Applied Soft Computing 17 (2014) 1–11 Contents lists available at ScienceDirect Applied Soft Computing j ourna l h o mepage: www.elsevier.com/locate/asoc Multi-level image thresholding by synergetic differential evolution Musrrat Ali a , Chang Wook Ahn a,∗ , Millie Pant b a Department of Computer Engineering, Sungkyunkwan University, Suwon 440746, Republic of Korea b Department of Applied Science and Engineering, IIT Roorkee 247667, India a r t i c l e i n f o Article history: Received 15 January 2013 Received in revised form 8 September 2013 Accepted 29 November 2013 Available online 31 December 2013 Keywords: Image segmentation Optimization Entropy Gaussian curve fitting a b s t r a c t The multi-level image thresholding is often treated as a problem of optimization. Typically, finding the parameters of these problems leads to a nonlinear optimization problem, for which obtaining the solution is computationally expensive and time-consuming. In this paper a new multi-level image thresholding technique using synergetic differential evolution (SDE), an advanced version of differential evolution (DE), is proposed. SDE is a fusion of three algorithmic concepts proposed in modified versions of DE. It utilizes two criteria (1) entropy and (2) approximation of normalized histogram of an image by a mixture of Gaussian distribution to find the optimal thresholds. The experimental results show that SDE can make optimal thresholding applicable in case of multi-level thresholding and the performance is better than some other multi-level thresholding methods. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Image segmentation is a very common image processing oper- ation, since all image processing schemes need some sort of operation of the pixels into different classes. In order to determine thresholds for segmentation, most methods analyze the histogram of the image. The optimal thresholds are those values of intensity that can separate different objects from each other or from the background to such an extent that a decision can be made with- out further processing [1,2] and these are often found by either minimizing or maximizing an objective function with respect to the values of the thresholds. It is typically simple and computa- tionally efficient and based on the assumption that the objects can be distinguished by their gray levels. The automatic fitting of these thresholds is one of the main challenges in image segmentation. There are a lot of approaches classifying thresholding methods. Sez- gin and Sankur [3] presented a survey of a variety of thresholding techniques. They classified the thresholding techniques in terms of parametric and non parametric approaches. Parametric thresholding methods exploit the first-order statis- tical characterization of the image to be segmented. An attempt to find an estimate of the parameters of the distribution that best fit the given histogram data is made by using the least-squares estimation method. Over the years, many researchers have pro- posed several algorithms to solve the problem of Gaussian curve ∗ Corresponding author. Tel.: +82 31 299 4588. E-mail addresses: musrrat.iitr@gmail.com (M. Ali), cwan@skku.edu (C.W. Ahn), millifpt@iitr.ernet.in (M. Pant). fitting for multi-level thresholding. Some instances of paramet- ric thresholding methods available in literature as follows: Snyder et al. [4] presented a method for fitting curves based on a heuris- tic method called tree annealing. Nakib et al. [5] proposed a fast scheme for optimal thresholding using a simulated annealing algo- rithm. Zahara et al. [6] proposed a hybrid Nelder–Mead Particle Swarm Optimization (NM-PSO) method, while a hybrid method based on Expectation Maximization (EM) and Particle Swarm Opti- mization (PSO + EM) is proposed by Fan and Lin [7] for dealing with image segmentation. Application of basic differential evolu- tion (DE) for solving image segmentation problem is given in [8]. Non-parametric approaches, on the other hand, find the thresh- olds that separate the gray-level regions of an image based on some discriminating criteria such as the between class variance, entropy and cross entropy. Otsu’s [2] proposed a method in which optimal thresholds are selected by maximizing the between class variance. However, inefficient formulation of between class variance makes the method very time-consuming for multi-level threshold selec- tion. To overcome this problem, Liao et al. [9] proposed a fast recursive algorithm called Fast Otsu method, along with a look- up-table and implemented it for multi-level thresholding. Ye et al. [10] applied PSO algorithm to optimize the Otsu’s criterion. Kapur et al. [11] have given a method for gray-level picture thresholding by using the entropy of the histogram. Dirami et al. [12] adopted a fast multilevel thresholding image segmentation scheme through a multiphase level set method. Madhubanti and Amitava [13] pre- sented a hybrid cooperative–comprehensive learning based PSO algorithm based on maximum entropy criterion. Yin [14] devel- oped a recursive programming technique to reduce the order of magnitude of computing the multi-level thresholds and further 1568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2013.11.018