Computing the q-index for Tsallis Nonextensive Image Segmentation

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.