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A badly calibrated camera in ego-motion estimation — propagation of uncertainty

  • Tomáš Svoboda
  • Peter Sturm
Motion and Calibration
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1296)

Abstract

This paper deals with the ego-motion estimation (motion of the camera) from two views. To estimate an ego-motion we have to find correspondences and we need a calibrated camera. In this paper we solve the problem how to propagate known camera calibration errors into the uncertainty of the motion parameters. We present a linear estimate of the uncertainty in ego-motion based on the uncertainty in the calibration parameters. We show that the linear estimate is very stable.

Keywords

Motion Parameter Euler Angle Calibration Parameter Camera Calibration Fundamental Matrix 
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.
    Giannoula Florou and Roger Mohr. What accuracy for 3D measurement with cameras? In International Conference on Pattern Recognition 1996, pages 354–358, Los Alamitos, California, August 1996. IEEE Computer Society Press.Google Scholar
  2. 2.
    Richard I. Hartley. Estimation of relative camera positions for uncalibrated cameras. In 2nd European Conference on Computer Vision, pages 579–587. Springer-Verlag, LNCS 588, May 1992.Google Scholar
  3. 3.
    Richard I. Hartley. In defence of the 8-point algorithm. In Fifth International Conference on Computer Vision, pages 1064–1070. IEEE Copmuter Society Press, 1995.Google Scholar
  4. 4.
    Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, 1985. 1987 reprinted with corrections, 1988,1990,1991,1992,1993.Google Scholar
  5. 5.
    Kenichi Kanatani. Group-Theoretic Methods in Image Understanding. Springer-Verlag, 1990.Google Scholar
  6. 6.
    H.C. Longuett-Higgins. A computer algorithm for reconstruction a scene from two projections. Nature, 293:133–135, 1981.CrossRefGoogle Scholar
  7. 7.
    Quang-Tuan Luong, Rachid Deriche, Olivier Faugeras, and Theo Papadopoulo. On determining the fundamental matrix: Analysis of different methods and experimental results. Research report 1894, INRIA, April 1993.Google Scholar
  8. 8.
    Tomáš Svoboda and Tom" Pajdla. Eficient motion analysis. Research report, K335/95/95, Czech Technical University, Faculty of Electrical Engineering, October 1995. 29 pages. Available at ftp://cmp.felk.cvut.cz/pub/cvl/articles/svoboda/egomot.ps.Z.Google Scholar
  9. 9.
    Tomáš Svoboda and Peter Sturm. What can be done with a badly calibrated camera in ego-motion analysis? Research report CTU-CMP-1996-O1, Czech Technical University, Faculty of Electrical Engineering, Center for Machine Perception, September 1996. Available at ftp://cmp.felk.cvut.cz/pub/cvl/articles/svoboda/weakcal.ps.Z.Google Scholar
  10. 10.
    Roger Y. Tsai. A versatile camera calibration technique for high-accurancy 3D machine vision metrology using off-the-shelf cameras and lenses. IEEE Journal of Robotics and Automation, RA-3(4):323–344, August 1987.Google Scholar
  11. 11.
    Juyang Weng, Thomas S. Huang, and Ahuja Narendra. Motion and structure from two perspective views: Algorithms, error analysis, and error estimation. IEEE Transactions on Pattern Analysis and Machine Inteligence, 11(5):451–476, May 1989.CrossRefGoogle Scholar
  12. 12.
    J.H. Wilkinson. The Algebraic Eigenvalue Problem. Oxford University Press, 1965.Google Scholar
  13. 13.
    Zhengyou Zhang, Rachid Deriche, Olivier Faugeras, and Quang-Twang Luog. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Research report RR-2273, INRIA, May 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Tomáš Svoboda
    • 1
  • Peter Sturm
    • 2
  1. 1.Center for Machine PerceptionCzech Technical UniversityPraha 2Czech Republic
  2. 2.GRAVIR-AMAG, project MOVI, INRIA Rhône-AlpesMonbonnot, GrenobleFrance

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