M. Grandis

Combinatorial Homology in a Perspective of Image Analysis

This is the sequel of a paper where we introduced an intrinsic homotopy 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 $\ve > 0$, and the corresponding combinatorial homology groups $H_n^\ve(X)$ 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.