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A Sampling Theory for Compact Sets in Euclidean Space

Frédéric Chazal 1 David Cohen-Steiner 1 André Lieutier 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes, critical points, and critical values of distance functions.
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https://hal.archives-ouvertes.fr/hal-00864493
Contributor : Brigitte Bidégaray-Fesquet <>
Submitted on : Saturday, September 21, 2013 - 9:51:13 PM
Last modification on : Thursday, November 19, 2020 - 1:01:01 PM

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Frédéric Chazal, David Cohen-Steiner, André Lieutier. A Sampling Theory for Compact Sets in Euclidean Space. Discrete and Computational Geometry, Springer Verlag, 2009, 41 (3), pp.461-479. ⟨10.1007/s00454-009-9144-8⟩. ⟨hal-00864493⟩

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