{"abstract":[{"text":"The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology.","lang":"eng"}],"department":[{"_id":"HeEd"}],"issue":"11","publication_status":"published","date_published":"2012-08-01T00:00:00Z","date_updated":"2021-01-12T07:42:34Z","month":"08","day":"01","type":"journal_article","file":[{"date_updated":"2020-07-14T12:46:06Z","date_created":"2018-12-12T10:15:00Z","file_size":280280,"file_id":"5116","relation":"main_file","checksum":"d65f79775b51258a604ca5ec741297cc","file_name":"IST-2016-542-v1+1_2012-J-01-Poinculus.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf"}],"status":"public","title":"A point calculus for interlevel set homology","quality_controlled":"1","scopus_import":1,"publisher":"Elsevier","date_created":"2018-12-11T12:02:36Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","oa":1,"_id":"3310","pubrep_id":"542","language":[{"iso":"eng"}],"citation":{"mla":"Bendich, Paul, et al. “A Point Calculus for Interlevel Set Homology.” <i>Pattern Recognition Letters</i>, vol. 33, no. 11, Elsevier, 2012, pp. 1436–44, doi:<a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">10.1016/j.patrec.2011.10.007</a>.","ieee":"P. Bendich, S. Cabello, and H. Edelsbrunner, “A point calculus for interlevel set homology,” <i>Pattern Recognition Letters</i>, vol. 33, no. 11. Elsevier, pp. 1436–1444, 2012.","apa":"Bendich, P., Cabello, S., &#38; Edelsbrunner, H. (2012). A point calculus for interlevel set homology. <i>Pattern Recognition Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">https://doi.org/10.1016/j.patrec.2011.10.007</a>","ista":"Bendich P, Cabello S, Edelsbrunner H. 2012. A point calculus for interlevel set homology. Pattern Recognition Letters. 33(11), 1436–1444.","chicago":"Bendich, Paul, Sergio Cabello, and Herbert Edelsbrunner. “A Point Calculus for Interlevel Set Homology.” <i>Pattern Recognition Letters</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">https://doi.org/10.1016/j.patrec.2011.10.007</a>.","ama":"Bendich P, Cabello S, Edelsbrunner H. A point calculus for interlevel set homology. <i>Pattern Recognition Letters</i>. 2012;33(11):1436-1444. doi:<a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">10.1016/j.patrec.2011.10.007</a>","short":"P. Bendich, S. Cabello, H. Edelsbrunner, Pattern Recognition Letters 33 (2012) 1436–1444."},"has_accepted_license":"1","publication":"Pattern Recognition Letters","author":[{"full_name":"Bendich, Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","last_name":"Bendich","first_name":"Paul"},{"full_name":"Cabello, Sergio","last_name":"Cabello","first_name":"Sergio"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"page":"1436 - 1444","doi":"10.1016/j.patrec.2011.10.007","ddc":["000"],"file_date_updated":"2020-07-14T12:46:06Z","acknowledgement":"Research by the third author is partially supported by the National Science Foundation (NSF) under grant DBI-0820624.","year":"2012","volume":33,"publist_id":"3330","intvolume":"        33"}