Canonic representations for the geometries of multiple projective views

  • Q. -T. Luong
  • T. Viéville
Stereo and Calibration
Part of the Lecture Notes in Computer Science book series (LNCS, volume 800)


We show how a special decomposition of general projection matrices, called canonic enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), affine, and projective, that we also relate to each other. In the last case, a new decomposition of the well-known fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established, as well as the link between local (ie for pairs of views) representations and global (ie for a sequence of images) representations.


Fundamental Matrix Intrinsic Parameter Canonic Representation Projection Matrice Canonic Decomposition 
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  1. 1.
    O. D. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig. In Proc. European Conference on Computer Vision, pages 563–578, 1992.Google Scholar
  2. 2.
    O.D. Faugeras. Three-dimensional computer vision: a geometric viewpoint. MIT Press, 1993.Google Scholar
  3. 3.
    O.D. Faugeras, Q.-T. Luong, and S.J. Maybank. Camera self-calibration: theory and experiments. In Proc. European Conference on Computer Vision, pages 321–334, Santa-Margerita, Italy, 1992.Google Scholar
  4. 4.
    O.D. Faugeras and S.J. Maybank. Motion from point matches: multiplicity of solutions. The International Journal of Computer Vision, 4(3):225–246, 1990. also INRIA Tech. Report 1157.Google Scholar
  5. 5.
    R. Hartley, R. Gupta, and T. Chang. Stereo from uncalibrated cameras. In Proc. of the conf. on Computer Vision and Pattern Recognition, pages 761–764, Urbana, 1992.Google Scholar
  6. 6.
    Q.-T. Luong and O.D. Faugeras. Determining the Fundamental matrix with planes: unstability and new algorithms. In Proc. Conference on Computer Vision and Pattern Recognition, pages 489–494, New-York, 1993.Google Scholar
  7. 7.
    Q.-T. Luong and O.D. Faugeras. Self-calibration of a stereo rig from unknown camera motions and point correspondences. In A. Grun and T.S. Huang, editors, Calibration and orientation of cameras in computer vision. Springer-Verlag, 1993. To appear. Also presented at XVII ISPRS, Washington, and INRIA Tech. Report RR-2014.Google Scholar
  8. 8.
    Q.-T. Luong and T. Viéville. Canonic representations for the geometries of multiple projective views. Technical Report UCB/CSD-93-772, University of California at Berkeley, Sept 1993. A shorter version appeared at ECCV'94.Google Scholar
  9. 9.
    S.J. Maybank and O.D. Faugeras. A Theory of Self-Calibration of a Moving Camera. The International Journal of Computer Vision, 8(2):123–151, 1992.Google Scholar
  10. 10.
    J. L. Mundy and A. Zisserman, editors. Geometric invariance in computer vision. MIT Press, 1992.Google Scholar
  11. 11.
    L.S. Shapiro, A. Zisserman, and M. Brady. Motion from point matches using affine epipolar geometry. Technical Report OUEL 1994/93, Oxford University., June 1993.Google Scholar
  12. 12.
    R.Y. Tsai and T.S. Huang. Estimating Three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Transactions on Acoustic, Speech and Signal Processing, 30, 1982.Google Scholar
  13. 13.
    T. Viéville and Q.T. Luong. Motion of points and lines in the uncalibrated case. Technical Report RR-2054, INRIA, Sept 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Q. -T. Luong
    • 1
    • 2
  • T. Viéville
    • 2
  1. 1.EECSUniversity of CaliforniaBerkeleyUSA
  2. 2.INRIASophia-AntipolisFrance

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