The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Computable Elastic Distances Between Shapes
Abstract
We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian distance on an infinite dimensional group acting on the curves, which can be explicitly computed. The obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed. An analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem, which can efficiently be implemented, as illustrated by experiments.
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Cites
Kass, M., Witkin, A., & Terzopoulos, D. (1988) · International Journal of Computer Vision · doi:10.1007/bf00133570 · Cited by 17,070
Hewitt, E., & Stromberg, K. R. (1965) · Springer eBooks · doi:10.1007/978-3-642-88047-6 · Cited by 1,527
Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
Kendall, D. G. (1984) · Bulletin of the London Mathematical Society · doi:10.1112/blms/16.2.81 · Cited by 1,466
Finite-element methods for active contour models and balloons for 2-D and 3-D images
Cohen, L. D., & Cohen, I. (1993) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.244675 · Cited by 1,378
Analyse fonctionnelle : Théorie et applications
Brézis, H. (1999) · Cited by 1,180
Introduction to differentiable manifolds
(1963) · Journal of the Franklin Institute · doi:10.1016/0016-0032(63)90664-1 · Cited by 555
Structural Image Restoration through Deformable Templates
Amit, Y., Grenander, U., & Piccioni, M. (1991) · Journal of the American Statistical Association · doi:10.1080/01621459.1991.10475053 · Cited by 328
Generalized Deformable Models, Statistical Physics, and Matching Problems
Yuille, A. L. (1990) · Neural Computation · doi:10.1162/neco.1990.2.1.1 · Cited by 222
Tracking points on deformable objects using curvature information
Cohen, I., Ayache, N., & Sulger, P. (1992) · Lecture Notes in Computer Science · doi:10.1007/3-540-55426-2_51 · Cited by 195
Grenander, U. (1978) · Springer eBooks · Cited by 81
Cited by
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Benamou, J.-D., & Brenier, Y. (2000) · Numerische Mathematik · doi:10.1007/s002110050002 · Cited by 1,609
Srivastava, A., Kurtek, S., & Klassen, E. (2014) · Computer Vision · doi:10.1007/978-0-387-31439-6_778 · Cited by 848
Shape Analysis of Elastic Curves in Euclidean Spaces
Srivastava, A., Klassen, E., Joshi, S. H., & Jermyn, I. H. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.184 · Cited by 638
Computational anatomy: an emerging discipline
Grenander, U., & Miller, M. I. (1998) · Quarterly of Applied Mathematics · doi:10.1090/qam/1668732 · Cited by 623
Landmark matching via large deformation diffeomorphisms
Joshi, S. C., & Miller, M. I. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.855431 · Cited by 501
Metadata
- Authors
- Younes, L.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1998-04
- Volume
- 58
- Issue
- 2
- Pages
- 565-586
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2093976044
- Cited by
- 349
- References
- 12
- FWCI
- 12.11
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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