International Journal of Computer Applications (0975 – 8887) Volume 91 – No.10, April 2014 32 A Comparison of Evolutionary Algorithms: PSO, DE and GA for Fuzzy C-Partition Assas Ouarda Department of Computer Science, University of M’sila, Algeria. Laboratory Analysis of Signals and Systems (LASS). University of M’sila, Algeria M. Bouamar Department of Electronics Science, University of M’sila, Algeria. Laboratory Analysis of Signals and Systems (LASS). University of M’sila, Algeria ABSTRACT The fuzzy c-partition entropy technique for threshold selection is one of the best image thresholding techniques, but its complexity increases with the number of thresholds. In this paper, the selection of thresholds (fuzzy parameters) was seen as an optimization problem and solved using particle swarm optimization (PSO), differential evolution (DE), genetic (GA) algorithms. The proposed fast approaches have been tested on many images. For example, the processing time of four-level thresholding using PSO, DE and GA is reduced to less than 0.4s. PSO, DE and GA show equal performance when the number of thresholds is small. When the number of thresholds is greater, the PSO algorithm performs better than GA and DE in terms of precision and robustness. But the GA algorithm is the most efficient with respect to the execution time. General Terms Partitioning algorithms, Pattern recognition, Image segmentation. Keywords Entropy, Histograms, Optimization, Particle swarm optimization, Thresholding, Fuzzy c-partition, Differential Evolution Algorithm 1. INTRODUCTION The image thresholding is the simplest method of image segmentation. Segmentation is a widely employed technique in many fields like: Optical Character Recognition, Signature Identification, Biomedical Imaging, and Target Identification. However, the automatic selection of an optimum threshold has remained a challenge in image segmentation. Many approaches have been studied for thresholding [1][2][3][4][5][6][7][8][9][10][11]. Sezgin and Sankur [2] have developed classification of thresholding algorithms based on the type of information used, and they measure their performance comparatively using a set of objective segmentation quality metrics. They distinguish six categories, namely, thresholding algorithms based on the exploitation of: 1. histogram shape information, 2. Measurement space clustering, 3. histogram entropy information, 4. image attribute information, 5. spatial information, and 6. local characteristics. The fuzzy set theory has been successfully applied in several areas such as control, image processing, pattern recognition, computer vision, medicine, social science, etc. With regard to automatic threshold selection and segmentation, the concept of fuzzy partition leads to a powerful and efficacious system [4] [9] [10]. Although, the thresholding results of the fuzzy c-partition entropy technique are much better than many existing approaches. The size of search space augments when the number of parameters of the membership function increases. Therefore, the computation time and storage space augment. For an image having L grey levels, and a membership function determined by c parameters, the size of search space is L!/((L-c)!.c!). For example, if L equals 256 and a membership function determined by two parameters, the search space will be 32 640. When the number of parameters is superior than or equal to 3, the exhausted search is too expensive or impracticable [4] [9]. To get optimal thresholds, it must find the optimal combination of the fuzzy parameters. Thus, the thresholding problem can be formulated as an optimization problem. The fuzzy entropy of the image has been chosen as the fitness function. Therefore, a strategy for effective research must be developed, where it can find the optimal combination of all the fuzzy parameters quickly. In recent years there has been a growing interest in evolutionary algorithms for diverse fields of science and engineering. The differential evolution algorithm (DE), is relatively novel optimization technique to solve numerical optimization problems. The algorithm has successfully been applied to several sorts of problems as it has claimed a wider acceptance and popularity following its simplicity, robustness, and good convergence properties [11]. Particle Swarm Optimization (PSO) has the distinction of being one of the simplest heuristic algorithms in terms of complexity of equations. Genetic algorithms (GA) are optimization algorithms based on techniques derived from genetics and natural evolution: crossovers, mutations, selection, , etc. And it is global searching technique capable, most often, to prevent from trapping into locally optimal solutions. In this work, we propose using PSO, DE and GA in finding the optimal combination of all fuzzy parameters efficiently, to render the multilevel thresholding technique more applicable and effective. The experimental study shows that the proposed approaches can obtain results with reduced computational time. The organization of the paper is as follows. In section 2 the fuzzy c-partition entropy technique of thresholding is reviewed. The section 3, deals with a review of the optimization techniques used: PSO, DE and GA. In Section 4, a complete description of proposed thresholding algorithms is presented, where each step of the algorithm is developed in detail. Section 5 illustrates the obtained experimental results and discussions and section 6 concludes this paper.