{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T11:54:50Z","timestamp":1775217290753,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"the National Key Cooperation between the BRICS of China","award":["2017YFE0100500"],"award-info":[{"award-number":["2017YFE0100500"]}]},{"name":"National Key R&D Program of China","award":["2017YFB1002604"],"award-info":[{"award-number":["2017YFB1002604"]}]},{"name":"Beijing Natural Science Foundation of China","award":["4172033"],"award-info":[{"award-number":["4172033"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multimed Tools Appl"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s11042-020-09420-5","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T16:03:59Z","timestamp":1599149039000},"page":"615-640","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["3D non-rigid shape similarity measure based on Fr\u00e9chet distance between spectral distance distribution curve"],"prefix":"10.1007","volume":"80","author":[{"given":"Dan","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Zhongke","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Xingce","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Chenlei","family":"Lv","sequence":"additional","affiliation":[]},{"given":"Mingquan","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"9420_CR1","doi-asserted-by":"crossref","unstructured":"Alt H, Knauer C, Wenk C (2001) Matching polygonal curves with respect to the fr\u00e9chet distance. In: Symposium on theoretical aspects of computer science, pp 63\u201374","DOI":"10.1007\/3-540-44693-1_6"},{"issue":"12","key":"9420_CR2","doi-asserted-by":"publisher","first-page":"2262","DOI":"10.1109\/TPAMI.2010.46","volume":"32","author":"M Andriy","year":"2010","unstructured":"Andriy M, Xubo S (2010) Point set registration: coherent point drift. IEEE Trans Patt Anal Mach Intel 32(12):2262\u20132275","journal-title":"IEEE Trans Patt Anal Mach Intel"},{"issue":"3","key":"9420_CR3","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1145\/1073204.1073207","volume":"24","author":"D Anguelov","year":"2005","unstructured":"Anguelov D, Srinivasan P, Koller D, Thrun S, Rodgers J, Davis J (2005) SCAPE: Shape completion and animation of people. ACM Trans Graph 24(3):408\u2013416","journal-title":"ACM Trans Graph"},{"key":"9420_CR4","doi-asserted-by":"crossref","unstructured":"Aspert N, Santa-Cruz D, Ebrahimi T (2002) MESH: Measuring errors between surfaces using the hausdorff distance. In: IEEE international conference on multimedia and expo, vol 1, pp 705\u2013708","DOI":"10.1109\/ICME.2002.1035879"},{"key":"9420_CR5","doi-asserted-by":"crossref","unstructured":"Aubry M, Schlickewei U, Cremers D (2011) The wave kernel signature: A quantum mechanical approach to shape analysis. In: IEEE international conference on computer vision workshops, pp 1626\u20131633","DOI":"10.1109\/ICCVW.2011.6130444"},{"issue":"5","key":"9420_CR6","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1109\/TCBB.2015.2498553","volume":"13","author":"A Axenopoulos","year":"2016","unstructured":"Axenopoulos A, Rafailidis D, Papadopoulos G, Houstis EN, Daras P (2016) Similarity search of flexible 3d molecules combining local and global shape descriptors. IEEE\/ACM Trans Comput Bio Bioinforma 13(5):954\u2013970","journal-title":"IEEE\/ACM Trans Comput Bio Bioinforma"},{"key":"9420_CR7","unstructured":"Belongie S, Malik J, Puzicha J (2010) Shape matching and object recognition using shape contexts. In: IEEE international conference on computer science and information technology, pp 483\u2013507"},{"issue":"8","key":"9420_CR8","doi-asserted-by":"publisher","first-page":"2249","DOI":"10.1109\/TIP.2006.875250","volume":"15","author":"HA Ben","year":"2006","unstructured":"Ben HA, Krim H (2006) Geodesic matching of triangulated surfaces. IEEE Trans Image Process 15(8):2249\u20132258","journal-title":"IEEE Trans Image Process"},{"issue":"2","key":"9420_CR9","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1109\/34.121791","volume":"14","author":"PJ Besl","year":"1992","unstructured":"Besl PJ, Mckay ND (1992) A method for registration of 3-D shapes. IEEE Trans Patt Anal Mach Intel 14(2):239\u2013256","journal-title":"IEEE Trans Patt Anal Mach Intel"},{"issue":"6","key":"9420_CR10","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1111\/cgf.12734","volume":"35","author":"S Biasotti","year":"2016","unstructured":"Biasotti S, Cerri A, Bronstein A, Bronstein