Conference Paper

Computing the q-index for Tsallis Nonextensive Image Segmentation

DOI: 10.1109/SIBGRAPI.2009.23 Conference: SIBGRAPI 2009, Proceedings of the XXII Brazilian Symposium on Computer Graphics and Image Processing, Rio de Janeiro, Brazil, 11-15 October 2009
Source: DBLP

ABSTRACT Abstract—The,concept,of entropy,based,on,Shannon,Theory,of Information has been applied in the field of image processing and analysis since the work,of T. Pun [1]. This concept,is based,on the traditional Boltzaman-Gibbs entropy, proposed under the classical thermodynamic. On the other hand, it is well known that this old formalism fails to explain some,physical system if they have complex,behavior,such as long rang interactions and long time memories. Recently, studies in mechanical statistics have proposed a new kind of entropy, called Tsallis entropy (or non-extensive entropy), which has been considered with promising results on several applications in order to explain such phenomena.,The main feature of Tsallis entropy is the q-index parameter, which is close related to the degree of system nonextensivity. In 2004 was proposed,[2] the first algorithm for image segmentation based on Tsallis entropy. However, the computation,of the q-index was,already an open,problem. On the other hand, in the field of image segmentation it is not an easy task to compare,the quality of segmentation,results. This is mainly,due to the lack of an image ground truth based on human reasoning. In this paper, we propose,the first methodology,in the field of image segmentation,for q-index computation,and compare,it with other similar approaches,using a human,based segmentation,ground,truth. The results suggest that our approach,is a forward,step for image segmentation,algorithms based on Information Theory. Index Terms—Image segmentation; q-entropy; Tsallis entropy

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    • "The Tsallis generalization of entropy has a vast spectrum of application, ranging from physics and chemistry to computer science. For instance, using the non-extensive entropy instead of the BGS entropy can produce gains in the results and efficiency of optimization algorithms [6], image segmentation [7] [8] [9] or edge detection algorithms [10]. "
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