Non-extensive entropy algorithm for multi-region segmentation: generalization and comparison

Since eighties, the concept of entropy has been applied in the field of image processing and analysis. This concept is based on Shannon entropy which is an application in the Theory of Information of the traditional Boltzmann-Gibbs entropy, proposed to the classical thermodynamic. For decades, it is known that this old formalism of entropy fails to explain some physical system if they have complex behavior such as long-rang and longmemory interactions. Recently, studies in mechanical statistics have proposed a new kind of entropy, called Tsallis entropy (or q-entropy or non-extensive entropy), which has been considered with promising results on several application in order to explain such phenomena. In this paper we proposed an algorithm for image segmentation which is based on this new kind of entropy. Our approach, called Non-Extensive Segmentation Recursive Algorithm (NESRA) is an extension of other previous methodologies to binarize images only. In order to show the robustness of the NESRA performance, we compare it with well known and traditional approaches such as bootstrap, fuzzy c-means, k-means, self-organizing map and watershed image clustering methods. We show that, in several cases, the NESRA is better or overcomes these traditional approaches in distinct class of images.