRODUCTION Medical imaging modalities provide an effective means of noninvasively mapping the anatomy of a subject. Examples include magnetic resonance imaging (MRI), computed tomography (CT), computed radiography (CR), and ultrasonography (US). These technologies haveincreased our knowledge of normal and diseased anatomy and are critical components in diagnosis. Image segmentation algorithms are important in many medical imaging applications such as the quantification of tissue volumes [7], diagnosis [9], localization of pathology [11], study of anatomical structure [10], treatment planning [6] and computer-integrated surgery [1], [4]. Among many image segmentation algorithms, fuzzy set theory has become increasingly attractive due to itsrobust ness for ambiguity and can retain much more information than any other segmentation methods. Fuzzy sets were introduced in 1965 by LotfiZadeh to reconcile mathematical modeling and human knowledge in the engineering sciences [12], and fuzzy algorithms are widely used today in advanced information technology [2]. Fuzzy C-Means (FCM) is one of the most well-known algorithms in image segmentation, and partitions medical images into non-overlapping, constituent regions that are homogeneous with respect to some characteristics such as texture intensity [5][3][8]. However, for large data set, FCM requires substantial amount of time which limits its applicability. It is not successful in segmenting the noise image because the algorithm disregards of spatial constraint information.if we speedup the computations involved in FCM, technicians and other health care professionals could access patient information with nearly no restrictions of time. 2. RELATED WORK 2.1. Image Segmentation: Fuzzy C-Means Image Segmentation is the process of partitioning an image into non-intersecting regions such that each region is homogeneous and the union of no two adjacent regions is homogeneous. Fuzzy c-means (FCM) clustering has been widely used in image segmentation. However, in spite of its computational efficiency and wide-spread prevalence, the FCM algorithm does not take the spatial information of pixels into consideration, and hence may result in low robustness to noise and less accurate segmentation. Application-specific integrated circuits (ASICs) can meet requirements for high performance and low power consumption in image segmentation algorithms. Generalpurpose microprocessors (GPPs) or digital signal processors (DSPs) offer the necessary programmability and flexibility for various applications. In addition, GPP manufacturers are also aware of the increased importance 296

2 of multimedia applications and have included multimedia extensions to their architectures to improve the performance of multimedia workloads Cluster Validity Functions One of the fundamental challenges of clustering is how to evaluate results, without auxiliary information. A common approach for evaluation of clustering results is to use validity indexes. Clustering validation is a technique to find a set of clusters that best fits natural partitions (number of clusters) without any class information. Generally speaking, there are two types of clustering techniques, which are based on external criteria and internal criteria. External validation: Based on previous knowledge about data. Internal validation: Based on the information intrinsicto the data alone. Considering these two types of cluster validation todetermine the correct number of groups from a dataset, one option is to use external validation indexes for which a priori knowledge of dataset information is required, but it is hard to say if they can be used in real problems. Another option is to use internal validity indexes which do not require a priori information from dataset. 3. OUR CONTRIBUTION The fuzzy clustering based on image intensity is done by initial segmentation which employs level set methods for object refinement by tracking boundary variation. The widely used conventional fuzzy c-means for medical image segmentations has limitations because of its squared-norm distance measure to measure the similarity between centers and data objects of medical images which are corrupted by heavy noise, outliers, and other imaging artifacts. To overcome the limitations the proposed technique Kernel Induced Possibilistic Fuzzy C Means (KFCM) with Level Set Segmentation has been introduced. Compared to previous method FCM, the proposed KFCM algorithm has significantly improved in the following aspects. First, the KFCM incorporates spatial information during an adaptive optimization, which eliminates the intermediate morphological operations. Second, the controlling parameters of level set segmentation are now derived from the results of fuzzy clustering directly. Finally the proposed algorithm is more robust to noise and outliers, and still retains computational simplicity Fuzzy Objective The fuzzy c-means assigns pixels to c partitions by using fuzzy memberships. Let X = {x1, x2, x3 xn} denote an image with n pixels to be partioned into c clusters, where x i (i = 1, 2, 3... n) is the pixel intensity. The objective function is to discover nonlinear relationships among data, kernel methods use embedding mappings that map features of the data to new feature spaces. The proposed technique Kernel Induced Possibilistic Fuzzy C-Means (KFCM) is an iterative clustering technique that minimizes the objective function. Given an image dataset, X = {x1 xn} R p, the original KFCM algorithm partitions X into c fuzzy subsets by minimizing the following objective function as, c n m 2 ik k i (1) i 1 k 1 J( w, U, V ) u x v where c is the number of clusters and selected as a specified value;nis the number of data points, u ik themembership of x k in class i, satisfying the c i 1 u ik 1, m the quantity controlling clustering fuzziness, and V the set of cluster centers or prototypes (v i R p ) Kernel Induced PossibilisticFuzzy C-Means In fuzzy clustering, the centroid and the scope of each subclass are estimated adaptively in order to minimize a pre-defined cost function. It is one of the most popular algorithms in fuzzy, and has been applied in medical problems. The fuzzy utilizes a membership function to indicate the degree of membership of the n th object to the m th cluster which is justifiable for medical image segmentation, as physiological tissues are usually not homogeneous. The fuzzy utilizes a membership function to indicate the degree of membership in finding the allocate space and allocate resources which is justifiable for medical image segmentation. Kernel Induced Possibilistic Fuzzy C Means (KFCM) clustering algorithm is incorporates the spatial neighborhood information with traditional FCM and updating the objective function of each cluster. The KFCM uses the probabilistic constraint that the memberships of a data point across classes are sum to one. The kernel induced possibilistic c-means algorithm is used to minimize the objective function using Gaussian kernel function. 297

