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 lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.
About this article
Cite this article
Edelsbrunner, Letscher & Zomorodian Topological Persistence and Simplification. Discrete Comput Geom 28, 511–533 (2002). https://doi.org/10.1007/s00454-002-2885-2