inria-00344903, version 1
Stability of Curvature Measures
Frédéric Chazal
1David Cohen-Steiner 1André Lieutier 2Boris Thibert a, 2, 3
N° RR-6756 (2008)
Résumé : 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.
- a – Université Joseph-Fourier - Grenoble I
- 1 : GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France)
- INRIA
- 2 : Laboratoire Jean Kuntzmann (LJK)
- CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
- 3 : Laboratoire de Modélisation et Calcul (LMC - IMAG)
- CNRS : UMR5523 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
- Domaine : Informatique/Géométrie algorithmique
Mathématiques/Géométrie différentielle - Mots-clés : curvature measures – normal cycle – geometric inference – mu-reach – distance function – point-cloud
- Référence interne : RR-6756
- inria-00344903, version 1
- http://hal.inria.fr/inria-00344903
- oai:hal.inria.fr:inria-00344903
- Contributeur : Frédéric Chazal
- Soumis le : Samedi 6 Décembre 2008, 15:17:52
- Dernière modification le : Vendredi 30 Janvier 2009, 17:13:50
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