(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This article examines the application of persistent homology in analyzing the structure of various shapes, including both standard and random forms. It focuses on the computation of genus, Betti numbers, and persistent homology, demonstrating how this method simplifies the analysis of complex structures. The approach proves valuable for tasks such as edge detection, thinning, restructuring, and identifying genus deformations. Furthermore, the study outlines future directions, including the development of a model leveraging persistent homology for tumor cell detection and structural genus estimation. These findings hold significant potential for advancing image processing and biomedical analysis.