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Article Dans Une Revue Acta Applicandae Mathematicae Année : 2011

Paths, homotopy and reduction in digital images

Résumé

The development of digital imaging (and its subsequent applications) has led to consider and investigate topological notions, well-defined in continuous spaces, but not necessarily in discrete/digital ones. In this article, we focus on the classical notion of path. We establish in particular that the standard definition of path in algebraic topology is coherent w.r.t. the ones (often empirically) used in digital imaging. From this statement, we retrieve, and actually extend, an important result related to homotopy-type preservation, namely the equivalence between the fundamental group of a digital space and the group induced by digital paths. Based on this sound definition of paths, we also (re)explore various (and sometimes equivalent) ways to reduce a digital image in a homotopy-type preserving fashion.
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Dates et versions

hal-00622495 , version 1 (07-11-2011)

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Loïc Mazo, Nicolas Passat, Michel Couprie, Christian Ronse. Paths, homotopy and reduction in digital images. Acta Applicandae Mathematicae, 2011, 113 (2), pp.167-193. ⟨10.1007/s10440-010-9591-5⟩. ⟨hal-00622495⟩
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