{"language":[{"iso":"eng"}],"date_updated":"2024-10-09T20:54:41Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publication":"Discrete & Computational Geometry","intvolume":" 47","ddc":["000"],"citation":{"ista":"Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414.","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-011-9382-4.","apa":"Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-011-9382-4","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:10.1007/s00454-011-9382-4.","ama":"Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4","short":"H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414.","ieee":"H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” Discrete & Computational Geometry, vol. 47, no. 2. Springer, pp. 393–414, 2012."},"department":[{"_id":"HeEd"}],"date_created":"2018-12-11T12:02:17Z","type":"journal_article","file_date_updated":"2020-07-14T12:46:05Z","oa_version":"Submitted Version","date_published":"2012-03-01T00:00:00Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","first_name":"Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"}],"month":"03","day":"01","page":"393 - 414","oa":1,"title":"Dual complexes of cubical subdivisions of ℝn","year":"2012","publist_id":"3398","issue":"2","publisher":"Springer","volume":47,"scopus_import":1,"pubrep_id":"543","doi":"10.1007/s00454-011-9382-4","_id":"3256","has_accepted_license":"1","status":"public","corr_author":"1","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.","file":[{"access_level":"open_access","date_updated":"2020-07-14T12:46:05Z","relation":"main_file","content_type":"application/pdf","file_id":"4675","creator":"system","checksum":"76486f3b2c9e7fd81342f3832ca387e7","file_name":"IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf","date_created":"2018-12-12T10:08:15Z","file_size":203636}],"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."}],"publication_status":"published"}