Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
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 and A. Zomorodian, "Topological persistence and simplification," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 454.