Stable length estimates of tube-like shapes

Herbert Edelsbrunner, Florian Pausinger*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)164-177
Number of pages14
JournalJournal of Mathematical Imaging and Vision
Volume50
Issue number1-2
Early online date10 Oct 2013
DOIs
Publication statusPublished - Sep 2014

Keywords

  • Algorithms
  • Discrepancy
  • Integral geometry
  • Length
  • Persistent homology
  • Quasi-Monte Carlo integration
  • Quermassintegrals
  • Stability
  • Tubes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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