H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete Comput. Geom., 28 (2002), 511--533.

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: 

@article{elz-tps-02,
  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",
}