The multiscale structure of non-differentiable image manifolds

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5914, Issue , 2005, Pages 1-17

  Wakin, Michael B ^a   Donoho, David L ^b   Choi, Hyeokho ^a   Baraniuk, Richard G ^a  

^a Rice University   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Angle between subspaces; Image appearance manifolds; Multiscale registration; Non differentiable manifolds; Pose estimation; Sampling theorems

Indexed keywords

ANGLE BETWEEN SUBSPACES; IMAGE APPEARANCE MANIFOLDS; NON-DIFFERENTIABLE MANIFOLDS; SAMPLING THEOREMS;

ALGORITHMS; APPROXIMATION THEORY; PROBLEM SOLVING; SAMPLING;

IMAGE PROCESSING;

EID: 30844444151     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.617822     Document Type: Conference Paper

References (22)

1. J. B. Tenenbaum, V. de Silva, and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science 290, pp. 2319-2323, December 2000.
2. S. T. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science 290, pp. 2323-2326, December 2000.
3. D. L. Donoho and C. E. Grimes, "Hessian Eigenmaps: Locally linear embedding techniques for high-dimensional data," Proc. Natl. Acad. Sci. USA 100, pp. 5591-5596, May 2003.
4. B. D. Lucas and T. Kanade, "An iterative image registration technique with an application to stereo vision," in Proc. 7th Int'l Joint Conf. on Artificial Intelligence, pp. 674-679, (Vancouver), 1981.
5. L. Quam, "Hierarchical warp stereo," in Proc. DARPA Image Understanding Workshop, pp. 149-155, September 1984.
6. W. Enkelmann, "Investigations of multigrid algorithms for the estimation of optical flow fields in image sequences," Comp. Vision, Graphics, and Image Processing 43, pp. 150-177, 1988.
7. M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graphical Models and Image Processing 53, pp. 231-239, May 1991.
8. E. P. Simoncelli, "Coarse-to-fine estimation of visual motion," in Proc 8th Workshop on Image and Multidimensional Signal Processing, pp. 128-129, IEEE Sig Proc Society, (Cannes, France), September 1993.
9. E. P. Simoncelli, "Bayesian multi-scale differential optical flow," in Handbook of Computer Vision and Applications, B. Jähne, H. Haussecker, and P. Geissler, eds., 2, ch. 14, pp. 397-422, Academic Press, San Diego, April 1999.
10. C. Grimes, New methods in nonlinear dimensionality reduction. PhD thesis, Department of Statistics, Stanford University, 2003.
11. D. L. Donoho and C. Grimes, "Image manifolds which are isometric to euclidean space," J. Math. Imaging and Computer Vision 23, July 2005.
12. D. L. Donoho, "Wedgelets: Nearly-minimax estimation of edges," Annals of Stat. 27, pp. 859-897, 1999.
13. M. B. Wakin, J. K. Romberg, H. Choi, and R. G. Baraniuk, "Wavelet-domain approximation and compression of piecewise smooth images," IEEE Trans. Image Processing, 2005. To appear.
14. P. N. Belhumeur and G. D. Hager, "Tracking in 3D: Image variability decomposition for recovering object pose and illumination," Pattern Analysis and Applications 2, pp. 82-91, 1999.
15. M. Turk and A. Pentland, "Eigenfaces for recognition," J. Cognitive Neuroscience 3(1), 1991.
16. C. Davis and W. Kahan, "The rotation of eigenvectors by a perturbation, III," SIAM J. Numer. Anal. 7(1), pp. 1-46, 1970.
17. G. W. Stewart and J. guang Sun, Matrix perturbation theory, Academic Press, Boston, 1990.
18. G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas, "Persistence barcodes for shapes," Int. J. of Shape Modeling. To appear.
19. W. T. Freeman, "Exploiting the generic viewpoint assumption," Int. J. Computer Vision 20(3), 1996.
20. D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications, John Wiley and Sons, New York, 1988.
21. Y. Keller and A. Averbach, "Fast motion estimation using bidirectional gradient methods," IEEE Trans. Image Processing 13, pp. 1042-1054, August 2004.
22. I. U. Rahman, I. Drori, V. C. Stodden, D. L. Donoho, and P. Schroeder, "Multiscale representations for manifold-valued data," 2005. Preprint.