TY - GEN
T1 - The offset filtration of convex objects
AU - Halperin, Dan
AU - Kerber, Michael
AU - Shaharabani, Doron
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84945565023&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-662-48350-3_59
DO - https://doi.org/10.1007/978-3-662-48350-3_59
M3 - منشور من مؤتمر
SN - 9783662483497
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 705
EP - 716
BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
A2 - Bansal, Nikhil
A2 - Finocchi, Irene
T2 - 23rd European Symposium on Algorithms, ESA 2015
Y2 - 14 September 2015 through 16 September 2015
ER -