{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:16:34Z","timestamp":1776867394226,"version":"3.51.2"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Comput Vis"],"published-print":{"date-parts":[[2010,8]]},"DOI":"10.1007\/s11263-010-0323-0","type":"journal-article","created":{"date-parts":[[2010,2,11]],"date-time":"2010-02-11T20:56:24Z","timestamp":1265921784000},"page":"69-83","source":"Crossref","is-referenced-by-count":15,"title":["A Computational Model of Multidimensional Shape"],"prefix":"10.1007","volume":"89","author":[{"given":"Xiuwen","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yonggang","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivo","family":"Dinov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Washington","family":"Mio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,2,12]]},"reference":[{"issue":"1","key":"323_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aos\/1046294456","volume":"31","author":"R. Bhattacharya","year":"2003","unstructured":"Bhattacharya, R., & Patrangenaru, V. (2003). Large sample theory of intrinsic and extrinsic sample means on manifolds.\u00a0I. Annals of Statistics, 31(1), 1\u201329.","journal-title":"Annals of Statistics"},{"key":"323_CR2","volume-title":"Riemannian geometry","author":"M. P. Carmo do","year":"1994","unstructured":"do Carmo, M. P. (1994). Riemannian geometry. Basel: Birkhauser."},{"key":"323_CR3","volume-title":"Statistical shape analysis","author":"I. L. Dryden","year":"1998","unstructured":"Dryden, I. L., & Mardia, K. V. (1998). Statistical shape analysis. New York: Wiley."},{"issue":"8","key":"323_CR4","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1109\/TMI.2004.831793","volume":"23","author":"P. Fletcher","year":"2004","unstructured":"Fletcher, P., Lu, C., Pizer, S., & Joshi, S. (2004). Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Transactions on Medical Imaging, 23(8), 995\u20131005.","journal-title":"IEEE Transactions on Medical Imaging"},{"key":"323_CR5","doi-asserted-by":"crossref","unstructured":"Fletcher, P. T., Venkatasubramanian, S., & Joshi, S. (2008). Robust statistics on Riemannian manifolds via the geometric median. In IEEE international conference on computer vision and pattern recognition.","DOI":"10.1109\/CVPR.2008.4587747"},{"issue":"1","key":"323_CR6","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s10851-009-0156-z","volume":"35","author":"M. Fuchs","year":"2009","unstructured":"Fuchs, M., J\u00fcttler, B., Scherzer, O., & Yang, H. (2009). Shape metrics based on elastic deformations. Journal of Mathematical Imaging and Vision, 35(1), 86\u2013102.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"323_CR7","unstructured":"Joshi, S., Klassen, E., Srivastava, A., & Jermyn, I. (2007). An efficient representation for computing geodesics between n-dimensional elastic shapes. In IEEE conference on computer vision and pattern recognition."},{"key":"323_CR8","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1002\/cpa.3160300502","volume":"30","author":"H. Karcher","year":"1977","unstructured":"Karcher, H. (1977). Riemann center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30, 509\u2013541.","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"323_CR9","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1112\/blms\/16.2.81","volume":"16","author":"D. G. Kendall","year":"1984","unstructured":"Kendall, D. G. (1984). Shape manifolds, Procrustean metrics and complex projective spaces. Bulletin of London Mathematical Society, 16, 81\u2013121.","journal-title":"Bulletin of London Mathematical Society"},{"key":"323_CR10","doi-asserted-by":"crossref","DOI":"10.1002\/9780470317006","volume-title":"Shape and shape theory","author":"D. G. Kendall","year":"1999","unstructured":"Kendall, D. G., Barden, D., Carne, T. K., & Le, H. (1999). Shape and shape theory. New York: Wiley."},{"issue":"3","key":"323_CR11","doi-asserted-by":"crossref","first-page":"64\u20133","DOI":"10.1145\/1276377.1276457","volume":"26","author":"M. Kilian","year":"2007","unstructured":"Kilian, M., Mitra, N., & Pottmann, H. (2007). Geometric modeling in shape space. ACM Transactions on Graphics, 26(3), 64\u20133\u201364\u20138.","journal-title":"ACM Transactions on Graphics"},{"key":"323_CR12","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1109\/TPAMI.2004.1262333","volume":"26","author":"E. Klassen","year":"2004","unstructured":"Klassen, E., Srivastava, A., Mio, W., & Joshi, S. (2004). Analysis of planar shapes using geodesic paths on shape manifolds. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 372\u2013383.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"323_CR13","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1214\/aos\/1176349259","volume":"21","author":"H. L. Le","year":"1993","unstructured":"Le, H. L., & Kendall, D. G. (1993). The Riemannian structure of euclidean shape spaces: a novel environment for statistics. Annals of Statistics, 21(3), 1225\u20131271.","journal-title":"Annals of Statistics"},{"key":"323_CR14","doi-asserted-by":"crossref","unstructured":"Liu, X., Mio, W., Shi, Y., Dinov, I., Liu, X., Lepore, N., Lepore, F., Fortin, M., Voss, P., Lassonde, M., & Thompson, P. M. (2008). Models of normal variation and local contrasts in hippocampal anatomy. In MICCAI.","DOI":"10.1007\/978-3-540-85990-1_49"},{"key":"323_CR15","doi-asserted-by":"crossref","unstructured":"Liu, X., Shi, Y., Morra, J., Liu, X., Thompson, P. M., & Mio, W. (2009). Mapping hippocampal atrophy with a multi-scale model of shape. In