An Analysis upon Basic Fundamental Application of Ring Theory

Exploring the Use of Ring Theory in Image Segmentation and Algorithm Analysis

Abstract

Ring theory is one of the branches of the abstract algebra that has been broadly used in images. However, ring theory has not been very related with image segmentation. In this paper, we propose a new index of similarity among images using __ rings and the entropy function. This new index was applied as a new stopping criterion to the Mean Shift Iterative Algorithm with the goal to reach a better segmentation. An analysis on the performance of the algorithm with this new stopping criterion is carried out. Whereas ring theory and category theory initially followed different directions it turned out in the 1970s – that the study of functor categories also reveals new aspects for module theory.In our presentation many of the results obtained this way are achieved by purely module theoretic methods avoiding the detour via abstract category theory.