The offset filtration of convex objects

Dan Halperin, Michael Kerber, Doron Shaharabani

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

Abstract

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based on the Voronoi diagram of the given convex objects. We prove that, in two and three dimensions, the size of the filtration is proportional to the size of the Voronoi diagram. Our algorithm runs in Ɵ(n log n) in the 2-dimensional case and in expected time O(n3+ ϵ), for any ϵ > 0, in the 3-dimensional case. Our approach is inspired by alpha-complexes for point sets, but requires more involved machinery and analysis primarily since Voronoi regions of general convex objects do not form a good cover. We show by experiments that our approach results in a similarly fast and topologically more stable method compared to approximating the input by point samples.

Original languageEnglish
Title of host publicationAlgorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
EditorsNikhil Bansal, Irene Finocchi
PublisherSpringer Verlag
Pages705-716
Number of pages12
ISBN (Print)9783662483497
DOIs
StatePublished - 2015
Event23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece
Duration: 14 Sep 201516 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9294
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd European Symposium on Algorithms, ESA 2015
Country/TerritoryGreece
CityPatras
Period14/09/1516/09/15

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