Boundary Measures for Geometric Inference

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.

• Content Type Journal Article
• DOI 10.1007/s10208-009-9056-2
• Authors
  
  
  • Frédéric Chazal, INRIA Saclay Geometrica Orsay France
  • David Cohen-Steiner, INRIA Sophia-Antipolis Geometrica Sophia-Antipolis France
  • Quentin Mérigot, INRIA Sophia-Antipolis Geometrica Sophia-Antipolis France
  
  

• Journal Foundations of Computational Mathematics
• Online ISSN 1615-3383
• Print ISSN 1615-3375

Published by

Original source : http://www.springerlink.com/content/t1834k344266k2...