Estimating the jacobian of the singular value decomposition: Theory and applications?

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1842, Issue , 2000, Pages 554-570

  Papadopoulo, Théodore ^a   Lourakis, Manolis I A ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTER VISION; JACOBIAN MATRICES; MOTION ESTIMATION; REGRESSION ANALYSIS; UNCERTAINTY ANALYSIS;

ANALYTIC TECHNIQUE; EPIPOLE; JACOBIANS; LINEAR ALGEBRA TOOLS; MULTIVARIATE REGRESSION; RIGID MOTION ESTIMATION; SELF CALIBRATION; VISION PROBLEMS;

SINGULAR VALUE DECOMPOSITION;

EID: 84944202588     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45054-8_36     Document Type: Conference Paper

References (43)

1. E. Anderson, Z. Bai, C. Bishof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen. LAPACK Users' Guide. Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688, second edition, 1994.
2. K. Arun, T. Huang, and S. Blostein. Least-squares fitting of two 3-D point sets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(5):698-700, Sept. 1987.
3. Å. Björck. Numerical methods for least squares problems. SIAM, 1996.
4. T. Chen, S. Amari, and Q. Lin. A unified algorithm for principal and minor components extraction. Neural Networks, 11(3):385-390, 1998.
5. G. Csurka, C. Zeller, Z. Zhang, and O. Faugeras. Characterizing the uncertainty of the fundamental matrix. CVGIP: Image Understanding, 68(1):18-36, Oct. 1997.
6. J. Demmel and K. Veselić. Jacobi's method is more accurate than QR. SIAM Journal on Matrix Analysis and Applications, 13:1204-1245, 1992.
7. K. Diamantaras and S. Kung. Multilayer neural networks for reduced-rank approximation. IEEE Trans. on Neural Networks, 5(5):684-697, 1994.
8. O. Faugeras. Three-Dimensional Computer Vision: a Geometric Viewpoint. MIT Press, 1993.
9. N. Georgis, M. Petrou, and J. Kittler. On the correspondence problem for wide angular separation of non-coplanar points. Image and Vision Computing, 16:35-41, 1998.
10. G. Golub and C. V. Loan. Matrix computations. The John Hopkins University Press, Baltimore, Maryland, second edition, 1989.
11. R. Hartley. Kruppa's equations derived from the fundamental matrix. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(2):133-135, Feb. 1997.
12. R. I. Hartley. Estimation of relative camera positions for uncalibrated cameras. In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, pages 579-587, Santa Margherita, Italy, May 1992. Springer-Verlag.
13. R. I. Hartley. Cheirality invariants. In Proceedings of the ARPA Image Understanding Workshop, pages 745-753, Washington, DC, Apr. 1993. Defense Advanced Research Projects Agency, Morgan Kaufmann Publishers, Inc.
14. D. Jones and J. Malik. Computational framework for determining stereo correspondence from a set of linear spatial filters. Image and Vision Computing, 10(10):699-708, 1992.
15. B. N. K. Konstantinides and G. Yovanof. Noise estimation and filtering using blockbased singular value decomposition. IEEE Trans. on Image Processing, 6(3):479-483, 1997.
16. K. Kanatani. Analysis of 3-D rotation fitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(5):543-54, 1994.
17. K. Kanatani. Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science, 1996.
18. R. Liu and T. Tan. A new SVD based image watermarking method. In Proc. of the 4th Asian Conference on Computer Vision, volume 1, pages 63-67, Jan. 2000.
19. H. Longuet-Higgins. A computer algorithm for reconstructing a scene from two projections. Nature, 293:133-135, 1981.
20. M. I. Lourakis and R. Deriche. Camera self-calibration using the singular value decomposition of the fundamental matrix: From point correspondences to 3D measurements. Research Report 3748, INRIA Sophia-Antipolis, Aug. 1999.
21. M. I. Lourakis and R. Deriche. Camera self-calibration using the Kruppa equations and the SVD of the fundamental matrix: The case of varying intrinsic parameters. Research report, INRIA Sophia-Antipolis, 2000. In preparation.
22. M. I. Lourakis and R. Deriche. Camera self-calibration using the singular value decomposition of the fundamental matrix. In Proc. of the 4th Asian Conference on Computer Vision, volume 1, pages 403-408, Jan. 2000.
23. Q.-T. Luong and O. Faugeras. Self-calibration of a moving camera from point correspondences and fundamental matrices. The International Journal of Computer Vision, 22(3):261-289, 1997.
24. Q.-T. Luong and O. Faugeras. On the determination of epipoles using cross-ratios. CVGIP: Image Understanding, 71(1):1-18, July 1998.
25. S. J. Maybank and O. D. Faugeras. A theory of self-calibration of a moving camera. The International Journal of Computer Vision, 8(2):123-152, Aug. 1992.
26. M. Moonen and B. D. Moor, editors. SVD and Signal Processing III: Algorithms, Analysis and Applications. Elsevier, Amsterdam, 1995.
27. T. Morita and T. Kanade. A sequential factorization method for recovering shape and motion from image streams. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(8):858-867, 1997.
28. C. Poelman and T. Kanade. A paraperspective factorization method for shape and motion recovery. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(3):206-218, 1997.
29. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press, 1988.
30. S. Roy, J. Meunier, and I. Cox. Cylindrical rectification to minimize epipolar distortion. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, pages 393-399, San Juan, Puerto Rico, June 1997. IEEE Computer Society.
31. L. Scharf. The SVD and reduced rank signal processing. Signal Processing, 25(2):113-133, 1991.
32. A. Shashua and N. Navab. Relative affine structure-canonical model for 3D from 2D geometry and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18:873-883, 1996.
33. G. W. Stewart. Error and perturbation bounds for subspaces associated with certain eigenvalue problems. SIAM Review, 15(4):727-764, Oct. 1973.
34. P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In B. Buxton, editor, Proceedings of the 4th European Conference on Computer Vision, pages 709-720, Cambridge, UK, Apr. 1996.
35. C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: a factorization method. The International Journal of Computer Vision, 9(2):137-154, 1992.
36. R. Tsai, T. Huang, and W. Zhu. Estimating three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Transactions on Acoustic, Speech and Signal Processing, 30(4):525-534, 1982.
37. S. Umeyama. Least-squares estimation of transformation parameters between two point patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(4):376-380, 1991
38. R. J. Vaccaro. A second-order perturbation expansion for the svd. SIAM Journal on Matrix Analysis and Applications, 15(2):661-671, Apr. 1994.
39. C. Wu, M. Berry, S. Shivakumar, and J. McLarty. Neural networks for full-scale protein sequence classification: Sequence encoding with singular value decomposition. Machine Learning, 21(1-2), 1995.
40. J. Yang and C. Lu. Combined techniques of singular value decomposition and vector quantization for image coding. IEEE Trans. on Image Processing, 4(8):1141-1146, 1995.
41. C. Zeller and O. Faugeras. Camera self-calibration from video sequences: the Kruppa equations revisited. Research Report 2793, INRIA, Feb. 1996.
42. M. Zhang, K. Yu, and R. Haralick. Fast correlation registration method using singular value decomposition. International Journal of Intelligent Systems, 1:181-194, 1986.
43. Z. Zhang, R. Deriche, O. Faugeras, and Q.-T. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Intelligence Journal, 78:87-119, Oct. 1995.