H. Edelsbrunner, D. Letscher, A. Zomorodian, Topological Persistence and Simplification, In Proc. 41st Ann. IEEE Sympos. Found Comput. Sci (2000), pp. 454-463.

Abstract:

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.

Bibtex: 

@InProceedings{elz-tps-00,
  author = "Edelsbrunner, H. and Letscher, D. and Zomorodian, A.",
  title = "Topological persistence and simplification",
  booktitle = "Proc. 41st Ann. IEEE Sympos. Found Comput. Sci.",
  year = 2000,
  pages = "454--463",
}