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Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>\n            We present an algorithm for\n            <jats:italic>hierarchical<\/jats:italic>\n            and\n            <jats:italic>layered<\/jats:italic>\n            analysis of\n            <jats:italic>irregular<\/jats:italic>\n            facades, seeking a high-level understanding of facade structures. By introducing layering into the analysis, we no longer view a facade as a flat structure, but allow it to be structurally separated into depth layers, enabling more compact and natural interpretations of building facades. Computationally, we perform a symmetry-driven search for an optimal hierarchical decomposition defined by split and layering operations applied to an input facade. The objective is\n            <jats:italic>symmetry maximization<\/jats:italic>\n            , i.e., to maximize the sum of symmetry of the substructures resulting from recursive decomposition. To this end, we propose a novel\n            <jats:italic>integral symmetry<\/jats:italic>\n            measure, which behaves well at both ends of the symmetry spectrum by accounting for all partial symmetries in a discrete structure. Our analysis results in a structural representation, which can be utilized for structural editing and exploration of building facades.\n          <\/jats:p>","DOI":"10.1145\/2461912.2461923","type":"journal-article","created":{"date-parts":[[2013,7,16]],"date-time":"2013-07-16T18:06:45Z","timestamp":1373998005000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":57,"title":["Layered analysis of irregular facades via symmetry maximization"],"prefix":"10.1145","volume":"32","author":[{"given":"Hao","family":"Zhang","sequence":"first","affiliation":[{"name":"Simon Fraser University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Xu","sequence":"additional","affiliation":[{"name":"Shenzhen VisuCA Key Lab\/SIAT and HPCL, NUDT"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Jiang","sequence":"additional","affiliation":[{"name":"HPCL, NUDT"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinjie","family":"Lin","sequence":"additional","affiliation":[{"name":"Shenzhen VisuCA Key Lab\/SIAT"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Cohen-Or","sequence":"additional","affiliation":[{"name":"Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoquan","family":"Chen","sequence":"additional","affiliation":[{"name":"Shenzhen VisuCA Key Lab\/SIAT"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,7,21]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.1024"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778841"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185574"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1037\/0096-1523.9.6.980"},{"key":"e_1_2_2_5_1","volume-title":"-L","author":"Chao Y.","year":"2012","unstructured":"Chao , Y. , Tian , H. , Long , Q. , and Tai , C . -L . 2012 . Parsing facade with rank-one approximation. In Proc. of CVPR. Chao, Y., Tian, H., Long, Q., and Tai, C.-L. 2012. Parsing facade with rank-one approximation. In Proc. of CVPR."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199507000-00005"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.3390\/sym2020466"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218443"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0896-6273(02)01091-7"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057448"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2006.68"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024217"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2011.02.003"},{"key":"e_1_2_2_15_1","volume-title":"Proc. of Eurographics STAR Report.","author":"Mitra N. J.","unstructured":"Mitra , N. J. , Pauly , M. , Wand , M. , and Ceylan , D . 2012. Symmetry in 3D geometry: Extraction and applications . In Proc. of Eurographics STAR Report. Mitra, N. J., Pauly, M., Wand, M., and Ceylan, D. 2012. Symmetry in 3D geometry: Extraction and applications. In Proc. of Eurographics STAR Report."},{"key":"e_1_2_2_16_1","doi-asserted-by":"crossref","unstructured":"Musialski P. Wonka P. Aliaga D. G. Wimmer M. van Gool L. and Purgathofer W. 2012. A survey of urban reconstruction. In Eurographics State-of-the-art Report.  Musialski P. Wonka P. Aliaga D. G. Wimmer M. van Gool L. and Purgathofer W. 2012. A survey of urban reconstruction. 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