On the approximation of intrinsic volumes Dissertation Thesis


Author(s): Pausinger, Florian
Advisor(s): Edelsbrunner, Herbert
Committee Chair(s): Edelsbrunner, Herbert
Committee Member(s): Guet, Calin; Tichy, Robert F
Title: On the approximation of intrinsic volumes
Affiliation IST Austria
Abstract: 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.
Publication Title: IST Dissertation
Degree Granting Institution: IST Austria  
Degree: PhD
Degree Date: 2015-06-01
Start Page: 1
Total Pages: 144
Open access: no
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