On computing metric upgrades of projective reconstructions under the rectangular pixel assumption

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

Volumn 2018, Issue , 2001, Pages 52-67

  Ponce, Jean ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; CAMERAS; EIGENVALUES AND EIGENFUNCTIONS; FACTORIZATION; GEOMETRY; MATLAB; PIXELS;

EIGEN-VALUE; LINE GEOMETRY; LINEAR OPERATIONS; METRIC UPGRADE; NON-LINEAR LEAST SQUARES; PROJECTIVE RECONSTRUCTION; SYMMETRIC MATRICES; UNIFIED FRAMEWORK;

MATRIX ALGEBRA;

EID: 84866045078     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45296-6_4     Document Type: Conference Paper

References (36)

1. B. Boufama, R. Mohr, and F. Veillon. Euclidian constraints for uncalibrated reconstruction. In Proc. Int. Conf. Comp. Vision, pages 466-470, Berlin, Germany, May 1993.
2. J. Costeira and T. Kanade. A multi-body factorization method for motion analysis. Int. J. of Comp. Vision, 29(3):159-180, September 1998.
3. O. Faugeras and B. Mourrain. On the geometry and algebra of the point and line correspondences between n images. Technical Report 2665, INRIA Sophia-Antipolis, 1995.
4. O. Faugeras and T. Papadopoulo. Gaussman-Caylay algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Technical Report 3225, INRIA Sophia-Antipolis, 1997.
5. O.D. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig? In G. Sandini, editor, Proc. European Conf. Comp. Vision, volume 588 of Lecture Notes in Computer Science, pages 563-578, Santa Margherita, Italy, 1992. Springer-Verlag.
6. O.D. Faugeras. Three-Dimensional Computer Vision. MIT Press, 1993.
7. O.D. Faugeras. Stratification of 3D vision: projective, affine and metric representations. J. Opt. Soc. Am. A, 12(3):465-484, March 1995.
8. O.D. Faugeras, Q.-T. Luong, and S.J. Maybank. Camera self-calibration: theory and experiments. In G. Sandini, editor, Proc. European Conf. Comp. Vision, volume 588 of Lecture Notes in Computer Science, pages 321-334, Santa Margherita, Italy, 1992. Springer-Verlag.
9. A. Fitzgibbon and A. Zisserman. Automatic 3D model acquisition and generation of new images from video sequences. In European Signal Processing Conference, pages 311-326, Rhodes, Greece, 1998.
10. P.E. Gill and W. Murray. Newton-type methods for unconstrained and linearly constrained optimization. Math. Programming, 28:311-350, 1974.
11. C. Harris and M. Stephens. A combined edge and corner detector. In 4th Alvey Vision Conference, pages 189-192, Manchester, UK, 1988.
12. R. Hartley. Lines and points in three views and the trifocal tensor. Int. J. of Comp. Vision, 22(2):125-140, March 1997.
13. R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908-912, Seattle,WA, June 1994.
14. R.I. Hartley. In defence of the 8-point algorithm. In Proc. Int. Conf. Comp. Vision, pages 1064-1070, Boston, MA, 1995.
15. R.I. Hartley, R. Gupta, and T. Chang. Stereo from uncalibrated cameras. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 761-764, Champaign, IL, 1992.
16. A. Heyden. Geometry and algebra of multiple projective transformations. PhD thesis, Lund University, Sweden, 1995.
17. A. Heyden and K. A ström. Minimal conditions on intrinsic parameters for Euclidean reconstruction. In Asian Conference on Computer Vision, Hong Kong, 1998.
18. A. Heyden and K. A ström. Flexible calibration: minimal cases for auto-calibration. In Proc. Int. Conf. Comp. Vision, pages 350-355, Kerkyra, Greece, September 1999.
19. J.J. Koenderink and A.J. Van Doorn. Affine structure from motion. J. Opt. Soc. Am. A, 8:377-385, 1990.
20. S.J. Maybank and O.D. Faugeras. A theory of self-calibration of a moving camera. Int. J. of Comp. Vision, 8(2):123-151, 1992.
21. R. Mohr, L. Quan, F. Veillon, and B. Boufama. Relative 3D reconstruction using multiple uncalibrated images. Technical Report RT 84-IMAG 12-LIFIA, LIFIA-IRIMAG, June 1992.
22. C.J. Poelman and T. Kanade. A paraperspective factorization method for shape and motion recovery. IEEE Trans. Patt. Anal. Mach. Intell., 19(3):206-218, March 1997.
23. M. Pollefeys. Self-calibration and metric 3D reconstruction from uncalibrated image sequences. PhD thesis, Katholieke Universiteit Leuven, 1999.
24. M. Pollefeys, R. Koch, and L. Van Gool. Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. Int. J. of Comp. Vision, 32(1):7-26, August 1999.
25. L. Quan. Self-calibration of an affine cameras from multiple views. Int. J. of Comp. Vision, 19:93-110, 1996.
26. R.B. Schnabel and E. Eskow. A new modified Cholesky factorization. SIAM J. Sci. Comput., 11:1136-1158, 1990.
27. A. Shashua. Projective depth: a geometric invariant for 3D reconstruction from two perspective/ orthographic views and for visual recognition. In Proc. Int. Conf. Comp. Vision, pages 583-590, Berlin, Germany, 1993.
28. A. Shashua. Trilinearity in visual recognition by alignment. In J.-O. Eklundh, editor, Proc. European Conf. Comp. Vision, volume 800 of Lecture Notes in Computer Science, pages 479-484. Springer-Verlag, 1994.
29. P. Sturm. Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 1100-1105, San Juan, Puerto Rico, June 1997.
30. C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: a factorization method. Int. J. of Comp. Vision, 9(2):137-154, 1992.
31. P.H.S. Torr, A.W. Fitzgibbon, and A. Zisserman. The problem of degeneracy in structure and motion estimation from uncalibrated motion sequences. Int. J. of Comp. Vision, 32(1):27-44, August 1999.
32. R.Y. Tsai and T.S. Huang. Uniqueness and estimation of 3D motion parameters of rigid bodies with curved surfaces. IEEE Trans. Patt. Anal. Mach. Intell., 6:13-27, 1984.
33. S. Ullman. The Interpretation of Visual Motion. The MIT Press, Cambridge, MA, 1979.
34. D. Weinshall and C. Tomasi. Linear and incremental acquisition of invariant shape models from image sequences. IEEE Trans. Patt. Anal. Mach. Intell., 17(5), May 1995.
35. Z. Zhang, R. Deriche, O.D. 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, October 1995.
36. T. Papadopoulo and M. Lourakis. Estimating the jacobian of the singular value decomposition: Theory and applications. In Proc. European Conference on Computer Vision, pages 554-570, 2000.