On the approximation of intrinsic volumes
ISTA Thesis
Pausinger, Florian
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 Austria
2015
info:eu-repo/semantics/doctoralThesis
doc-type:doctoralThesis
text
http://purl.org/coar/resource_type/c_46ec
https://research-explorer.ista.ac.at/record/1399
Pausinger F. On the approximation of intrinsic volumes. 2015.
eng
info:eu-repo/semantics/altIdentifier/issn/2663-337X
info:eu-repo/semantics/closedAccess