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Topology preservation within digital surfaces

Malgouyres R., Lenoir A.

Machine Graphics and Vision

1998

Vol. 7, No. 1/2

417-425

Given two connected subsets Y ⊂ X of the set of the surfels of a connected digital surface. we propose three equivalent way to express that Y is homotopic to X. The first characterization is based on sequential deletion of simple surfels. This 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 wheter Y is n - homotopic to X. The third characterization is based on of the (digital) fundamental group.