Approximation and convergence of the intrinsic volume

Herbert Edelsbrunner, Florian Pausinger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)674-703
JournalAdvances in Mathematics
Volume287
Early online date20 Nov 2015
DOIs
Publication statusEarly online date - 20 Nov 2015
Externally publishedYes

Keywords

  • Crofton formula
  • Digital image processing
  • Distorted normals
  • Intrinsic volume
  • Persistent homology

ASJC Scopus subject areas

  • Mathematics(all)

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