TY - GEN
T1 - The Morse theory of Čech and Delaunay filtrations
AU - Bauer, Ulrich
AU - Edelsbrunner, Herbert
PY - 2014
Y1 - 2014
N2 - Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s).
AB - Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s).
UR - http://www.scopus.com/inward/record.url?scp=84904430210&partnerID=8YFLogxK
U2 - 10.1145/2582112.2582167
DO - 10.1145/2582112.2582167
M3 - Conference contribution
AN - SCOPUS:84904430210
SN - 9781450325943
T3 - Proceedings of the Annual Symposium on Computational Geometry
SP - 484
EP - 490
BT - Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PB - Association for Computing Machinery
T2 - 30th Annual Symposium on Computational Geometry, SoCG 2014
Y2 - 8 June 2014 through 11 June 2014
ER -