New similarity index based on entropy and group theory

In this work, we propose a new similarity index for images considering the entropy function and group theory. This index considers an algebraic group of images, it is defined by an inner law that provides a novel approach for the subtraction of images. Through an equivalence relationship in the field of images, we prove the existence of the quotient group, on which the new similarity index is defined. We also present the main properties of the new index, and the immediate application thereof as a stopping criterion of the “Mean Shift Iterative Algorithm”.