Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
H. Edelsbrunner , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
D. Letscher , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
A. Zomorodian , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise, depending on its life-time or persistence within the filtration. We give fast algorithms for completing persistence and experimental evidence for their speed and utility.
topology; algorithm theory; computational geometry; topological persistence; topological simplification; filtration; growing complex; topological change; fast algorithms; computational geometry; computational topology; homology groups; alpha shapes
H. Edelsbrunner, D. Letscher, A. Zomorodian, "Topological persistence and simplification", FOCS, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 454, doi:10.1109/SFCS.2000.892133