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Distortions of stereoscopic visual space and quadratic Cremona transformations

  • Gregory Baratoff
Structure from Motion
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1296)

Abstract

When incorrect values for the extrinsic and intrinsic parameters of the two cameras of a stereo rig are used in the reconstruction of a three-dimensional scene from image correspondences, the resulting reconstruction is distorted in a systematic way. We show here that the transformation between the true scene structure and its distorted reconstruction is a quadratic Cremona transformation — a rational transformation which is one-to-one almost everywhere, but which does not in general preserve collinearity.

We study the distortion of points in the fixation plane on a global, qualitative, level, and on a local, quantitative level. Both global and local viewpoints provide evidence of severe non-linear distortions in the vicinity of the camera centers, thereby indicating that their consideration is of particularly high relevance for near regions of the stereo rig. This is consistent with experimental evidence from psychophysics, which shows that distortions in the near range can not be adequately described by linear transformations.

Our distortion framework describes and enables the analysis of situations where insufficient information is available to compute even a weak calibration of a stereo rig. It also makes possible a thorough error analysis of systematic errors in computing structure from motion.

Keywords

Base Point Intrinsic Parameter Epipolar Geometry Fixation Plane Camera Center 
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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References

  1. 1.
    G. Baratoff, “Distortion of Stereoscopic Visual Space”, Tech. Rep. CAR-TR-861, Center for Automation Research, Univ. of Maryland, College Park, USA, May 1997.Google Scholar
  2. 2.
    L. Cheong and Y. Aloimonos, “Iso-distortion contours and Egomotion Estimation,” in Proc. Int. Symposium on Computer Vision, pp. 55–60, 1995.Google Scholar
  3. 3.
    L. Cheong, C. Fermüller and Y. Aloimonos, “Interaction Between 3D Shape and Motion: Theory and Applications,” Technical Report CAR-TR-773, Center for Automation Research, Univ. of Maryland, College Park, USA, June 1996.Google Scholar
  4. 4.
    O. Faugeras, “What can be seen in three dimensions with an uncalibrated stereo rig,” in Proc. 2nd European Conf. on Computer Vision, G. Sandini, ed., Vol. 538 of Lecture Notes in Computer Science (Springer Verlag, Berlin), pp. 563–578, 1992.Google Scholar
  5. 5.
    C. Fermüller, L. Cheong and Y. Aloimonos, “Explaining Human Visual Space Distortion,” Technical Report CAR-TR-833, Center for Automation Research, Univ. of Maryland, College Park, USA, July 1996.Google Scholar
  6. 6.
    S. Maybank, “Theory of Reconstruction from Image Motion”, Springer-Verlag, Berlin, 1993.Google Scholar
  7. 7.
    C. C. Slama and C. Theurer and S. W. Henriksen, “Manual of Photogrammetry”, Am. Soc. of Photogrammetry, 1980.Google Scholar
  8. 8.
    J.G. Semple and L. Roth, Introduction to Algebraic Geometry, Oxford, 1949.Google Scholar
  9. 9.
    J. S. Tittle, J. T. Todd, V. J. Perotti, and J. F. Norman, “Systematic Distortion of Perceived Three-Dimensional Structure From Motion and Binocular Stereopsis”, J. of Experimental Psychology, vol. 21 (1995), no. 3, pp. 663–678.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gregory Baratoff
    • 1
  1. 1.Center for Automation ResearchUniversity of MarylandCollege ParkUSA

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