{"has_accepted_license":"1","pubrep_id":"543","volume":47,"acknowledgement":"This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624.","quality_controlled":"1","day":"01","status":"public","abstract":[{"lang":"eng","text":"We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n."}],"date_updated":"2021-01-12T07:42:10Z","intvolume":"        47","citation":{"chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00454-011-9382-4\">https://doi.org/10.1007/s00454-011-9382-4</a>.","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:<a href=\"https://doi.org/10.1007/s00454-011-9382-4\">10.1007/s00454-011-9382-4</a>.","ieee":"H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2. Springer, pp. 393–414, 2012.","ista":"Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete &#38; Computational Geometry. 47(2), 393–414.","ama":"Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. <i>Discrete &#38; Computational Geometry</i>. 2012;47(2):393-414. doi:<a href=\"https://doi.org/10.1007/s00454-011-9382-4\">10.1007/s00454-011-9382-4</a>","apa":"Edelsbrunner, H., &#38; Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-011-9382-4\">https://doi.org/10.1007/s00454-011-9382-4</a>","short":"H. Edelsbrunner, M. Kerber, Discrete &#38; Computational Geometry 47 (2012) 393–414."},"type":"journal_article","oa_version":"Submitted Version","title":"Dual complexes of cubical subdivisions of ℝn","issue":"2","month":"03","doi":"10.1007/s00454-011-9382-4","_id":"3256","publication_status":"published","oa":1,"scopus_import":1,"publisher":"Springer","department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"393 - 414","publist_id":"3398","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Kerber, Michael","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber"}],"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:46:05Z","date_published":"2012-03-01T00:00:00Z","ddc":["000"],"year":"2012","file":[{"creator":"system","checksum":"76486f3b2c9e7fd81342f3832ca387e7","access_level":"open_access","file_id":"4675","relation":"main_file","date_created":"2018-12-12T10:08:15Z","file_name":"IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf","file_size":203636,"date_updated":"2020-07-14T12:46:05Z","content_type":"application/pdf"}],"date_created":"2018-12-11T12:02:17Z","publication":"Discrete & Computational Geometry"}