H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete Comput. Geom., 28 (2002), 511--533.
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.
author = "Edelsbrunner, H. and Letscher, D. and Zomorodian, A.",
title = "Topological persistence and simplification",
journal = "Discrete Comput. Geom.",
year = 2002,
volume = 28,
pages = "511--533",