Multilevel Thresholding Method for Image Segmentation Based on an Adaptive Particle Swarm Optimization Algorithm
The multilevel thresholding method with maximum entropy is one of the most important image segmentation methods in image processing. However, its time-consuming computation is often an obstacle in real time application systems. Particle swarm optimization
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Abstract. The multilevel thresholding method with maximum entropy is one of the most important image segmentation methods in image processing. However, its time-consuming computation is often an obstacle in real time application systems. Particle swarm optimization (PSO) algorithm is a class of heuristic global optimization algorithms which appeared recently. In this paper, the maximum entropy is obtained through an adaptive particle swarm optimization (APSO) algorithm. The APSO algorithm is shown to obtain the maximum entropy of multilevel thresholding effectively on experiments of image segmentation.
1 Introduction Thresholding is a popular tool for image segmentation which is essentially a pixels classification problem which can be classified into two groups: global and local [5]. Global thresholding methods select one threshold value for the entire image based on different criteria, such as minimum error thresholding [6]and Otsu’s method [7]. Entropy is a useful criterion in communications [8]. It was firstly introduced into thresholding by Pun [9] and then many methods based on entropy are developed. Local thresholding methods select different threshold values for different regions, or even for each pixel [10]. To segment complex images, a multilevel thresholding method is required. However, its time-consuming computation is often an obstacle in real time application systems. The particle swarm optimization algorithm (PSO) has been proven to be a powerful competitor to other heuristic algorithms, such as genetic algorithm, tabu search and simulated annealing algorithm for global optimization problems [11, 12]. Clerc improved the standard PSO algorithm by introducing a constriction factor (CPSO) [13]. Du et al. segmented infrared image with 2-D maximum entropy based on PSO [14]. In this paper, considering the complexity of multilevel thresholding method with maximum entropy, we take use of an adaptive particle swarm optimization (APSO) algorithm [15], which introduces two adaptive acceleration factors and a new weight function in terms of the convergence speed and global search capability of the PSO algorithm, to search the maximum entropy of image segmentation. M.A. Orgun and J. Thornton (Eds.): AI 2007, LNAI 4830, pp. 654–658, 2007. © Springer-Verlag Berlin Heidelberg 2007
Multilevel Thresholding Method for Image Segmentation
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2 Maximum Entropy Thresholding In image segmentation, the most commonly method is to segment the image into two parts by one threshold. For an image with n gray-levels, let p1 , p2 ,L , pn be the probability distribution of the levels. From the distribution we derive two probability distributions given a threshold value t, one for the object A1 and another for the background
A2 . The probability distributions of the object A1 and background A2
are given by
A1 :
p1
,
p2
PA PA 1
where PA1 =
,L ,
1
,
PA
A2 :
1
t
∑ pi , PA = 2
i =1
pt
pt +1 pt + 2 p , ,L , n , PA PA PA 2
2
(1)
2
n
∑p. i
i = t +1
The Shannon entropy for each distribution is defined as t
H (
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