On shape of plane elastic curves

International Journal of Computer Vision

Volumn 73, Issue 3, 2007, Pages 307-324

  Mio, Washington ^a   Srivastava, Anuj ^a   Joshi, Shantanu ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b FAMU FSU COLLEGE OF ENGINEERING   (United States)

Author keywords

Clustering shapes; Mean shape; Planar shapes; Shape analysis; Shape geodesics

Indexed keywords

CLUSTERING SHAPES; MEAN SHAPE; PLANAR SHAPES; SHAPE ANALYSIS; SHAPE GEODESICS;

CONTOUR MEASUREMENT; CURVE FITTING; ELASTICITY; MATHEMATICAL TRANSFORMATIONS; METRIC SYSTEM;

IMAGE ANALYSIS;

EID: 33846880717     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-006-9968-0     Document Type: Article

References (23)

1. Beg, M.F., Miller, M.I., Trouve, A., and Younes, L. 2005. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision, 61:139-157.
2. Bookstein, F.L. 1986. Size and shape spaces for landmark data in two dimensions. Statistical Science, 1:181-242.
3. Cohen, I., Ayache, N., and Sulger, P. 1992. Tracking points on deformable objects using curvature information. In Lecture Notes in Computer Science, vol. 588.
4. Cootes, T.F., Taylor, C.J., Cooper, D.H., and Graham, J. 1995. Active shape models: Their training and applications. Computer Vision and Image Understanding, 61:38-59.
5. do Carmo, Manfredo, 1994. Riemannian Geometry. Birkhauser.
6. Dryden, I.L. and Mardia, K.V. 1998. Statistical Shape Analysis. John Wiley & Son.
7. Geiger, D., Gupta, A., Costa, L.A., and Vlontzos, J. 1995. Dynamic programming for detecting, tracking and matching elastic contours. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):294-302.
8. Grenander, U. 1993. General Pattern Theory. Oxford University Press.
9. Karcher, H. 1977. Riemann center of mass and mollifier smoothing. Comm. Pure Appl. Math., 30:509-541.
10. Kendall, D.G. 1984. Shape manifolds, Procrustean metrics and complex projective spaces. Bulletin of London Mathematical Society, 16:81-121.
11. Klassen, E., Srivastava, A., Mio, W., and Joshi, S. 2004. Analysis of planar shapes using geodesic paths on shape manifolds. IEEE Trans. on Pattern Analysis and Machine Intelligence, 26:372-383.
12. Le, H.L. and Kendall, D.G. 1993. The Riemannian structure of euclidean shape spaces: a novel environment for statistics. Annals of Statistics, 21(3):1225-1271.
13. Mennucci, A. and Yezzi, A. 2004. Metrics in the space of curves. Technical report.
14. Michor, P. and Mumford, D. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc. in press.
15. Sebastian, T.B., Klein, P.N., and Kimia, B.B. 2003. On aligning curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(1):116-125.
16. Sharon, E. and Mumford, D. 2004. 2D-Shape analysis using conformai mappings. In Proceedings of IEEE Conference on Computer Vision, pp. 350-357.
17. Srivastava, A., Joshi, S., Mio, W., and Liu, X. 2005. Statistical shape analysis: Clustering, learning and testing. IEEE Trans. on Pattern Analysis and Machine Intelligence, 27:590-602.
18. Tagare, H.D. 1999. Shape-based non-rigid correspondence with applications to heart motion analysis. IEEE Trans. on Medical Imaging, 8(7):570-579.
19. Tagare, H.D., O'Shea, D., and Graisser, D. 2002. Non-rigid shape comparison of plane curves in images. Journal of Mathematical Imaging and Vision, 16:57-68.
20. Thompson, D.W. 1992. On Growth and Form: The Complete Revised Edition, Dover.
21. Vailliant, M., Miller, M.I., and Younes, L. 2004. Statistics on diffeomorphisms via tangent space representations. NeuroImage, 23:161-169.
22. Younes, L. 1998. Computable elastic distance between shapes. SIAM Journal of Applied Mathematics, 58:565-586.
23. Younes, L. 1999. Optimal matching between shapes via elastic deformations. Journal of Image and Vision Computing, 17(5/6):381-389.