Approximation and convergence of the intrinsic volume

Edelsbrunner, Herbert and Pausinger, Florian (2016) Approximation and convergence of the intrinsic volume. Advances in Mathematics, 287. pp. 674-703. ISSN 1090-2082

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Official URL: http://dx.doi.org/10.1016/j.aim.2015.10.004

Abstract

We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.

Item Type: Article
DOI: 10.1016/j.aim.2015.10.004
Uncontrolled Keywords: persistent homology, Crofton formula, Digital image processing, Distorted normals, Intrinsic volume
Subjects: 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems > 004 Data processing & computer science
Research Group: Edelsbrunner Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 27 Feb 2017 13:12
Last Modified: 04 Sep 2017 14:31
URI: https://repository.ist.ac.at/id/eprint/774

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