Boundary Measures for Geometric Inference

12 years 4 months ago
Boundary Measures for Geometric Inference
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. Keywords Geometric inference · Curvature measures · Convex functions · Nearest neighbors · Point clouds Mathematics Subject Classification (2000) 52A39 · 51K10 · 49Q15
Frédéric Chazal, David Cohen-Steiner
Added 25 Jan 2011
Updated 25 Jan 2011
Type Journal
Year 2010
Where FOCM
Authors Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot
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