M (2016) Recent trends, applications, and perspectives in 3D shape similarity assessment. Computer Graphics Forum 35(6):87\u2013119","journal-title":"Computer Graphics Forum"},{"issue":"5","key":"9420_CR11","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.1109\/TPAMI.2010.210","volume":"33","author":"MM Bronstein","year":"2011","unstructured":"Bronstein MM, Bronstein AM (2011) Shape recognition with spectral distances. IEEE Trans Patt Anal Mach Intel 33(5):1065","journal-title":"IEEE Trans Patt Anal Mach Intel"},{"key":"9420_CR12","doi-asserted-by":"crossref","unstructured":"Bronstein MM, Kokkinos I (2010) Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Computer vision and pattern recognition, pp 1704\u20131711","DOI":"10.1109\/CVPR.2010.5539838"},{"key":"9420_CR13","doi-asserted-by":"publisher","unstructured":"Bronstein AM, Bronstein MM, Kimmel R (2009) Monographs in computer science, Numerical geometry of non-rigid shapes. Multidimensional Scaling[J] (Chapter 7):137\u2013167, https:\/\/doi.org\/10.1007\/978-0-387-73301-2","DOI":"10.1007\/978-0-387-73301-2"},{"issue":"2","key":"9420_CR14","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1111\/j.1467-8659.2008.01162.x","volume":"27","author":"U Castellani","year":"2010","unstructured":"Castellani U, Cristani M, Fantoni S, Murino V (2010) Sparse points matching by combining 3D mesh saliency with statistical descriptors. Computer Graphics Forum 27(2):643\u2013652","journal-title":"Computer Graphics Forum"},{"issue":"2","key":"9420_CR15","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/S1077-3142(03)00009-2","volume":"89","author":"H Chui","year":"2003","unstructured":"Chui H, Rangarajan A (2003) A new point matching algorithm for non-rigid registration. Comput Vis Image Underst 89(2):114\u2013141","journal-title":"Comput Vis Image Underst"},{"key":"9420_CR16","unstructured":"Eiter T, Mannila H (1994) Computing discrete fr\u00e9chet distance. Tech. rep., Citeseer"},{"issue":"1","key":"9420_CR17","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1186\/1472-6807-9-29","volume":"9","author":"Y Fang","year":"2009","unstructured":"Fang Y, Liu YS, Ramani K (2009) Three dimensional shape comparison of flexible proteins using the local-diameter descriptor. Bmc Structural Bio 9(1):29\u201329","journal-title":"Bmc Structural Bio"},{"issue":"1","key":"9420_CR18","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1186\/s13634-017-0483-y","volume":"2017","author":"VK Ghorpade","year":"2017","unstructured":"Ghorpade VK, Checchin P, Malaterre L, Trassoudaine L (2017) 3D Shape representation with spatial probabilistic distribution of intrinsic shape keypoints. Eurasip J Advances Signal Process 2017(1):52","journal-title":"Eurasip J Advances Signal Process"},{"key":"9420_CR19","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.neucom.2015.12.130","volume":"211","author":"AB Hamza","year":"2016","unstructured":"Hamza AB (2016) A graph-theoretic approach to 3d shape classification. Neurocomputing 211:11\u201321","journal-title":"Neurocomputing"},{"key":"9420_CR20","doi-asserted-by":"crossref","unstructured":"Havens TC, Bezdek JC, Keller JM, Popescu M (2009) Dunn\u2019s cluster validity index as a contrast measure of vat images. In: International conference on pattern recognition, pp 1\u20134","DOI":"10.1109\/ICPR.2008.4761772"},{"issue":"C","key":"9420_CR21","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.cagd.2015.08.004","volume":"39","author":"S He","year":"2015","unstructured":"He S, Choi YK, Guo Y, Guo X, Wang W (2015) A 3D shape descriptor based on spectral analysis of medial axis. Computer Aided Geometric Design 39 (C):50\u201366","journal-title":"Computer Aided Geometric Design"},{"key":"9420_CR22","doi-asserted-by":"crossref","unstructured":"Ion A, Artner NM, Peyre G, Marmol SBL (2009) 3D shape matching by geodesic eccentricity. In: IEEE computer society conference on computer vision and pattern recognition workshops, pp 1\u20138","DOI":"10.1109\/CVPRW.2008.4563032"},{"key":"9420_CR23","doi-asserted-by":"crossref","unstructured":"Levy B (2006) Laplace-Beltrami eigenfunctions towards an algorithm that understands geometry. In: IEEE international conference on shape modeling and applications, pp 13\u201313","DOI":"10.1109\/SMI.2006.21"},{"key":"9420_CR24","unstructured":"Lian Z, Godil A, Bustos B, Daoudi Mea (2011) SHREC\u201911 track: shape retrieval on non-rigid 3d watertight meshes. In: Proceedings