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These methods allow representing images as collections of \u201cvisual words\u201d and treat them using text search approaches following the \u201cbag of features\u201d paradigm. In this article, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as \u201cgeometric words,\u201d we construct compact and informative shape descriptors by means of the \u201cbag of features\u201d approach. We also show that considering pairs of \u201cgeometric words\u201d (\u201cgeometric expressions\u201d) allows creating spatially sensitive bags of features with better discriminative power. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.<\/jats:p>","DOI":"10.1145\/1899404.1899405","type":"journal-article","created":{"date-parts":[[2011,1,25]],"date-time":"2011-01-25T19:12:52Z","timestamp":1295982772000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":434,"title":["Shape google"],"prefix":"10.1145","volume":"30","author":[{"given":"Alexander M.","family":"Bronstein","sequence":"first","affiliation":[{"name":"Tel-Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael M.","family":"Bronstein","sequence":"additional","affiliation":[{"name":"Universit\u00e0 della Svizzera Italiana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonidas J.","family":"Guibas","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maks","family":"Ovsjanikov","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,2,2]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1098"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2003.821351"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/293347.293348"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMM.2006.886271"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/11744023_32"},{"key":"e_1_2_2_6_1","volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08)","author":"Behmo R.","unstructured":"Behmo , R. , Paragios , N. , and Prinet , V . 2008. 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