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What and Who

Approximation of intrinsic volumes

Florian Pausinger
IST Austria
AG1 Mittagsseminar (own work)
AG 1, AG 2, AG 3, AG 4, AG 5, RG1, SWS, MMCI  
Public Audience
English

Date, Time and Location

Tuesday, 2 December 2014
13:00
30 Minutes
E1 4
024
Saarbrücken

Abstract

Let M be a compact body in R^n with sufficiently smooth boundary. A digital approximation M_t of M is a set of axis aligned cubes with edge length t whose centers lie in M \cap t Z^n. It is well-known that the volume of M_t converges to the volume of M as the resolution t goes to 0 providing an easy-to-implement algorithm.


From a computational point of view, it is desirable to have similar algorithms for the other intrinsic volumes of M. However, already in R^3 the surface area and the total mean curvature of these cube-approximations can significantly differ from the values of M.

To overcome this problem, we introduce modified intrinsic volumes of M_t which are based on persistent homology. The main goal of this talk is to outline these new ideas and to sketch applications in the special case of bodies in R^3.

This is joint work with Herbert Edelsbrunner.

Contact

Michael Kerber
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Michael Kerber, 10/27/2014 12:17
Michael Kerber, 10/22/2014 13:03
Michael Kerber, 10/22/2014 13:02 -- Created document.