of the 4th Eurographics conference on 3D object retrieval, EG 3DOR\u201911, Eurographics Association, pp 79\u201388"},{"issue":"8","key":"9420_CR25","doi-asserted-by":"publisher","first-page":"1685","DOI":"10.1007\/s00138-013-0501-5","volume":"24","author":"Z Lian","year":"2013","unstructured":"Lian Z, Godil A, Sun X, Xiao J (2013) CM-BOF: Visual similarity-based 3D shape retrieval using Clock Matching and Bag-of-Features. Mach Vis Appl 24(8):1685\u20131704","journal-title":"Mach Vis Appl"},{"issue":"2","key":"9420_CR26","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1109\/TPAMI.2007.41","volume":"29","author":"H Ling","year":"2007","unstructured":"Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Patt Anal Mach Intel 29(2):286","journal-title":"IEEE Trans Patt Anal Mach Intel"},{"key":"9420_CR27","unstructured":"Ling H, Okada K (2006) Diffusion distance for histogram comparison. In: IEEE computer society conference on computer vision and pattern recognition, pp 246\u2013253"},{"issue":"3","key":"9420_CR28","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1145\/1805964.1805971","volume":"29","author":"Y Lipman","year":"2010","unstructured":"Lipman Y, Rustamov RM, Funkhouser TA (2010) Biharmonic distance. ACM Trans Graph 29(3):27","journal-title":"ACM Trans Graph"},{"key":"9420_CR29","doi-asserted-by":"crossref","unstructured":"Lowe DG (1999) Object recognition from local scale-invariant features. In: IEEE international conference on computer vision, pp 1150","DOI":"10.1109\/ICCV.1999.790410"},{"issue":"1","key":"9420_CR30","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.gmod.2008.10.002","volume":"71","author":"M Mahmoudi","year":"2009","unstructured":"Mahmoudi M, Sapiro G (2009) Three-dimensional point cloud recognition via distributions of geometric distances. Graph Model 71(1):22\u201331","journal-title":"Graph Model"},{"issue":"12","key":"9420_CR31","doi-asserted-by":"publisher","first-page":"13805","DOI":"10.1007\/s11042-016-3741-3","volume":"76","author":"F Marcolin","year":"2017","unstructured":"Marcolin F, Vezzetti E (2017) Novel descriptors for geometrical 3d face analysis. Multimedia Tools and Applications 76(12):13805\u201313834","journal-title":"Multimedia Tools and Applications"},{"issue":"4","key":"9420_CR32","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1145\/571647.571648","volume":"21","author":"R Osada","year":"2002","unstructured":"Osada R, Funkhouser TA, Chazelle B, Dobkin DP (2002) Shape distributions. ACM Trans Graph 21(4):807\u2013832","journal-title":"ACM Trans Graph"},{"key":"9420_CR33","doi-asserted-by":"crossref","unstructured":"Ovsjanikov M, Sun J, Guibas L (2008) Global intrinsic symmetries of shapes. In: Computer graphics forum, vol 27, pp 1341\u20131348","DOI":"10.1111\/j.1467-8659.2008.01273.x"},{"key":"9420_CR34","doi-asserted-by":"crossref","unstructured":"Patan\u00e9 G, Barsky BA (2017) An introduction to Laplacian spectral distances and kernels: Theory, computation, and applications. In: ACM SIGGRAPH, pp 3","DOI":"10.1145\/3084873.3084919"},{"key":"9420_CR35","doi-asserted-by":"crossref","unstructured":"Pickup D, Sun Xea (2015) Canonical forms for non-rigid 3d shape retrieval. In: Eurographics workshop on 3d object retrieval","DOI":"10.1007\/s41095-016-0045-5"},{"key":"9420_CR36","unstructured":"Pickup D, Sun X, Rosin PL, Martin RRea (2014) SHREC\u201914 track: Shape retrieval of non-rigid 3d human models. In: Proceedings of the 7th eurographics workshop on 3D object retrieval, EG 3DOR\u201914, Eurographics Association"},{"issue":"3","key":"9420_CR37","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s41095-016-0045-5","volume":"2","author":"D Pickup","year":"2016","unstructured":"Pickup D, Sun X, Rosin PL, Martin RR (2016) Skeleton-based canonical forms for non-rigid 3d shape retrieval. Comput Vis Med 2(3):231\u2013243","journal-title":"Comput Vis Med"},{"key":"9420_CR38","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1016\/j.neucom.2015.06.093","volume":"175","author":"E Roman-Rangel","year":"2016","unstructured":"Roman-Rangel E, Wang C, Marchand-Maillet S (2016) Simmap: Similarity maps for scale invariant local shape descriptors. Neurocomputing 175:888\u2013898","journal-title":"Neurocomputing"},{"key":"9420_CR39","unstructured":"Rustamov RM (2007) Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics symposium on geometry processing, pp 