{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T20:54:16Z","timestamp":1777496056948,"version":"3.51.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,5,20]],"date-time":"2009-05-20T00:00:00Z","timestamp":1242777600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2009,9]]},"DOI":"10.1007\/s10851-009-0156-z","type":"journal-article","created":{"date-parts":[[2009,5,19]],"date-time":"2009-05-19T15:19:27Z","timestamp":1242746367000},"page":"86-102","source":"Crossref","is-referenced-by-count":46,"title":["Shape Metrics Based on Elastic Deformations"],"prefix":"10.1007","volume":"35","author":[{"given":"Matthias","family":"Fuchs","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bert","family":"J\u00fcttler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otmar","family":"Scherzer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaiping","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,5,20]]},"reference":[{"key":"156_CR1","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)"},{"issue":"1","key":"156_CR2","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.jcp.2003.09.032","volume":"194","author":"G. Allaire","year":"2004","unstructured":"Allaire, G., de Gournay, F., Jouve, F., Toader, A.-M.: Structural optimization using sensitivity analysis and a level-set method. J.\u00a0Comput. Phys. 194(1), 363\u2013393 (2004)","journal-title":"J.\u00a0Comput. Phys."},{"key":"156_CR3","series-title":"Pure and Applied Mathematics","volume-title":"An Introduction to Differentiable Manifolds and Riemannian Geometry","author":"W.M. Boothby","year":"1975","unstructured":"Boothby, W.M.: An Introduction to Differentiable Manifolds and Riemannian Geometry. Pure and Applied Mathematics, vol.\u00a063. Academic Press, New York (1975)"},{"issue":"1","key":"156_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10208-003-0094-x","volume":"5","author":"G. Charpiat","year":"2005","unstructured":"Charpiat, G., Faugeras, O., Keriven, R.: Approximations of shape metrics and application to shape warping and empirical shape statistics. Found. Comput. Math. 5(1), 1\u201358 (2005)","journal-title":"Found. Comput. Math."},{"issue":"3","key":"156_CR5","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s11263-006-9966-2","volume":"73","author":"G. Charpiat","year":"2007","unstructured":"Charpiat, G., Maurel, P., Pons, J.-P., Keriven, R., Faugeras, O.: Generalized gradients: Priors on minimization flows. Int. J. Comput. Vis. 73(3), 325\u2013344 (2007)","journal-title":"Int. J. Comput. Vis."},{"key":"156_CR6","volume-title":"Mathematical Elasticity, Volume\u00a0I: Three-Dimensional Elasticity","author":"P.G. Ciarlet","year":"1988","unstructured":"Ciarlet, P.G.: Mathematical Elasticity, Volume\u00a0I: Three-Dimensional Elasticity. North-Holland, Amsterdam (1988)"},{"issue":"339","key":"156_CR7","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.crma.2004.06.021","volume":"I","author":"P.G. Ciarlet","year":"2004","unstructured":"Ciarlet, P.G., Ciarlet, P. Jr.: Another approach to linearized elasticity and Korn\u2019s inequality. C.\u00a0R. Acad. Sci. I(339), 307\u2013312 (2004)","journal-title":"C.\u00a0R. Acad. Sci."},{"issue":"2\u20133","key":"156_CR8","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10851-007-0026-5","volume":"29","author":"S.L. Keeling","year":"2007","unstructured":"Keeling, S.L.: Generalized rigid and generalized affine image registration and interpolation by geometric multigrid. J.\u00a0Math. Imaging Vis. 29(2\u20133), 163\u2013183 (2007)","journal-title":"J.\u00a0Math. Imaging Vis."},{"issue":"1","key":"156_CR9","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s10851-005-4967-2","volume":"23","author":"S.L. Keeling","year":"2005","unstructured":"Keeling, S.L., Ring, W.: Medical image registration and interpolation by optical flow with maximal rigidity. J.\u00a0Math. Imaging Vis. 23(1), 47\u201365 (2005)","journal-title":"J.\u00a0Math. Imaging Vis."},{"issue":"2","key":"156_CR10","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.: Shape manifolds, procrustean metrics, and complex projective spaces. Bull. Lond. Math. Soc. 16(2), 81\u2013121 (1984)","journal-title":"Bull. Lond. Math. Soc."},{"issue":"3","key":"156_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1276377.1276457","volume":"26","author":"M. Kilian","year":"2007","unstructured":"Kilian, M., Mitra, N.J., Pottmann, H.: Geometric modeling in shape space. ACM Trans. Graph. 26(3), 1\u20138 (2007)","journal-title":"ACM Trans. Graph."},{"issue":"3","key":"156_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, M., Joshi, S.H.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Trans. Pattern Anal. Mach. Intell. 