Topological Persistence and Simplification

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 computing persistence and experimental evidence for their speed and utility. Keywords. Computational geometry, computational topology, homology groups, filtrations, alpha shapes.

• Type: Conference
• Year: 2000
• Where: FOCS
• Authors: Herbert Edelsbrunner, David Letscher, Afra Zomorodian
• Keywords: Fast Algorithms, FOCS 2000, Theoretical Computer Science, Topological Change, Topological Simplification