Stability of Curvature Measures
Computational Geometry
2008-12-09 v1 Differential Geometry
Abstract
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 -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 -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.
Keywords
Cite
@article{arxiv.0812.1390,
title = {Stability of Curvature Measures},
author = {Frédéric Chazal and David Cohen-Steiner and André Lieutier and Boris Thibert},
journal= {arXiv preprint arXiv:0812.1390},
year = {2008}
}