Application of the Ring Theory in the Segmentation of Digital Images
This work addresses image segmentation for computer vision applications, but it is incremental as it builds on existing methods with a new criterion.
The paper tackled the problem of image segmentation by proposing a new similarity index based on Zn rings and entropy, applied as a stopping criterion in the Mean Shift Iterative Algorithm, with results proving it is a suitable tool for comparing images.
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 Zn 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. The obtained results proved that the new index is a suitable tool to compare images.