ISBI.","DOI":"10.1109\/ISBI.2009.5193193"},{"key":"323_CR16","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.acha.2006.07.004","volume":"23","author":"P. Michor","year":"2007","unstructured":"Michor, P., & Mumford, D. (2007). An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Applied and Computational Harmonic Analysis, 23, 74\u2013113.","journal-title":"Applied and Computational Harmonic Analysis"},{"key":"323_CR17","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1090\/qam\/2054604","volume":"62","author":"W. Mio","year":"2004","unstructured":"Mio, W., Srivastava, A., & Klassen, E. (2004). Interpolations with elasticae in Euclidean spaces. Quarterly of Applied Mathematics, 62, 359\u2013378.","journal-title":"Quarterly of Applied Mathematics"},{"issue":"3","key":"323_CR18","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s11263-006-9968-0","volume":"73","author":"W. Mio","year":"2007","unstructured":"Mio, W., Srivastava, A., & Joshi, S. (2007). On shape of plane elastic curves. International Journal of Computer Vision, 73(3), 307\u2013324.","journal-title":"International Journal of Computer Vision"},{"key":"323_CR19","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s11263-008-0190-0","volume":"82","author":"W. Mio","year":"2009","unstructured":"Mio, W., Bowers, J. C., & Liu, X. (2009). Shape of elastic strings in Euclidean space. International Journal of Computer Vision, 82, 96\u2013112.","journal-title":"International Journal of Computer Vision"},{"issue":"1","key":"323_CR20","doi-asserted-by":"crossref","first-page":"S3","DOI":"10.1016\/j.neuroimage.2008.10.043","volume":"45","author":"J. Morra","year":"2009","unstructured":"Morra, J., Tu, Z., Apostolova, L. G., Green, A., Avedissian, C., Madsen, S., Parikshak, N., Toga, A., Jack, C., Schuff, N., Weiner, M.\u00a0W., & Thompson, P. M., & the ADNI (2009). Automated mapping of hippocampal atrophy in 1-year repeat MRI data from 490 subjects with Alzheimer\u2019s disease, mild cognitive impairment, and elderly controls. NeuroImage, 45(1), S3\u2013S15. Supplement\u00a01.","journal-title":"NeuroImage"},{"key":"323_CR21","volume-title":"Elements of algebraic topology","author":"J. Munkres","year":"1984","unstructured":"Munkres, J. (1984). Elements of algebraic topology. New York: Perseus Books."},{"key":"323_CR22","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/11861898_15","volume-title":"Pattern Recognition (Proc. DAGM)","author":"F. R. Schmidt","year":"2006","unstructured":"Schmidt, F. R., Clausen, M., & Cremers, D. (2006). Shape matching by variational computation of geodesics on a manifold. In LNCS : Vol.\u00a04174. Pattern Recognition (Proc. DAGM) (pp.\u00a0142\u2013151). Berlin: Springer."},{"issue":"3","key":"323_CR23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.media.2007.02.001","volume":"11","author":"Y. Shi","year":"2007","unstructured":"Shi, Y., Thompson, P., Dinov, I., Osher, S., & Toga, A. (2007a). Direct cortical mapping via solving partial differential equations on implicit surfaces. Medical Image Analysis, 11(3), 207\u2013223.","journal-title":"Medical Image Analysis"},{"issue":"3","key":"323_CR24","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.neuroimage.2007.05.016","volume":"36","author":"Y. Shi","year":"2007","unstructured":"Shi, Y., Thompson, P., Zubicaray, G., Ross, S., Tu, Z., Dinov, I., & Toga, A. (2007b). Direct mapping of hippocampal surfaces with intrinsic shape context. NeuroImage, 36(3), 792\u2013807.","journal-title":"NeuroImage"},{"key":"323_CR25","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1109\/TPAMI.2005.86","volume":"27","author":"A. Srivastava","year":"2005","unstructured":"Srivastava, A., Joshi, S., Mio, W., & Liu, X. (2005). Statistical shape analysis: Clustering, learning and testing. IEEE Transaction on Pattern Analysis and Machine Intelligence, 27, 590\u2013602.","journal-title":"IEEE Transaction on Pattern Analysis and Machine Intelligence"},{"key":"323_CR26","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s11263-006-0635-2","volume":"73","author":"G. Sundaramoorthi","year":"2007","unstructured":"Sundaramoorthi, G., Yezzi, A., & Mennucci, A. (2007). Sobolev active contours. The International Journal of Computer Vision, 73, 345\u2013366.","journal-title":"The International Journal of Computer Vision"},{"key":"323_CR27","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1137\/S0036139995287685","volume":"58","author":"L. Younes","year":"1998","unstructured":"Younes, L. (1998). Computable elastic distance between shapes. SIAM Journal of Applied Mathematics, 58, 565\u2013586.","journal-title":"SIAM Journal of Applied Mathematics"},{"issue":"5\/6","key":"323_CR28","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/S0262-8856(98)00125-5","volume":"17","author":"L. Younes","year":"1999","unstructured":"Younes, L. (1999). Optimal matching between shapes via elastic deformations. Journal of Image and Vision Computing, 17(5\/6), 381\u2013389.","journal-title":"Journal of Image and Vision Computing"},{"key":"323_CR29","unstructured":"Younes, L., Michor, P., Shah, J., & Mumford, D. (2007). A metric on shape space with explicit geodesics. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, Mat. Appl., 9."}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s11263-010-0323-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,26]],"date-time":"2019-02-26T15:03:16Z","timestamp":1551193396000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-010-0323-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,12]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,8]]}},"alternative-id":["323"],"URL":"https:\/\/doi.org\/10.1007\/s11263-010-0323-0","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,12]]}}}