{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T05:03:47Z","timestamp":1781586227735,"version":"3.54.5"},"reference-count":33,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2013,7,21]],"date-time":"2013-07-21T00:00:00Z","timestamp":1374364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["CCF 1011228, DMS 1228304"],"award-info":[{"award-number":["CCF 1011228, DMS 1228304"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"name":"INRIA Associated team COMET"},{"DOI":"10.13039\/501100004794","name":"Centre National de la Recherche Scientifique","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004794","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006785","name":"Google","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006785","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["699\/12"],"award-info":[{"award-number":["699\/12"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF 1011228, DMS 1228304"],"award-info":[{"award-number":["CCF 1011228, DMS 1228304"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001663","name":"Volkswagen Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Lower-Saxony"},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["GIGA (ANR-09-BLAN-0331-01)"],"award-info":[{"award-number":["GIGA (ANR-09-BLAN-0331-01)"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0372"],"award-info":[{"award-number":["FA9550-12-1-0372"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004963","name":"Seventh Framework Programme","doi-asserted-by":"publisher","award":["CIG 303511"],"award-info":[{"award-number":["CIG 303511"]}],"id":[{"id":"10.13039\/501100004963","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>We develop a novel formulation for the notion of shape differences, aimed at providing detailed information about the location and nature of the differences or distortions between the two shapes being compared. Our difference operator, derived from a shape map, is much more informative than just a scalar global shape similarity score, rendering it useful in a variety of applications where more refined shape comparisons are necessary. The approach is intrinsic and is based on a linear algebraic framework, allowing the use of many common linear algebra tools (e.g, SVD, PCA) for studying a matrix representation of the operator. Remarkably, the formulation allows us not only to localize shape differences on the shapes involved, but also to compare shape differences across pairs of shapes, and to analyze the variability in entire shape collections based on the differences between the shapes. Moreover, while we use a map or correspondence to define each shape difference, consistent correspondences between the shapes are not necessary for comparing shape differences, although they can be exploited if available. We give a number of applications of shape differences, including parameterizing the intrinsic variability in a shape collection, exploring shape collections using local variability at different scales, performing shape analogies, and aligning shape collections.<\/jats:p>","DOI":"10.1145\/2461912.2461959","type":"journal-article","created":{"date-parts":[[2013,7,16]],"date-time":"2013-07-16T18:06:45Z","timestamp":1373998005000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":115,"title":["Map-based exploration of intrinsic shape differences and variability"],"prefix":"10.1145","volume":"32","author":[{"given":"Raif M.","family":"Rustamov","sequence":"first","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maks","family":"Ovsjanikov","sequence":"additional","affiliation":[{"name":"LIX, \u00c9cole Polytechnique"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omri","family":"Azencot","sequence":"additional","affiliation":[{"name":"Technion"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mirela","family":"Ben-Chen","sequence":"additional","affiliation":[{"name":"Technion"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Chazal","sequence":"additional","affiliation":[{"name":"Geometrica, INRIA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leonidas","family":"Guibas","sequence":"additional","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2013,7,21]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882311"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073207"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531340"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/MMBIA.1996.534052"},{"key":"e_1_2_1_5_1","volume-title":"Functional Analysis, Sobolev Spaces and Partial Differential Equations","author":"Brezis H.","unstructured":"Brezis , H. 2010. Functional Analysis, Sobolev Spaces and Partial Differential Equations . Springer-Verlag . Brezis, H. 2010. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer-Verlag."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0508601103"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"Bronstein A. Bronstein M. and Kimmel R. 2008. Numerical Geometry of Non-Rigid Shapes. Springer.   Bronstein A. Bronstein M. and Kimmel R. 2008. Numerical Geometry of Non-Rigid Shapes . Springer.","DOI":"10.1007\/978-0-387-73301-2"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1117\/12.431093"},{"key":"e_1_2_1_9_1","unstructured":"Dryden I. L. and Mardia K. V. 1998. Statistical Shape Analysis. John Wiley and Sons.  