Session B2: RFIA JIG’2007 - 3 èmes Journées Internationales sur l’Informatique Graphique 130 A PSO Based Approach for Fuzzy Image Clustering Salima Ouadfel Said Talhi Mohamed Batouche Computer science department, University of Batna souadfel@yahoo.fr Computer science department, University of Batna s_talhi@yahoo.fr Computer science department , University of Constantine batouche@yahoo.fr Abstract In this paper a particule swarm optimization (PSO) algorithm is proposed for fuzzy image clustering. The algorithm uses a swarm of particules to find the centroids of a specified number of clusters that optimizes the fuzzy objective function. The proposed algorithm has been applied successfully to differents types of images to illustrate its wide applicability. The results obtained from our algorithm outperform those obtained from the classical FCM algorithm which requires a good starting partition and can be often trapped in a local minimum. 1. Introduction Image segmentation is a low-level image processing task in a vision system. It is a crucial ingredient for object recognition and a very difficult task to perform [16, 19]. Its purpose is to subdivide an image into meaningful non-overlapping regions. Image segmentation can be viewed as a clustering problem, which aims to partition the image into clusters such that the pixels within a cluster are as homogenous as possible whereas the clusters among each other are as heterogeneous as possible with respect to a similarity measure [10]. Several clustering methods are provided, broad ranges of clustering methods have been proposed in the literature [9-10]. They fall into two categories: hierarchical and partitioning methods. Hierarchical methods proceed by stages producing a sequence of partitions, where each partition corresponds to a different number of clusters. A hierarchical algorithm yields a dendrogram representing the nested grouping of patterns. Partitioning methods obtain a single partition of the data by moving observations iteratively from one group to another, starting from an initial partition. Fuzzy c-means (FCM) clustering [3-5] is an unsupervised technique that has been successfully applied to image clustering. In the FCM algorithm, pixels with similar features like gray levels or colors are grouped in the same cluster. This clustering is obtanied by iteratively minimizing a cost function that is dependent on the distance of the pixels to the cluster centers. FCM has been widely used because of its simplicity and its rapid convergence [1, 14, 20]. However, it requires a good starting partition (good initial centroids) and is a descend gradient method and so can be often trapped in a local minimum which may be far from the global minimum [21]. Many heuristics have been proposed in the litterature such as genetic algorithm (GA)[13] and Ant Colony Optimization (ACO) [24] to solve such combinatorial optimization problem. Particule swarm optimization is a new computational intelligence method that has been applied succefuuly to the clustering tasks [11, 12, 15, 17, and 22]. In this paper, we propose the use of Particule Swarm Optimizationto (PSO) to fuzzy image clustering. The underlying idea is to take advantage from the PSO characteristics to develop a cooperative approach to segment an image and which outperforms conventional methods. The remainder of the paper is organized as follows. In section 2, we present an overview of the FCM algorithm. A general description of PSO principle is given in section 3. In section 4, we describe our fuzzy PSO clustering algorithm. Experimental results and comparaison with the FCM algorithm are reported in section 5. Finally concluding remarks are drawn in section 6. 2. FCM algorithm The fuzzy c~means algorithm seems to be the best known and best performing fuzzy clustering algorithms [3-4]. Its aim is to create a Fuzzy partition U(X) representing a possible grouping of a given image { } N x x x X ,..... , 2 1 = with N pixels into a number c of clusters such that pixels in the same group are similar in some sense and pixels in different groups are dissimilar in the same sense. The fuzzy partition matrix U(X) of size N C × is represented as [ ] ik u U = where each value ik u represents the membership of the i th pixel to the j th cluster and satifys the following conditions: