Combinatorial Homology in a Perspective of Image Analysis
Marco Grandis · Georgian Mathematical Journal · 2003
Abstract This is the sequel of a paper where we introduced an intrinsic ho-motopy theory and homotopy groups for simplicial complexes. We study here the relations of this homotopy theory with the well-known homology theory of simplicial complexes. Also, our investigation is aimed at applications in image analysis. A metric space 𝑋 representing an image, has a structure of simplicial complex at each resolution ε > 0, and the corresponding combinatorial homology groups give information on the image. Combining the methods developed here with programs for automatic computation of combinatorial homology might open the way to realistic applications.