Homology Functionality For Grayscale Image Segmentation

Topological tools provide features about spaces, which are insensitive to continuous deformations. Applied to images, the topological analysis reveals important characteristics: how many connected components are present, which ones have holes and how many, how are they related one to another, how to measure them and find their locations. We show in this paper that the extraction of such features by computing persistent homology is suitable for grayscale image segmentation.