The Calibration Problem for Stereoscopic Vision

  • O. D. Faugueras
  • G. Toscani
Part of the NATO ASI Series book series (volume 52)


The problem of calibrating a stereo system is extremely important in practical applications. We describe in this paper our approach for coming up with an efficient and accurate solution. We first review the pinhole camera model that is used and analyze its relationship with respect to the internal camera parameters and its position in space. We then study its behavior with respect to changes of coordinate systems.

This yields a constraint which is used in the meansquare solution of the calibration problem that we propose. Since an estimation of the uncertainty is also important, we suggest another solution based on Kaiman filtering.

We show a number of experimental results and compare them with those obtained by Tsai [8]. We finish with two practical applications of our calibration technique: reconstructing 3D points and computing the epipolar geometry of a stereo system.


Kalman Filter Intrinsic Parameter Stereo Pair Epipolar Line Distortion Correction 
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.


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  1. [1]
    O.D. FAUGERAS, G. TOSCANI, 1986, “The Calibration Problem for Stereo”, Proc. IEEE Computer Vision and Pattern Recognition, Miami, pp. 15–20.Google Scholar
  2. [2]
    O.D. FAUGERAS, N. AYACHE, AND B. FAVERJON, 1986, “Building visual maps by combining noisy stereo measurements”, Proc. IEEE Robotics and Automation, San Francisco.Google Scholar
  3. [3]
    O.D. FAUGERAS, F. LUSTMAN, AND G. TOSCANI, 1987, “Motion and Structure from Motion from Point and Line Matches”, Proc. ICVV, London, U.K., June 8–11, 1987, pp. 25–34.Google Scholar
  4. [4]
    S. GANAPATHY, 1984, “Decomposition of Transformation Matrices for Robot Vision”, Proceedings of Int. Conf. on Robotics and Automation, pp 130–139.Google Scholar
  5. [5]
    O.D. FAUGERAS, J.D. BOISSONNAT, 1987, “The Delaunay Triangulation and Passive Stereo”, INRIA, in preparation.Google Scholar
  6. [6]
    R.M. HARALICK, 1980, “Using perspective Transformations in Scene Analysis”, Computer graphics and Image Processing, 13, p 191–221.Google Scholar
  7. [7]
    A.P. SAGE, J.L. MELSEA, 1971, “Estimation theory with applications to communications and control”, McGraw-Hill, NY, pp 89–90.MATHGoogle Scholar
  8. [8]
    R.Y. TSAI, 1985,“A versatile Camera Calibration Technique for High Accuracy 3D Machine Vision Metrology using Off-the-Shelf TV Cameras and Lenses”, IBM Research Report RC 11413.Google Scholar
  9. [9]
    Y. YAKIMOVSKY, R. CUNNINGHAM, 1978, “A System for Extracting Three-Dimensional Measurements from a Stereo Pair of TV Cameras”, Computer Graphics and Image Processing, 7, pp 195–210.CrossRefGoogle Scholar
  10. [10]
    Y.I. ABDEL-AZIZ, H.M. KARARA, 1974, “Photogrammetric Potentials of Non-Metric Cameras”, Civil Engineering Studies, University of Illinois, Urbana, Illinois.Google Scholar
  11. [11]
    D. C. BROWN, 1971, “Close-Range Camera Calibration”, Photogrammetric Engineering, Vol. 37, N° 8, pp 855–866.Google Scholar
  12. [12]
    H. M. KARARA, Editor, 1979, “Handbook of Non-Topographic Photogrammetry”, American Society of Photogrammetry.Google Scholar
  13. [13]
    D. C. BROWN, 1966, “Decentering Distortion of Lenses”, Photogrammetric Engineering, Vol. 32, N° 3, May 1966.Google Scholar
  14. [14]
    G. FRANKE, 1966, “Physical Optics in Photography”, London; New York, Focal Press, 1966.Google Scholar
  15. [15]
    A. CONRADY, 1919, “Decentering Lens Systems”, Monthly Notice of Royal Astronomical Society, Vol. 39, N° 9, September 1919.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • O. D. Faugueras
    • 1
  • G. Toscani
    • 1
  1. 1.INRIALe ChesnayFrance

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