@inproceedings{f4a875f5a5634f4796d3f73b552116bd,
title = "The offset filtration of convex objects",
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.",
author = "Dan Halperin and Michael Kerber and Doron Shaharabani",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2015.; 23rd European Symposium on Algorithms, ESA 2015 ; Conference date: 14-09-2015 Through 16-09-2015",
year = "2015",
doi = "10.1007/978-3-662-48350-3\_59",
language = "الإنجليزيّة",
isbn = "9783662483497",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "705--716",
editor = "Nikhil Bansal and Irene Finocchi",
booktitle = "Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings",
address = "ألمانيا",
}