Closed-form solutions for the Euclidean calibration of a stereo rig

  • G. Csurka
  • D. Demirdjian
  • A. Ruf
  • R. Horaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)


In this paper we describe a method for estimating the internal parameters of the left and right cameras associated with a stereo image pair. The stereo pair has known epipolar geometry and therefore 3-D projective reconstruction of pairs of matched image points is available. The stereo pair is allowed to move and hence there is a collineation relating the two projective reconstructions computed before and after the motion. We show that this collineation has similar but different parameterizations for general and ground-plane rigid motions and we make explicit the relationship between the internal camera parameters and such a collineation. We devise a practical method for recovering four camera parameters from a single general motion or three camera parameters from a single ground-plane motion. Numerous experiments with simulated, calibrated and natural data validate the calibration method.


Planar Motion General Motion Rigid Motion Intrinsic Parameter Camera Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    P. A. Beardsley and A. Zisserman. Affine calibration of mobile vehicles. In Proceedings of Europe-China Workshop on Geometrical Modelling and Invariants for Computer Vision, pages 214–221, Xi'an, China, April 1995. Xidan University Press.Google Scholar
  2. 2.
    P.A. Beardsley, I.D. Reid, A. Zisserman, and D.W. Murray. Active visual navigation using non-metric structure. In E. Grimson, editor, Proceedings of the 5th International Conference on Computer Vision, Cambridge, Massachusetts, USA, pages 58–64. IEEE Computer Society Press, June 1995.Google Scholar
  3. 3.
    F. Devernay and O. Faugeras. From projective to Euclidean reconstruction. In Proceedings Computer Vision and Pattern Recognition Conference, pages 264–269, San Francisco, CA., June 1996.Google Scholar
  4. 4.
    O. D. Faugeras. Three Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Boston, 1993.Google Scholar
  5. 5.
    R. Hartley and P. Sturm. Triangulation. Computer Vision and Image Understanding, 68(2):146–157, 1997.CrossRefGoogle Scholar
  6. 6.
    R. I. Hartley. Euclidean reconstruction from uncalibrated views. In Mundy Zisserman Forsyth, editor, Applications of Invariance in Computer Vision, pages 237–256. Springer Verlag, Berlin Heidelberg, 1994.Google Scholar
  7. 7.
    A. Heyden and K. åström. Euclidean reconstruction from constant intrinsic parameters. In Proceedings of the 13th International Conference on Pattern Recognition, Vienna, Austria, volume I, pages 339–343, August 1996.Google Scholar
  8. 8.
    R. Horaud and G. Csurka. Self-calibration and euclidean reconstruction using motions of a stereo rig. In Proceedings of the 6th International Conference on Computer Vision, Bombay, India, pages 96–103, January 1998.Google Scholar
  9. 9.
    R.A. Horn and C.R. Johnson. Matrix analysis. Cambridge University Press, 1985.Google Scholar
  10. 10.
    Q-T. Luong and O. D. Faugeras. Self-calibration of a moving camera from point correspondences and fundamental matrices. International Journal of Computer Vision, 22(3):261–289, 1997.CrossRefGoogle Scholar
  11. 11.
    Q.T. Luong and T. Vieville. Canonic representations for the geometries of multiple projective views. In Proceedings of the 3rd European Conference on Computer Vision, Stockholm, Sweden, pages 589–599, May 1994.Google Scholar
  12. 12.
    T. Moons, L. Van Gool, M. Proesmans, and E Pauwels. Affine reconstruction from perspective image pairs with a relative object-camera translation in between. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(1):77–83, January 1996.CrossRefGoogle Scholar
  13. 13.
    M. Pollefeys and L. Van Gool. A stratified approach to metric self-calibration. In Proceedings of the Conference on Computer Vision and Pattern Recognition, Puerto Rico, USA, pages 407–412. IEEE Computer Society Press, June 1997.Google Scholar
  14. 14.
    P. Sturm. Critical motion sequences for monocular self-calibration and uncalibrated euclidean reconstruction. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 1100–1105, Puerto-Rico, June 1997.Google Scholar
  15. 15.
    B. Triggs. Autocalibration and the absolute quadric. In Proceedings of the Conference on Computer Vision and Pattern Recognition, Puerto Rico, USA, pages 609–614. IEEE Computer Society Press, June 1997.Google Scholar
  16. 16.
    J.H. Wilkinson. The algebraic eigenvalue problem. Clarendon Press-Oxford, 1965.Google Scholar
  17. 17.
    A. Zisserman, P. A. Beardsley, and I. D. Reid. Metric calibration of a stereo rig. In Proc. IEEE Workshop on Representation of Visual Scenes, pages 93–100, Cambridge, Mass., June 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • G. Csurka
    • 1
  • D. Demirdjian
    • 1
  • A. Ruf
    • 1
  • R. Horaud
    • 1
  1. 1.INRIA RhÔne-AlpesMontbonnot Saint MartinFrance

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