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We leverage the robustness of correspondences between similar shapes to address the difficulties associated with this problem. In our approach, pairs of similar shapes are extracted from the collection, analyzed and matched in an efficient and reliable manner, culminating in the construction of a network of correspondences that connects the entire collection. The correspondence between any pair of shapes then amounts to a simple propagation along the minimax path between the two shapes in the network. At the heart of our approach is the introduction of a robust, structure-oriented shape matching method. Leveraging the idea of projective analysis, we partition 2D projections of a shape to obtain a set of 1D ordered regions, which are both simple and efficient to match. We lift the matched projections back to the 3D domain to obtain a pairwise shape correspondence. The emphasis given to structural compatibility is a central tool in estimating the reliability and completeness of a computed correspondence, uncovering any non-negligible semantic discrepancies that may exist between shapes. These detected differences are a deciding factor in the establishment of a network aiming to capture local similarities. We demonstrate that the combination of the presented observations into a co-analysis method allows us to establish reliable correspondences among shapes within large collections.<\/jats:p>","DOI":"10.1145\/2980179.2982409","type":"journal-article","created":{"date-parts":[[2016,11,11]],"date-time":"2016-11-11T17:02:54Z","timestamp":1478883774000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Structure-oriented networks of shape collections"],"prefix":"10.1145","volume":"35","author":[{"given":"Noa","family":"Fish","sequence":"first","affiliation":[{"name":"Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"van Kaick","sequence":"additional","affiliation":[{"name":"Carleton University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amit","family":"Bermano","sequence":"additional","affiliation":[{"name":"Princeton University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Cohen-Or","sequence":"additional","affiliation":[{"name":"Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,12,5]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818088"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1899404.1899405"},{"key":"e_1_2_2_3_1","unstructured":"Chang A. X. Funkhouser T. Guibas L. Hanrahan P. Huang Q. Li Z. Savarese S. Savva M. Song S. Su H. Xiao J. Yi L. and Yu F. 2015. ShapeNet: An Information-Rich 3D Model Repository. Tech. Rep. arXiv:1512.03012 {cs.GR} Stanford University --- Princeton University --- Toyota Technological Institute at Chicago.  Chang A. X. Funkhouser T. Guibas L. Hanrahan P. Huang Q. Li Z. Savarese S. Savva M. Song S. Su H. Xiao J. Yi L. and Yu F. 2015. ShapeNet: An Information-Rich 3D Model Repository. Tech. Rep. arXiv:1512.03012 {cs.GR} Stanford University --- Princeton University --- Toyota Technological Institute at Chicago."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00669"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.006"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2005.177"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03175.x"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/2600289.2600314"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024159"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366186"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601111"},{"key":"e_1_2_2_12_1","unstructured":"Kaibel V. and Peinhardt M. A. 2006. On the bottleneck shortest path problem. Konrad-Zuse-Zentrum f\u00fcr Informationstechnik.  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Geometry Processing, 225--233","author":"Rustamov R. M.","year":"2007","unstructured":"Rustamov , R. M. 2007 . Laplace-Beltrami eigenfunctions for deformation invariant shape representation . In Proc. Symp. Geometry Processing, 225--233 . Rustamov, R. M. 2007. Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In Proc. Symp. Geometry Processing, 225--233."},{"volume-title":"Eurographics Workshop on 3D Object Retrieval, The Eurographics Association, A. Ferreira, A. Giachetti, and D. Giorgi, Eds.","author":"Savva M.","key":"e_1_2_2_23_1","unstructured":"Savva , M. , Yu , F. , Su , H. , Aono , M. , Chen , B. , Cohen-Or , D. , Deng , W. , Su , H. , Bai , S. , Bai , X. , Fish , N. , Han , J. , Kalogerakis , E. , Learned-Miller , E. G. , Li , Y. , Liao , M. , Maji , S. , Tatsuma , A. , Wang , Y. , Zhang , N. , and Zhou , Z . 2016. Large-Scale 3D Shape Retrieval from ShapeNet Core55 . In Eurographics Workshop on 3D Object Retrieval, The Eurographics Association, A. Ferreira, A. Giachetti, and D. Giorgi, Eds. Savva, M., Yu, F., Su, H., Aono, M., Chen, B., Cohen-Or, D., Deng, W., Su, H., Bai, S., Bai, X., Fish, N., Han, J., Kalogerakis, E., Learned-Miller, E. G., Li, Y., Liao, M., Maji, S., Tatsuma, A., Wang, Y., Zhang, N., and Zhou, Z. 2016. Large-Scale 3D Shape Retrieval from ShapeNet Core55. In Eurographics Workshop on 3D Object Retrieval, The Eurographics Association, A. Ferreira, A. Giachetti, and D. Giorgi, Eds."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024160"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925903"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.114"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-007-0181-0"},{"key":"e_1_2_2_28_1","doi-asserted-by":"crossref","unstructured":"Tenenbaum J. B. de Silva V. and Langford J. 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