3 The Gaussian function η i are estimated using, i K n k 1 u m ik 2(1 K( xk, vi)) n k 1 u m ik (2) The fuzzy membership function u ik is that the edges connecting the inner data points in a cluster may have a larger degree of belonging to a cluster than the peripheral edges (which, in a sense, reflects a greater strength of connectivity between a pair of data points). For instance, the edges (indexed i) connecting the inner point in a cluster (indexed k) are assigned u ik = 1 whereas the edges linking the boundary points in a cluster have u ik < 1. Each cluster is represented by a data point called a cluster center, and the method searches for clusters so as to maximize a fitness function called net similarity. The method is iterative and stops after maximum iterations (default of 500). It automatically determines the number of clusters, based on the input p, which is an Nx1 matrix of real numbers called preferences. A good choice is to set all preference values to the median of the similarity values. The number of identified clusters can be increased or decreased by changing this value accordingly. The objective function in the clustering problem becomes more general so that the weights of data points are being taken into account, as follows: S(C) = K k =1 C k i=1 u m i j k, kλk + γ jk n j=1 (C k ) (3) where C denotes the decomposition of the given clusters, C 1,, C K are not-necessarily disjointclustersin the decomposition C, γ denotes the modulatingargument,s(c) denotes the total strength of connectivity cluster, designates, as in the edge connectivity of cluster, the weight u i(j) k,k is the membership degree of i(j) containing data point j in cluster k, and finally, it is the fitness of cluster j to cluster k Level Set Segmentation The fuzzy using pixel classification with level set methods utilizes dynamic variational boundaries for image segmentation. Segmenting images by means of active contours is well known approach instead of parametric characterization of active contours.level set methods embed them into a time dependent PDE function. It is possible to approximate the evolution of active contours implicitly by tracking the zero level set. The level set evolution of active contour implicitly tracking the zero level setγ(t), φ t, x, y < 0 φ t, x, y = 0 φ t, x, y > 0 x, y is inside Γ t x, y is at Γ t x, y is outside Γ(t) 3.4. Fuzzy With Level Set Algorithm (4) Both fuzzy algorithms and level set methods are generalpurposed computational model that can be applied to problems of any dimensions. A new fuzzy level set algorithm is proposed for automated medical image segmentation. The algorithm automates the initialization and parameter configuration of the level set segmentation, using Kernel Fuzzy clustering. A new fuzzy level set algorithm automates the initialization and parameter configuration of the level set segmentation, using spatial kernel fuzzy clustering. It employs a KFCM with spatial constraints to determine the approximate contours of interest in a medical image. Benefitting from the flexible initializations, the enhanced level set function can accommodate KFCM results directly for evolution. The enhancement achieves several practical benefits. The objective function now is derived from spatial fuzzy clustering directly. The level set function will automatically slow down the evolution and will become totally dependent on the smoothing term. 4. IMPLEMENTATION Step 1: Infuzzy clustering process, the input MRI image and number of clusters areto be initialized. In this process, fuzzy objective function, membership function and weights are calculated. To separate the partition matrix with help of cluster centroid value, the distance matrix is used to find the similarity index value of black and white pixels of the image. In the last iteration, the final partitioned objective function is derived. Step 2:Contour plot is defined to separate thebackground and foreground region in the image. The regionsof object in binary images are found using initial contour and perimeter functions. Step 3: 2-D convolution process, Gaussian filter function creates an image smoothness value which returns the central part of the image convolution. Step 4: The image pixel directionsare estimated with the help of gradient function which can either be scalars to specify the spacing between points in each direction or 298