225\u2013233"},{"issue":"6","key":"9420_CR40","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1109\/38.103393","volume":"11","author":"Y Shinagawa","year":"1991","unstructured":"Shinagawa Y, Kunii TL (1991) Constructing a reeb graph automatically from cross sections. IEEE Comput Graph Appl 11(6):44\u201351","journal-title":"IEEE Comput Graph Appl"},{"issue":"7","key":"9420_CR41","doi-asserted-by":"publisher","first-page":"2817","DOI":"10.1016\/j.patcog.2012.01.020","volume":"45","author":"D Smeets","year":"2012","unstructured":"Smeets D, Hermans J, Vandermeulen D, Suetens P (2012) Isometric deformation invariant 3D shape recognition. Pattern Recogn 45 (7):2817\u20132831","journal-title":"Pattern Recogn"},{"key":"9420_CR42","doi-asserted-by":"crossref","unstructured":"Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. In: Computer fraphics forum, vol 28, pp 1383\u20131392","DOI":"10.1111\/j.1467-8659.2009.01515.x"},{"key":"9420_CR43","doi-asserted-by":"crossref","unstructured":"Sundar H, Silver D, Gagvani N, Dickinson S (2003) Skeleton based shape matching and retrieval. In: Shape modeling international, pp 130\u2013139","DOI":"10.1109\/SMI.2003.1199609"},{"key":"9420_CR44","unstructured":"Tatsuma A, Koyanagi H, Aono M (2012) A large-scale shape benchmark for 3d object retrieval: Toyohashi shape benchmark"},{"issue":"1","key":"9420_CR45","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1111\/j.1467-8659.2008.01190.x","volume":"28","author":"J Tierny","year":"2010","unstructured":"Tierny J, Vandeborre JP, Daoudi M (2010) Partial 3D shape retrieval by reeb pattern unfolding. Computer Graphics Forum 28(1):41\u201355","journal-title":"Computer Graphics Forum"},{"issue":"11","key":"9420_CR46","doi-asserted-by":"publisher","first-page":"14177","DOI":"10.1007\/s11042-017-5025-y","volume":"77","author":"E Vezzetti","year":"2018","unstructured":"Vezzetti E, Marcolin F, Tornincasa S, Ulrich L, Dagnes N (2018) 3D geometry-based automatic landmark localization in presence of facial occlusions. Multimedia Tools and Applications 77(11):14177\u201314205","journal-title":"Multimedia Tools and Applications"},{"issue":"5","key":"9420_CR47","first-page":"S195\u2014S199","volume":"5","author":"H Wang","year":"2003","unstructured":"Wang H, Li Y, Jin H, Yin C, Su X, Chen W (2003) Three-dimensional visualization of shape measurement data based on a computer generated hologram. J Opt A Pure Appl Opt 5(5):S195\u2014S199","journal-title":"J Opt A Pure Appl Opt"},{"issue":"8","key":"9420_CR48","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1016\/j.cagd.2004.07.007","volume":"21","author":"G Xu","year":"2004","unstructured":"Xu G (2004) Discrete laplace\u2013beltrami operators and their convergence. Computer Aided Geometric Design 21(8):767\u2013784","journal-title":"Computer Aided Geometric Design"},{"issue":"1","key":"9420_CR49","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1186\/s12859-016-0983-z","volume":"17","author":"B Yao","year":"2016","unstructured":"Yao B, Li Z, Ding M, Chen M (2016) Three-dimensional protein model similarity analysis based on salient shape index. BMC Bioinforma 17 (1):131\u2013131","journal-title":"BMC Bioinforma"},{"key":"9420_CR50","first-page":"47","volume":"1","author":"ASAD \u00c7eliktutanBerk G\u00f6kberkB\u00fclent Sankur","year":"2008","unstructured":"\u00c7eliktutanBerk G\u00f6kberkB\u00fclent SankurLale Akarun ASAD (2008) Bosphorus database for 3d face analysis. Biomet Ident Manage 1:47\u201356","journal-title":"Biomet Ident Manage"}],"container-title":["Multimedia Tools and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-020-09420-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11042-020-09420-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-020-09420-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T20:50:41Z","timestamp":1630702241000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11042-020-09420-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,3]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["9420"],"URL":"https:\/\/doi.org\/10.1007\/s11042-020-09420-5","relation":{},"ISSN":["1380-7501","1573-7721"],"issn-type":[{"value":"1380-7501","type":"print"},{"value":"1573-7721","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,3]]},"assertion":[{"value":"24 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 July 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with Ethical Standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interests"}}]}}