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Riemannian Optimization for Registration of Curves in Elastic Shape Analysis

Bibliographic reference Huang, Wen ; Gallivan, Kyle A. ; Srivastava, Anuj ; Absil, Pierre-Antoine. Riemannian Optimization for Registration of Curves in Elastic Shape Analysis. In: Journal of Mathematical Imaging and Vision, Vol. 54, no. 3, p. 320-343 (2016)
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  1. Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ (2008)
  2. Baker, C.G.: Riemannian manifold trust-region methods with applications to eigenproblems. PhD thesis, Florida State University, Department of Computational Science (2008)
  3. Bertsekas, D.P.: Dynamic Programming and Optimal Control. Athena Scientific, Belmont (1995)
  4. Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. Wiley, Chichester (1998)
  5. Huang Wen, Absil P.-A., Gallivan K. A., A Riemannian symmetric rank-one trust-region method, 10.1007/s10107-014-0765-1
  6. Huang Wen, Gallivan K. A., Absil P.-A., A Broyden Class of Quasi-Newton Methods for Riemannian Optimization, 10.1137/140955483
  7. Huang, W., Gallivan, K.A., Srivastava, A., Absil, P.-A.: Riemannian optimization for elastic shape analysis. In: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (2014)
  8. Huang, W.: Optimization algorithms on Riemannian manifolds with applications. PhD thesis, Florida State University, Department of Mathematics (2013)
  9. Huang Wen, You Yaqing, Gallivan Kyle, Absil Pierre-Antoine, Karcher Mean in Elastic Shape Analysis, 10.5244/c.29.diffcv.2
  10. Kendall David G., Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces, 10.1112/blms/16.2.81
  11. Klassen E., Srivastava A., Mio W., Joshi S.H., Analysis of planar shapes using geodesic paths on shape spaces, 10.1109/tpami.2004.1262333
  12. Lahiri, S., Robinson, D., Klassen, E.: Precise matching of PL curves in $$\mathbb{R}^{n}$$ R n in the square root velocity framework, pp. 1–41 (January 2015). arXiv:1501.00577
  13. O’Neill, B.: Semi-Riemannian Geometry. Academic Press Incorporated (Harcourt Brace Jovanovich Publishers), New York (1983)
  14. Qi, C.: Numerical optimization methods on Riemannian manifolds. PhD thesis, Florida State University, Department of Mathematics (2011)
  15. Ring Wolfgang, Wirth Benedikt, Optimization Methods on Riemannian Manifolds and Their Application to Shape Space, 10.1137/11082885x
  16. Srivastava A, Klassen E, Joshi S H, Jermyn I H, Shape Analysis of Elastic Curves in Euclidean Spaces, 10.1109/tpami.2010.184
  17. Sebastian T.B., Klein P.N., Kimia B.B., On aligning curves, 10.1109/tpami.2003.1159951
  18. Temple University. Shape similarity research project.
  19. Wu, S.G., Bao, F.S., Xu, E.Y., Wang, Y.-X., Chang, Y.-F., Xiang, Q.-L.: A leaf recognition algorithm for plant classification using probabilistic neural network. In: 2007 IEEE International Symposium on Signal Processing and Information Technology, pp. 11–16 (2007). arXiv:0707.4289v1
  20. You, Y., Huang, W., Gallivan, K.A., Absil, P.-A.: A Riemannian approach for computing geodesics in elastic shape analysis. In: 3rd IEEE Global Conference on Signal and Information Processing (December 2015). To appear
  21. Younes Laurent, Michor Peter, Shah Jayant, Mumford David, A metric on shape space with explicit geodesics, 10.4171/rlm/506
  22. Younes Laurent, Computable Elastic Distances Between Shapes, 10.1137/s0036139995287685