4 vectors to specify the coordinates of the values along corresponding dimensions. The variation in space of any quantity can be represented (e.g. graphically) by a slope. The gradient represents the steepness and direction of that slope. Step 5: The Neumann boundary or second-type boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is to take on the boundary of the domain. Table 1: Structural Similarity Ratio Comparison Image type FCM SKFC Level Set Liver tumor Ultrasound artery carotid Step 6: In Level set evolution there arethree types of processes that are integratedin the final segmentation. (i) The Neumann boundary condition specifies the normal derivative of the function on a surface. (ii) The Direct Adaptive Controller method is used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. (iii) The curvature central method is used to separate the gradient coordinate s directions and sum of these points is used to find out the position which evaluates the final segmentation. 5. RESULTS SSIM Ratio Structural Similarity Ratio FCM SKFC Level Set Liver tumor Ultrasound carotid artery Figure 5 : Comparison of FCM and SKFC - Level Set Methods using SSIM The result of experiments and performance evolution were carried on medical images from different modalities, including an ultrasound image, liver tumors and MRI slice of cerebral tissues. Both the algorithms of spatial Kernel Fuzzy induced Clustering and fuzzy level set method were implemented in matlab R2010. The experiments were designed to evaluate the usefulness of initial fuzzy clustering for level set segmentation. It adopted the fast level set algorithm as in the curve optimization, where the initialization was by manual demarcation, intensity thersholding and Spatial KFCM. Due to weak boundaries and strong background noise, manual initialization did not lead to an optimal level set segmentation. The intensity thersholding and fuzzy clustering attracted the dynamic curve quickly to the boundaries of interest. For the preprocessing process the following measures are used, the structural similarity (SSIM) index is a method for measuring the similarity between two images. The SSIM index is a full reference metric, in other words, the measuring of image quality based on an initial uncompressed or distortion-free image as reference. Table - 1 shows the comparison of SSIM between the two methods FCM and SKFC Level Set. The test image is matched with existing database to identify high frequency regions. The Peak signal-to-noise ratio (PSNR) fraction is most commonly used to measure the quality of reconstruction of lossy compression coder decoder. The signal in this case is the original data, and the noise is the error introduced by compression. PSNR MAX MSE 20 log 10( I) 10 log 10( ) m 1 n 1 1 MSE [ I( i, j) K( i, j)] mn i 0 j 0 2 (5) Table 2: Peak Signal to Noise Ratio Comparison Image type FCM SKFC Level Set Liver tumor dB dB Ultrasound carotid artery dB dB 299

5 PSNR Ratio Peak Signal to Noise Ratio FCM SKFC - Level Set Figure 6: Comparison of FCM and SKFC - Levelset using PSNR Liver Tumor The ultrasound carotid artery tumor is done the SKFC level set algorithm. The improvements are used to incorporate fuzzy clustering into level set segmentation for an automatic parameter configuration. Fig. 3&4 illustrates its performance on the ultrasound image of carotid artery. The liver tumor segmentation from the MRI scan is done by the fast level set evolution. Segmentation is difficult because of the weak and irregular boundaries. The liver tissue itself is in-homogeneous, due to blood vessels. Again, it is challenging to determine an optimal initialization and the corresponding level set parameters. The results show that a fuzzy clustering has the best performance in terms of level set evolution. The proposed algorithm seems trivial in medical images with comparatively clear boundaries. However, in images without distinct boundaries, it would be very important to control the motion of the level set contours. In contrast, the new fuzzy level set algorithm is able to find out the controlling parameters from fuzzy clustering automatically. Fig. 3: Kernel Induced Possibilistic C-means Cluster indexing ultrasound carotid artery Result. Fig. 4: SKFC level set segmentation of ultrasound carotid artery. 6. CONCLUSION Fig. 1: Kernel Induced Possibilistic C-means Cluster Indexing of Liver tumor Result. In this paper we have worked with a spatial kernel induced Fuzzy level set algorithm that has been proposed for automated MRI image segmentation. The enhanced FCM algorithms with spatial information can approximate the boundaries of interest well. The level set evolution will start from a region close to the genuine boundaries. The algorithm estimates the controlling parameters from spatial clustering automatically. This has reduced the manual intervention. Finally the fuzzy level set evolution is modified locally by means of spatial fuzzy clustering. All these improvements lead to a robust algorithm for medical image segmentation. Fig. 2:SKFC level set segmentation of CT Liver tissue 300

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