High order reconstruction from cross-sections

Yael Kagan, David Levin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Given parallel cross-sections data of a smooth object in IRd, one of the ways of generating approximation to the object is by interpolating the signed-distance functions corresponding to the cross-sections. This well-known method is useful in many applications, and yet its approximation properties are not fully established. The known result is that away from cross-sections that are parallel to the boundary of the object, this method gives high approximation order. However, near such tangent cross-sections the approximation order is drastically reduced. This is due to the singular behaviour of the signed-distance function near tangent cross-sections. In this paper we suggest a way to restore the high approximation order everywhere. The new method involves a recent development in the approximation of functions with singularities. We present the application of this approach to our case, analyze its approximation properties, and discuss the numerical issues involved.

Original languageEnglish
Title of host publicationCurves and Surfaces - 8th International Conference, Revised Selected Papers
EditorsAlbert Cohen, Olivier Gibaru, Jean-Daniel Boissonnat, Marie-Laurence Mazure, Christian Gout, Tom Lyche, Larry L. Schumaker
PublisherSpringer Verlag
Pages289-303
Number of pages15
ISBN (Print)9783319228037
DOIs
StatePublished - 2015
Event8th International Conference on Curves and Surfaces, 2014 - Paris, France
Duration: 12 Jun 201418 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9213
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th International Conference on Curves and Surfaces, 2014
Country/TerritoryFrance
CityParis
Period12/06/1418/06/14

Keywords

  • Multivariate reconstruction
  • Set-valued approximation
  • Singularity detection

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