New similarity index based on entropy and group theory

TL;DR

This paper introduces a novel image similarity index based on entropy and group theory, providing a new algebraic framework for image comparison and an application as a stopping criterion in an iterative algorithm.

Contribution

It proposes a new similarity index using algebraic group structures and entropy, with a proof of quotient group existence and properties, applied to image processing.

Findings

The similarity index is mathematically well-defined within the quotient group.

The index has specific properties useful for image comparison.

Application as a stopping criterion improves the Mean Shift Algorithm.

Abstract

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".