inria-00154798, version 2
Stability of boundary measures
Frédéric Chazal
1David Cohen-Steiner 1Quentin Mérigot 2
N° RR-6219 (2007)
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.
- 1: GEOMETRICA (INRIA Sophia Antipolis / INRIA Futurs)
- INRIA
- 2: GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France)
- INRIA
- Domain : Computer Science/Computational Geometry
Mathematics/Classical Analysis and ODEsMathematics/Metric Geometry - Keywords : dimension detection – point clouds – curvature measures – volume of tubes – convex functions – nearest neighbor
- Internal note : RR-6219
- Available versions : v1 (2007-06-14) v2 (2007-06-18)
- inria-00154798, version 2
- http://hal.inria.fr/inria-00154798
- oai:hal.inria.fr:inria-00154798
- From: Rapport De Recherche Inria
- Submitted on: Monday, 18 June 2007 11:06:22
- Updated on: Tuesday, 15 June 2010 17:06:14
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