The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
Shape Analysis of Elastic Curves in Euclidean Spaces
Open accessAbstract
This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL(2) metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is the quotient space of (a submanifold of) the unit sphere, modulo rotation, and reparameterization groups, and we find geodesics in that space using a path straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming, and comparing shapes. These ideas are demonstrated using: 1) shape analysis of cylindrical helices for studying protein structure, 2) shape analysis of facial curves for recognizing faces, 3) a wrapped probability distribution for capturing shapes of planar closed curves, and 4) parallel transport of deformations for predicting shapes from novel poses.
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Citations
Cites
One-shot learning of object categories
Fei-Fei, L., Fergus, R., & Perona, P. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.79 · Cited by 3,029
Statistical shape analysis: clustering, learning, and testing
Srivastava, A., Joshi, S. H., Mio, W., & Liu, X. (2005) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2005.86 · Cited by 2,727
Self-citationBhattacharyya, A. (1943) · Medical Entomology and Zoology · Cited by 2,002
Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
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
Topology from the Differentiable Viewpoint.
Brown, E. H., & Milnor, J. W. (1967) · The American Mathematical Monthly · doi:10.2307/2314613 · Cited by 1,418
Riemannian center of mass and mollifier smoothing
Karcher, H. (1977) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160300502 · Cited by 995
Statistical Decision Rules and Optimal Inference
Čencov, N. (2000) · Translations of Mathematical Monographs · doi:10.1090/mmono/053 · Cited by 522
Analysis of planar shapes using geodesic paths on shape spaces
Klassen, E., Srivastava, A., Mio, W., & Joshi, S. H. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1262333 · Cited by 479
Self-citationThree-Dimensional Face Recognition
Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2005) · International Journal of Computer Vision · doi:10.1007/s11263-005-1085-y · Cited by 424
Cited by
Srivastava, A., Kurtek, S., & Klassen, E. (2014) · Computer Vision · doi:10.1007/978-0-387-31439-6_778 · Cited by 848
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Metadata
- Authors
- Srivastava, A., Klassen, E., Joshi, S. H., & Jermyn, I. H.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2011-07
- Volume
- 33
- Issue
- 7
- Pages
- 1415-1428
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2165168736
- Cited by
- 638
- References
- 30
- FWCI
- 29.47
- Type
- journal article
- Language
- en
- Open access
- green
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