Physica A 391 (2012) 4899–4908 Contents lists available at SciVerse ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Generalized ICM for image segmentation based on Tsallis statistics Ilker Kilic a , Ozhan Kayacan b,∗ a Department of Electrical and Electronics Engineering, Faculty of Engineering, Celal Bayar University, Manisa, Turkey b Department of Physics, Faculty of Arts and Sciences, Celal Bayar University, Manisa, Turkey article info Article history: Received 12 October 2011 Received in revised form 17 December 2011 Available online 20 January 2012 Keywords: Tsallis entropy Image segmentation Markov random field Iterated conditional modes abstract In this paper, the iterated conditional modes optimization method of a Markov random field technique for image segmentation is generalized based on Tsallis statistics. It is observed that, for some q entropic index values the new algorithm performs better segmentation than the classical one. The proposed algorithm also does not have a local minimum problem and reaches a global minimum energy point although the number of iterations remains the same as ICM. Based on the findings of the new algorithm, it can be expressed that the new technique can be used for the image segmentation processes in which the objects are Gaussian or nearly Gaussian distributed. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Image segmentation is a fundamental process in digital image processing which has many applications in areas such as content-based image retrieval, medical image processing, and remote sensing image processing. The main goal is to extract labeled regions or boundaries for targeted objects for subsequent processing such as surface description and object recognition. Numerous segmentation methods have been proposed in the literature: histogram shape based thresholding methods [1,2], clustering based thresholding methods [3–5], entropy based thresholding methods [6–9], clustering methods [10,11], edge-based methods [12], region splitting and merging methods [13–15], and multi-resolution techniques [16–18]. The Markov random field (MRF) theory provides a convenient way of modeling context dependent entities such as image pixels and other spatially correlated features. This is achieved by characterizing these entries using MRF probabilities. The practical use of MRF models was achieved and developed by Besag [19] in 1974 and then became an efficient tool for image analysis in the Bayesian framework [20,21]. MRF has been widely used to solve vision problems at all levels including image segmentation [22], texture analysis [23], restoration [24], and edge detection [25]. Since it is difficult to maximize the joint probability of an MRF, Besag proposes a deterministic algorithm called iterated conditional modes (ICM) which maximizes local conditional probabilities sequentially [26]. The ICM algorithm uses the ‘‘greedy’’ strategy in the iterative local maximization. Given the initial labeled data x s and the other labels that are x k ∈ L = {1, 2}, the algorithm sequentially updates each x n s into x n+1 s by maximizing p(x s |y) the conditional (posterior) probability, with respect to x s . In the literature the ICM algorithm has been improved [27–29]. In Ref. [27], the ICM algorithm is adopted as a fast (‘‘greedy’’) strategy for cooling by redefining the energy and neighborhood definitions in a more flexible case that makes the result better. A new distributed image segmentation algorithm structured as a multiagent system composed of a set of segmentation agents and a coordinator agent is presented in Ref. [28]. Starting from its own initial image, each segmentation agent performs the iterated conditional modes method, known as ICM, in applications based on Markov ∗ Corresponding author. E-mail address: ozhan.kayacan@bayar.edu.tr (O. Kayacan). 0378-4371/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2011.12.062