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 $\mu$-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 $\mu$-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample. These results can also be interpreted as a framework for an effective and robust notion of curvature.
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Submitted on : Saturday, December 6, 2008 - 3:17:52 PM
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  • ARXIV : 0812.1390

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Frédéric Chazal, David Cohen-Steiner, André Lieutier, Boris Thibert. Stability of Curvature Measures. [Research Report] RR-6756, INRIA. 2008, pp.34. ⟨inria-00344903⟩

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