Approximation and convergence of the intrinsic volume Journal Article

Author(s): Edelsbrunner, Herbert; Pausinger, Florian
Article Title: Approximation and convergence of the intrinsic volume
Affiliation IST Austria
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.
Keywords: persistent homology; Crofton formula; Digital image processing; Distorted normals; Intrinsic volume
Journal Title: Advances in Mathematics
Volume: 287
ISSN: 1090-2082
Publisher: Academic Press  
Date Published: 2016-01-10
Start Page: 674
End Page: 703
Sponsor: This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.
DOI: 10.1016/j.aim.2015.10.004
Notes: Both authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.
Open access: yes (repository)