On parallel thinning algorithms: minimal non-simple sets, P-simple points and critical kernels - Archive ouverte HAL Access content directly
Journal Articles Journal of Mathematical Imaging and Vision Year : 2009

On parallel thinning algorithms: minimal non-simple sets, P-simple points and critical kernels

Abstract

Critical kernels constitute a general framework in the category of abstract complexes for the study of parallel homotopic thinning in any dimension. In this article, we present new results linking critical kernels to minimal non-simple sets (MNS) and P-simple points, which are notions conceived to study parallel thinning in discrete grids. We show that these two previously introduced notions can be retrieved, better understood and enriched in the framework of critical kernels. In particular, we propose new characterizations which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting P-simple points and minimal non-simple sets.
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Dates and versions

hal-00731784 , version 1 (13-09-2012)

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Cite

Gilles Bertrand, Michel Couprie. On parallel thinning algorithms: minimal non-simple sets, P-simple points and critical kernels. Journal of Mathematical Imaging and Vision, 2009, 35 (1), pp.23-35. ⟨10.1007/s10851-009-0152-3⟩. ⟨hal-00731784⟩
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