26(3), 372\u2013383 (2004)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"156_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0541-8","volume-title":"Fundamentals of Differential Geometry","author":"S. Lang","year":"1999","unstructured":"Lang, S.: Fundamentals of Differential Geometry. Springer, Berlin (1999)"},{"issue":"3","key":"156_CR14","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/BF01589116","volume":"45","author":"D.C. Liu","year":"1989","unstructured":"Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Program.\u00a0B 45(3), 503\u2013528 (1989)","journal-title":"Math. Program.\u00a0B"},{"key":"156_CR15","doi-asserted-by":"crossref","first-page":"217","DOI":"10.4171\/dm\/187","volume":"10","author":"P.W. Michor","year":"2005","unstructured":"Michor, P.W., Mumford, D.B.: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Doc. Math. 10, 217\u2013245 (2005)","journal-title":"Doc. Math."},{"issue":"1","key":"156_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/jems\/37","volume":"8","author":"P.W. Michor","year":"2006","unstructured":"Michor, P.W., Mumford, D.B.: Riemannian geometries on spaces of plane curves. J.\u00a0Eur. Math. Soc. 8(1), 1\u201348 (2006)","journal-title":"J.\u00a0Eur. Math. Soc."},{"issue":"1\u20132","key":"156_CR17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1011161132514","volume":"41","author":"M.I. Miller","year":"2001","unstructured":"Miller, M.I., Younes, L.: Group actions, homeomorphisms, and matching: A\u00a0general framework. Int. J. Comput. Vis. 41(1\u20132), 61\u201384 (2001)","journal-title":"Int. J. Comput. Vis."},{"issue":"3","key":"156_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.: On shape of plane elastic curves. Int. J. Comput. Vis. 73(3), 307\u2013324 (2007)","journal-title":"Int. J. Comput. Vis."},{"issue":"3","key":"156_CR19","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1145\/882262.882295","volume":"22","author":"T.W. Sederberg","year":"2003","unstructured":"Sederberg, T.W., Zheng, J., Bakenov, A., Nasri, A.: T-splines and T-NURCCs. ACM Trans. Graph. 22(3), 477\u2013484 (2003)","journal-title":"ACM Trans. Graph."},{"issue":"3","key":"156_CR20","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.: Sobolev active contours. Int. J. Comput. Vis. 73(3), 345\u2013366 (2007)","journal-title":"Int. J. Comput. Vis."},{"issue":"2","key":"156_CR21","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","volume":"13","author":"H.A. van der Vorst","year":"1992","unstructured":"van der Vorst, H.A.: Bi-CGSTAB: A\u00a0fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Comput. 13(2), 631\u2013644 (1992)","journal-title":"SIAM J. Sci. Comput."},{"key":"156_CR22","first-page":"247","volume-title":"IEEE International Conference on Shape Modeling and Applications 2006 (SMI\u201906)","author":"H. Yang","year":"2006","unstructured":"Yang, H., Fuchs, M., J\u00fcttler, B., Scherzer, O.: Evolution of T-spline level sets with distance field constraints for geometry reconstruction and image segmentation. In: IEEE International Conference on Shape Modeling and Applications 2006 (SMI\u201906), pp.\u00a0247\u2013252. IEEE Computer Society, Los Alamitos (2006)"},{"key":"156_CR23","unstructured":"Yezzi, A., Mennucci, A.: Metrics in the Space of Curves (2004)"},{"key":"156_CR24","volume-title":"Functional Analysis","author":"K. Yosida","year":"1965","unstructured":"Yosida, K.: Functional Analysis. Springer, Berlin (1965)"},{"issue":"2","key":"156_CR25","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1137\/S0036139995287685","volume":"58","author":"L. Younes","year":"1998","unstructured":"Younes, L.: Computable elastic distances between shapes. SIAM J. Appl. Math. 58(2), 565\u2013586 (1998)","journal-title":"SIAM J. Appl. Math."},{"key":"156_CR26","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/978-3-7643-7721-2_15","volume":"155","author":"J.-P. Zol\u00e9sio","year":"2007","unstructured":"Zol\u00e9sio, J.-P.: Control of moving domains, shape stabilization and variational tube formulations. Int. Ser. Numer. Math. 155, 329\u2013382 (2007)","journal-title":"Int. Ser. Numer. Math."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-009-0156-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-009-0156-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-009-0156-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T15:47:09Z","timestamp":1739116029000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-009-0156-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,20]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["156"],"URL":"https:\/\/doi.org\/10.1007\/s10851-009-0156-z","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,20]]}}}