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Stability of boundary measures

Frédéric Chazal 1 David Cohen-Steiner 1 Quentin Mérigot 2
1 GEOMETRICA - Geometric computing
INRIA Futurs, CRISAM - Inria Sophia Antipolis - Méditerranée
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We introduce the boundary measure at scale r of a compact subset of the n-dimensional Euclidean space. We show how it can be computed for point clouds and suggest these measures can be used for feature detection. The main contribution of this work is the proof a quantitative stability theorem for boundary measures using tools of convex analysis and geometric measure theory. As a corollary we obtain a stability result for Federer's curvature measures of a compact, allowing to compute them from point-cloud approximations of the compact.
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Submitted on : Monday, June 18, 2007 - 11:06:22 AM
Last modification on : Wednesday, February 2, 2022 - 3:52:20 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:28:51 PM


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  • HAL Id : inria-00154798, version 2
  • ARXIV : 0706.2153



Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot. Stability of boundary measures. [Research Report] RR-6219, INRIA. 2007, pp.20. ⟨inria-00154798v2⟩



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