Stable length estimates of tube-like shapes Journal Article


Author(s): Edelsbrunner, Herbert; Pausinger, Florian
Article Title: Stable length estimates of tube-like shapes
Affiliation IST Austria
Abstract: Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm.
Keywords: Algorithms; persistent homology; length; Stability; Discrepancy; Integral geometry; Quasi-Monte Carlo integration; Quermassintegrals; Tubes
Journal Title: Journal of Mathematical Imaging and Vision
Volume: 50
Issue 1
ISSN: 1573-7683
Publisher: Springer  
Date Published: 2014-09-01
Start Page: 164
End Page: 177
Sponsor: This research is partially supported by the NSF (DBI-0820624), ESF, ERC (FP7-ICT-318493-STREP) and 11.G34.31.0053.
URL:
DOI: 10.1007/s10851-013-0468-x
Notes: The authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. Furthermore, they thank three reviewers for their careful reading of two earlier manuscripts and for a number of insightful comments which helped improve the paper.
Open access: yes (repository)