{"_id":"3560","abstract":[{"text":"We continue the study of topological persistence [5] by investigat- ing the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ∥f − g∥∞ ≤ ε, and the persistence diagrams of g are the same as those of f except all points within L1-distance at most ε from the diagonal have been removed. We prove that for func- tions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.","lang":"eng"}],"main_file_link":[{"open_access":"0","url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.4465"}],"conference":{"name":"SCG: Symposium on Computational Geometry"},"quality_controlled":0,"date_updated":"2021-01-12T07:44:19Z","acknowledgement":"Partially supported by NSF under grant CCR-00-86013, by DARPA under grant HR0011-05-1-0007, and by the Lawrence Livermore National Laboratory under grant B543154.","page":"127 - 134","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner"},{"first_name":"Dmitriy","full_name":"Morozov, Dmitriy","last_name":"Morozov"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"}],"publist_id":"2825","citation":{"chicago":"Edelsbrunner, Herbert, Dmitriy Morozov, and Valerio Pascucci. “Persistence-Sensitive Simplification of Functions on 2-Manifolds,” 127–34. ACM, 2006. <a href=\"https://doi.org/10.1145/1137856.1137878\">https://doi.org/10.1145/1137856.1137878</a>.","mla":"Edelsbrunner, Herbert, et al. <i>Persistence-Sensitive Simplification of Functions on 2-Manifolds</i>. ACM, 2006, pp. 127–34, doi:<a href=\"https://doi.org/10.1145/1137856.1137878\">10.1145/1137856.1137878</a>.","apa":"Edelsbrunner, H., Morozov, D., &#38; Pascucci, V. (2006). Persistence-sensitive simplification of functions on 2-manifolds (pp. 127–134). Presented at the SCG: Symposium on Computational Geometry, ACM. <a href=\"https://doi.org/10.1145/1137856.1137878\">https://doi.org/10.1145/1137856.1137878</a>","ieee":"H. Edelsbrunner, D. Morozov, and V. Pascucci, “Persistence-sensitive simplification of functions on 2-manifolds,” presented at the SCG: Symposium on Computational Geometry, 2006, pp. 127–134.","ista":"Edelsbrunner H, Morozov D, Pascucci V. 2006. Persistence-sensitive simplification of functions on 2-manifolds. SCG: Symposium on Computational Geometry, 127–134.","ama":"Edelsbrunner H, Morozov D, Pascucci V. Persistence-sensitive simplification of functions on 2-manifolds. In: ACM; 2006:127-134. doi:<a href=\"https://doi.org/10.1145/1137856.1137878\">10.1145/1137856.1137878</a>","short":"H. Edelsbrunner, D. Morozov, V. Pascucci, in:, ACM, 2006, pp. 127–134."},"doi":"10.1145/1137856.1137878","publication_status":"published","title":"Persistence-sensitive simplification of functions on 2-manifolds","extern":1,"status":"public","date_created":"2018-12-11T12:03:58Z","date_published":"2006-06-01T00:00:00Z","month":"06","type":"conference","publisher":"ACM","year":"2006","day":"01"}