Stability of Curvature Measures

Frédéric Chazal 1 David Cohen-Steiner 1 André Lieutier 2 Boris Thibert 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the Gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive μ-reach can be estimated by the same curvature measures of the offset of a compact set K' close to K in the Hausdorff sense. We show how these curvature measures can be computed for finite unions of balls. The curvature measures of the offset of a compact set with positive μ-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00864486
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Submitted on : Saturday, September 21, 2013 - 9:32:47 PM
Last modification on : Friday, February 8, 2019 - 4:30:12 PM

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Frédéric Chazal, David Cohen-Steiner, André Lieutier, Boris Thibert. Stability of Curvature Measures. Computer Graphics Forum, Wiley, 2009, 28 (5), pp.1485-1496. ⟨10.1111/j.1467-8659.2009.01525.x⟩. ⟨hal-00864486⟩

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