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Foundations of Computational Mathematics

, Volume 10, Issue 2, pp 221–240 | Cite as

Boundary Measures for Geometric Inference

  • Frédéric Chazal
  • David Cohen-Steiner
  • Quentin Mérigot
Article

Abstract

We study the boundary measures of compact subsets of the d-dimensional Euclidean space, which are closely related to Federer’s curvature measures. We show that they can be computed efficiently for point clouds and suggest that these measures can be used for geometric inference. The main contribution of this work is the proof of 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 set, showing that they can be reliably estimated from point-cloud approximations.

Geometric inference Curvature measures Convex functions Nearest neighbors Point clouds 

Mathematics Subject Classification (2000)

52A39 51K10 49Q15 

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Copyright information

© SFoCM 2009

Authors and Affiliations

  • Frédéric Chazal
    • 1
  • David Cohen-Steiner
    • 2
  • Quentin Mérigot
    • 2
  1. 1.GeometricaINRIA SaclayOrsayFrance
  2. 2.GeometricaINRIA Sophia-AntipolisSophia-AntipolisFrance

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