{"title":"Stable length estimates of tube-like shapes","citation":{"short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” <i>Journal of Mathematical Imaging and Vision</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s10851-013-0468-x\">https://doi.org/10.1007/s10851-013-0468-x</a>.","apa":"Edelsbrunner, H., &#38; Pausinger, F. (2014). Stable length estimates of tube-like shapes. <i>Journal of Mathematical Imaging and Vision</i>. Springer. <a href=\"https://doi.org/10.1007/s10851-013-0468-x\">https://doi.org/10.1007/s10851-013-0468-x</a>","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1. Springer, pp. 164–177, 2014.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:<a href=\"https://doi.org/10.1007/s10851-013-0468-x\">10.1007/s10851-013-0468-x</a>.","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. <i>Journal of Mathematical Imaging and Vision</i>. 2014;50(1):164-177. doi:<a href=\"https://doi.org/10.1007/s10851-013-0468-x\">10.1007/s10851-013-0468-x</a>"},"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7"}],"date_updated":"2023-09-07T11:41:25Z","_id":"2255","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","file_date_updated":"2020-07-14T12:45:35Z","ddc":["000"],"year":"2014","volume":50,"oa_version":"Submitted Version","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"2843"},{"relation":"dissertation_contains","id":"1399","status":"public"}]},"page":"164 - 177","day":"01","publication_status":"published","date_published":"2014-09-01T00:00:00Z","doi":"10.1007/s10851-013-0468-x","date_created":"2018-12-11T11:56:36Z","language":[{"iso":"eng"}],"issue":"1","scopus_import":1,"quality_controlled":"1","publication":"Journal of Mathematical Imaging and Vision","intvolume":"        50","file":[{"date_updated":"2020-07-14T12:45:35Z","checksum":"2f93f3e63a38a85cd4404d7953913b14","access_level":"open_access","date_created":"2018-12-12T10:16:18Z","file_size":3941391,"relation":"main_file","file_id":"5204","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","content_type":"application/pdf","creator":"system"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"}],"publisher":"Springer","publist_id":"4691","month":"09","department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["09249907"]},"has_accepted_license":"1","oa":1,"ec_funded":1,"pubrep_id":"549","abstract":[{"lang":"eng","text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm."}]}