Dryden I. L. and Mardia K. V. 1998. Statistical Shape Analysis . John Wiley and Sons."},{"key":"e_1_2_1_10_1","volume-title":"First Workshop on Fine-Grained Visual Categorization (FGVC) at CVPR","author":"Farrell R.","year":"2011","unstructured":"Farrell , R. , Branson , S. , and Welinder , P ., 2011 . First Workshop on Fine-Grained Visual Categorization (FGVC) at CVPR 2011 . http:\/\/http:\/\/www.fgvc.org\/. Farrell, R., Branson, S., and Welinder, P., 2011. First Workshop on Fine-Grained Visual Categorization (FGVC) at CVPR 2011. http:\/\/http:\/\/www.fgvc.org\/."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2004.831793"},{"key":"e_1_2_1_12_1","volume-title":"Proc. MICCAI, 24--32","author":"Gerig G.","unstructured":"Gerig , G. , Styner , M. , Shenton , M. , and Lieberman , J . 2001. Shape versus size: Improved understanding of the morphology of brain structures . In Proc. MICCAI, 24--32 . Gerig, G., Styner, M., Shenton, M., and Lieberman, J. 2001. Shape versus size: Improved understanding of the morphology of brain structures. In Proc. MICCAI, 24--32."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2004.07.003"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01373.x"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383295"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00133570"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276457"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964974"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185550"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","unstructured":"Lai R. Shi Y. Scheibel K. Fears S. Woods R. Toga A. and Chan T. 2010. Metric-induced optimal embedding for intrinsic 3d shape analysis. In CVPR 2871--2878.  Lai R. Shi Y. Scheibel K. Fears S. Woods R. Toga A. and Chan T. 2010. Metric-induced optimal embedding for intrinsic 3d shape analysis. In CVPR 2871--2878.","DOI":"10.1109\/CVPR.2010.5540023"},{"key":"e_1_2_1_21_1","volume-title":"Proc. ISBI, 209--212","author":"Nain D.","unstructured":"Nain , D. , Styner , M. , Niethammer , M. , Levitt , J. , Shenton , M. , Gerig , G. , Bobick , A. , and Tannenbaum , A . 2007. Statistical shape analysis of brain structures using spherical wavelets . In Proc. ISBI, 209--212 . Nain, D., Styner, M., Niethammer, M., Levitt, J., Shenton, M., Gerig, G., Bobick, A., and Tannenbaum, A. 2007. Statistical shape analysis of brain structures using spherical wavelets. In Proc. ISBI, 209--212."},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964928"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185526"},{"key":"e_1_2_1_24_1","doi-asserted-by":"crossref","unstructured":"Ovsjanikov M. Ben-Chen M. Chazal F. and Guibas L. 2013. Analysis and visualization of maps between shapes. Computer Graphics Forum. To appear.  Ovsjanikov M. Ben-Chen M. Chazal F. and Guibas L. 2013. Analysis and visualization of maps between shapes. Computer Graphics Forum . To appear.","DOI":"10.1111\/cgf.12076"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02020.x"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141920"},{"key":"e_1_2_1_28_1","volume-title":"Conformal maps and p-Dirichlet energies. Tech. rep","author":"Schumacher H.","unstructured":"Schumacher , H. 2013. Conformal maps and p-Dirichlet energies. Tech. rep ., Univ. of G\u00f6ttingen . Schumacher, H. 2013. Conformal maps and p-Dirichlet energies. Tech. rep., Univ. of G\u00f6ttingen."},{"key":"e_1_2_1_29_1","volume-title":"Proc. NORDIA Workshop (CVPR), 29--36","author":"Sharma A.","unstructured":"Sharma , A. , and Horaud , R . 2010. Shape matching based on diffusion embedding and on mutual isometric consistency . In Proc. NORDIA Workshop (CVPR), 29--36 . Sharma, A., and Horaud, R. 2010. Shape matching based on diffusion embedding and on mutual isometric consistency. In Proc. NORDIA Workshop (CVPR), 29--36."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015736"},{"key":"e_1_2_1_31_1","doi-asserted-by":"crossref","unstructured":"Vasilescu M. and Terzopoulos D. 2007. Multilinear (tensor) ICA and dimensionality reduction. Independent Component Analysis and Signal Separation 818--826.   Vasilescu M. and Terzopoulos D. 2007. Multilinear (tensor) ICA and dimensionality reduction. Independent Component Analysis and Signal Separation 818--826.","DOI":"10.1007\/978-3-540-74494-8_102"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2009.10.086"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2012.03.026"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2461912.2461959","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2461912.2461959","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:35:48Z","timestamp":1750235748000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2461912.2461959"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,21]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7,21]]}},"alternative-id":["10.1145\/2461912.2461959"],"URL":"https:\/\/doi.org\/10.1145\/2461912.2461959","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,21]]},"assertion":[{"value":"2013-07-21","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}