Stability of Curvature Measures

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.