{"title":"Homology and robustness of level and interlevel sets","scopus_import":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1102.3389v1"}],"oa_version":"Preprint","issue":"1","publist_id":"3930","language":[{"iso":"eng"}],"intvolume":"        15","day":"01","year":"2013","publisher":"International Press","date_published":"2013-05-01T00:00:00Z","author":[{"first_name":"Paul","full_name":"Bendich, Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","last_name":"Bendich"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Morozov","first_name":"Dmitriy","full_name":"Morozov, Dmitriy"},{"full_name":"Patel, Amit","first_name":"Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","last_name":"Patel"}],"doi":"10.4310/HHA.2013.v15.n1.a3","_id":"2859","abstract":[{"lang":"eng","text":"Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization."}],"publication":"Homology, Homotopy and Applications","publication_status":"published","type":"journal_article","volume":15,"date_updated":"2021-01-12T07:00:18Z","external_id":{"arxiv":["1102.3389"]},"page":"51 - 72","status":"public","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:59:58Z","month":"05","citation":{"apa":"Bendich, P., Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2013). Homology and robustness of level and interlevel sets. <i>Homology, Homotopy and Applications</i>. International Press. <a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">https://doi.org/10.4310/HHA.2013.v15.n1.a3</a>","chicago":"Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology and Robustness of Level and Interlevel Sets.” <i>Homology, Homotopy and Applications</i>. International Press, 2013. <a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">https://doi.org/10.4310/HHA.2013.v15.n1.a3</a>.","ista":"Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.","ieee":"P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” <i>Homology, Homotopy and Applications</i>, vol. 15, no. 1. International Press, pp. 51–72, 2013.","ama":"Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. <i>Homology, Homotopy and Applications</i>. 2013;15(1):51-72. doi:<a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">10.4310/HHA.2013.v15.n1.a3</a>","mla":"Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” <i>Homology, Homotopy and Applications</i>, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:<a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">10.4310/HHA.2013.v15.n1.a3</a>.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72."}}