A Bayesian Approach for Affine Auto-calibration

  • S. S. Brandt
  • K. Palander
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)

Abstract

In this paper, we propose a Bayesian approach for affine auto-calibration. By the Bayesian approach, a posterior distribution for the affine camera parameters can be constructed, where also the prior knowledge can be taken into account. Moreover, due to the linearity of the affine camera model, the structure and translations can be analytically marginalised out from the posterior distribution, if certain prior distributions are assumed. The marginalisation reduces the dimensionality of the problem substantially that makes the MCMC methods better suitable for exploring the posterior of the intrinsic camera parameters. The experiments verify that the proposed approach is a versatile, statistically sound alternative for the existing affine auto-calibration methods.

Keywords

Posterior Distribution Bayesian Approach MCMC Method Camera Parameter Camera Model 
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.

References

  1. 1.
    Brandt, S.S.: Conditional solutions for the affine reconstruction of N views. Image and Vision Computing (2005) (In press)Google Scholar
  2. 2.
    Bretthorst, G.L.: Bayesian Spectrum Analysis and Parameter Estimation. Lecture Notes in Statistics, vol. 48. Springer, Heidelberg (1988)Google Scholar
  3. 3.
    Faugeras, O., Luong, Q., Maybank, S.: Camera self-calibration: Theory and experiments. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 321–334. Springer, Heidelberg (1992)Google Scholar
  4. 4.
    Faugeras, O., Luong, Q.-T.: Geometry of Multiple Images. MIT Press, Cambridge (2001)MATHGoogle Scholar
  5. 5.
    Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC, Boca Raton (2004)MATHGoogle Scholar
  6. 6.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  7. 7.
    Koenderink, J.J., van Doorn, A.J.: Affine structure from motion. J. Opt. Soc. Am. A 8(2), 377–385 (1991)CrossRefGoogle Scholar
  8. 8.
    MacKay, D.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
  9. 9.
    Micusik, B., Pajdla, T.: Estimation of omnidirectional camera model from epipolar geometry. In: Proc. CVPR, vol. 1, pp. 485–490 (2003)Google Scholar
  10. 10.
    Micusik, B., Pajdla, T.: Autocalibration & 3d reconstruction with non-central catadioptric cameras. In: Proc. CVPR, vol. 1, pp. 58–65 (2004)Google Scholar
  11. 11.
    Mundy, J.L., Zisserman, A.: Geometric Invariance in Computer Vision. MIT Press, Cambridge (1992)Google Scholar
  12. 12.
    Poelman, C.J., Kanade, T.: A paraperspective factorization method for shape and motion recovery. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 800, pp. 97–108. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  13. 13.
    Quan, L.: Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis. 19(1), 93–105 (1996)CrossRefGoogle Scholar
  14. 14.
    Quan, L., Kanade, T.: A factorization method for affine structure from line correspondences. In: Proc. CVPR, pp. 803–808 (1996)Google Scholar
  15. 15.
    Quan, L., Triggs, B.: A unification of autocalibration methods. In: Proc. ACCV 2000 (2000)Google Scholar
  16. 16.
    Robert, C.P., Casella, G.: Monte Carlo Statistical Methods. Springer, Heidelberg (1999)MATHGoogle Scholar
  17. 17.
    Tomasi, C., Kanade, T.: Shape and motion form image streams under orthography: A factorization approach. Int. J. Comput. Vis. 9(2), 137–154 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • S. S. Brandt
    • 1
  • K. Palander
    • 1
  1. 1.Laboratory of Computational EngineeringHelsinki University of TechnologyFinland

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