The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Statistics of shape via principal geodesic analysis on Lie groups
Abstract
Principal component analysis has proven to be useful for understanding geometric variability in populations of parameterized objects. The statistical framework is well understood when the parameters of the objects are elements of a Euclidean vector space. This is certainly the case when the objects are described via landmarks or as a dense collection of boundary points. We have been developing representations of geometry based on the medial axis description or m-rep. Although this description has proven to be effective, the medial parameters are not naturally elements of a Euclidean space. In this paper we show that medial descriptions are in fact elements of a Lie group. We develop methodology based on Lie groups for the statistical analysis of medially-defined anatomical objects.
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Cites
Turk, M., & Pentland, A. (1991) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1991.3.1.71 · Cited by 13,733
Cootes, T. F., Edwards, G. J., & Taylor, C. J. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.927467 · Cited by 5,409
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Hartley, R., Trumpf, J., Dai, Y., & Li, H. (2013) · International Journal of Computer Vision · doi:10.1007/s11263-012-0601-0 · Cited by 486
Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors
Fletcher, P. T., & Joshi, S. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-27816-0_8 · Cited by 259
Self-citationLenglet, C., Rousson, M., Deriche, R., & Faugeras, O. (2006) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-006-6897-z · Cited by 253
Statistics on diffeomorphisms via tangent space representations
Vaillant, M., Miller, M. I., Younes, L., & Trouvé, A. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.07.023 · Cited by 215
Metadata
- Authors
- Fletcher, P. T., Lu, C., & Joshi, S.
- Venue
- 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.
- Publisher
- IEEE Comput. Soc
- Published
- 2003-11-04
- Pages
- I-95-I-101
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W2168412719
- Cited by
- 161
- References
- 2
- FWCI
- 7.01
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Fletcher, P. T., Lu, C., & Joshi, S. (2003). Statistics of shape via principal geodesic analysis on Lie groups. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings. https://doi.org/10.1109/cvpr.2003.1211342
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