thesis
On the approximation of intrinsic volumes
ISTA Thesis
published
Florian
Pausinger
author 2A77D7A2-F248-11E8-B48F-1D18A9856A870000-0002-8379-3768
Herbert
Edelsbrunner
supervisor
HeEd
department
This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold.
Institute of Science and Technology Austria2015
eng
2663-337X
144
https://research-explorer.ista.ac.at/record/2255 https://research-explorer.ista.ac.at/record/1792 https://research-explorer.ista.ac.at/record/1662
Pausinger, Florian. <i>On the Approximation of Intrinsic Volumes</i>. Institute of Science and Technology Austria, 2015.
Pausinger F. On the approximation of intrinsic volumes. 2015.
F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.
Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.
Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.
F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.
Pausinger, F. (2015). <i>On the approximation of intrinsic volumes</i>. Institute of Science and Technology Austria.
13992018-12-11T11:51:48Z2024-10-09T20:56:38Z