{"type":"journal_article","has_accepted_license":"1","volume":287,"date_updated":"2023-09-07T11:41:25Z","abstract":[{"lang":"eng","text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball."}],"publication_status":"published","publication":"Advances in Mathematics","related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Pausinger, Florian","first_name":"Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1016/j.aim.2015.10.004","_id":"1662","date_created":"2018-12-11T11:53:20Z","month":"01","citation":{"ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” <i>Advances in Mathematics</i>, vol. 287. Academic Press, pp. 674–703, 2016.","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. 2016;287:674-703. doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>, vol. 287, Academic Press, 2016, pp. 674–703, doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","apa":"Edelsbrunner, H., &#38; Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703."},"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:10Z","oa":1,"ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"674 - 703","status":"public","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"language":[{"iso":"eng"}],"intvolume":"       287","pubrep_id":"774","file":[{"file_size":248985,"content_type":"application/pdf","file_id":"4928","creator":"system","date_updated":"2020-07-14T12:45:10Z","access_level":"open_access","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","relation":"main_file","date_created":"2018-12-12T10:12:10Z","checksum":"f8869ec110c35c852ef6a37425374af7"}],"publist_id":"5488","oa_version":"Published Version","title":"Approximation and convergence of the intrinsic volume","quality_controlled":"1","scopus_import":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_published":"2016-01-10T00:00:00Z","tmp":{"image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"day":"10","ec_funded":1,"publisher":"Academic Press","year":"2016"}