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Combinatorial homology in a perspective of image analysis. (English) Zbl 1049.55009
This paper contains results on the homology of simplicial complexes. There is a Hurewicz theorem relating the homology groups to the intrinsic homotopy groups (these are defined combinatorially and are not the same as the homotopy groups of the geometric realisations). There is an application to open-spot dilations, which arise in mathematical morphology. There are also methods of calculation designed for use in image analysis.
MSC:
55U10 Simplicial sets and complexes in algebraic topology
68U10 Computing methodologies for image processing
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