Stability of boundary measures
Computational Geometry
2010-03-31 v2 Classical Analysis and ODEs
Metric Geometry
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.
Cite
@article{arxiv.0706.2153,
title = {Stability of boundary measures},
author = {Frédéric Chazal and David Cohen-Steiner and Quentin Mérigot},
journal= {arXiv preprint arXiv:0706.2153},
year = {2010}
}