**M. Grandis**

## Combinatorial Homology in a Perspective of Image
Analysis

**abstract:**

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.