Stability of boundary measures

Details Stability of boundary measures Stability of boundary measures

2007-06-14

arxiv.org/abs/0706.2153v2

Boundary measures for geometric inference, Found. Comput. Math., 10 (2), pp. 221-240, 2010

Computer Science

Computational Geometry

Scientific paper

10.1007/s10208-009-9056-2

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.

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