{"article_processing_charge":"No","language":[{"iso":"eng"}],"issue":"4","abstract":[{"lang":"eng","text":"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."}],"publist_id":"2130","publisher":"Springer","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","doi":"10.1007/s00454-002-2885-2","scopus_import":"1","citation":{"ieee":"H. Edelsbrunner, D. Letscher, and A. Zomorodian, “Topological persistence and simplification,” <i>Discrete &#38; Computational Geometry</i>, vol. 28, no. 4. Springer, pp. 511–533, 2002.","ama":"Edelsbrunner H, Letscher D, Zomorodian A. Topological persistence and simplification. <i>Discrete &#38; Computational Geometry</i>. 2002;28(4):511-533. doi:<a href=\"https://doi.org/10.1007/s00454-002-2885-2\">10.1007/s00454-002-2885-2</a>","chicago":"Edelsbrunner, Herbert, David Letscher, and Afra Zomorodian. “Topological Persistence and Simplification.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2002. <a href=\"https://doi.org/10.1007/s00454-002-2885-2\">https://doi.org/10.1007/s00454-002-2885-2</a>.","apa":"Edelsbrunner, H., Letscher, D., &#38; Zomorodian, A. (2002). Topological persistence and simplification. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-002-2885-2\">https://doi.org/10.1007/s00454-002-2885-2</a>","short":"H. Edelsbrunner, D. Letscher, A. Zomorodian, Discrete &#38; Computational Geometry 28 (2002) 511–533.","mla":"Edelsbrunner, Herbert, et al. “Topological Persistence and Simplification.” <i>Discrete &#38; Computational Geometry</i>, vol. 28, no. 4, Springer, 2002, pp. 511–33, doi:<a href=\"https://doi.org/10.1007/s00454-002-2885-2\">10.1007/s00454-002-2885-2</a>.","ista":"Edelsbrunner H, Letscher D, Zomorodian A. 2002. Topological persistence and simplification. Discrete &#38; Computational Geometry. 28(4), 511–533."},"day":"01","status":"public","date_published":"2002-12-01T00:00:00Z","publication_identifier":{"issn":["0179-5376"]},"quality_controlled":"1","publication":"Discrete & Computational Geometry","extern":"1","intvolume":"        28","article_type":"original","acknowledgement":"We thank Jeff Erickson and John Harer for helpful discussions during early stages of this\r\npaper. We also thank Daniel Huson for the zeolite dataset Z, Thomas LaBean for the DNA\r\ndataset D, and the Stanford Graphics Lab for the Buddha dataset S. To generate the bone\r\ndataset B, we sampled an iso-surface generated by Dominique Attali. The volume data\r\nTopological Persistence and Simplification 533 was provided by Francoise Peyrin from CNRS CREATIS in Lyon and was issued from ¸ Synchrotron Radiation Microtomography from the ID19 beamline at ESRF in Grenoble.\r\nWe generated Fig. 17 using the Protein Explorer [6].","publication_status":"published","oa_version":"None","year":"2002","type":"journal_article","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"David","full_name":"Letscher, David","last_name":"Letscher"},{"full_name":"Zomorodian, Afra","last_name":"Zomorodian","first_name":"Afra"}],"_id":"3996","title":"Topological persistence and simplification","month":"12","page":"511 - 533","date_updated":"2023-06-13T11:41:19Z","volume":28,"date_created":"2018-12-11T12:06:20Z"}