Topology Preservation Within Digital Surfaces

Given two connected subsets Y?X of the set of the surfels of a connected digital surface, we propose three equivalent ways to express Y being homotopic to X. The first characterization is based on sequential deletion of simple surfels. This characterization enables us to define thinning algorithms within a digital Jordan surface. The second characterization is based on the Euler characteristics of sets of surfels. This characterization enables us, given two connected sets Y?X of surfels, to decide whether Y is n-homotopic to X. The third characterization is based on the (digital) fundamental group.

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