Determining the Entropic Index q of Tsallis Entropy in Images through Redundancy

The Boltzmann-Gibbs and Tsallis entropies are essential concepts in statistical physics, which have found multiple applications in many engineering and science areas. In particular, we focus our interest on their applications to image processing through information theory. We present in this article a novel numeric method to calculate the Tsallis entropic index q characteristic to a given image, considering the image as a non-extensive system. The entropic index q is calculated through q-redundancy maximization, which is a methodology that comes from information theory. We find better results in the image processing in the grayscale by using the Tsallis entropy and thresholding q instead of the Shannon entropy.