A Markov Chain Monte Carlo Approach to Stereovision

  • Julien Sénégas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2352)


We propose Markov chain Monte Carlo sampling methods to address uncertainty estimation in disparity computation. We consider this problem at a postprocessing stage, i.e. once the disparity map has been computed, and suppose that the only information available is the stereoscopic pair. The method, which consists of sampling from the posterior distribution given the stereoscopic pair, allows the prediction of large errors which occur with low probability, and accounts for spatial correlations. The model we use is oriented towards an application to mid-resolution stereo systems, but we give insights on how it can be extended. Moreover, we propose a new sampling algorithm relying on Markov chain theory and the use of importance sampling to speed up the computation. The efficiency of the algorithm is demonstrated, and we illustrate our method with the computation of confidence intervals and probability maps of large errors, which may be applied to optimize a trajectory in a three dimensional environment.


stereoscopic vision digital terrain models disparity uncertainty estimation sampling algorithms Bayesian computation inverse problems 


  1. [1]
    P.N. Belhumeur. A Bayesian approach to binocular stereopsis. International Journal of Computer Vision, 19(3):237–262, 1996.CrossRefGoogle Scholar
  2. [2]
    J. Besag. On the statistical analysis of dirty pictures (with discussion). J. Roy. Statist. Soc. Ser. B, 48:259–302, 1986.zbMATHMathSciNetGoogle Scholar
  3. [3]
    J. Besag, P. Green, D. Higdon, and K. Mengersen. Bayesian computation and stochastic systems. Statistical Science, 10(1):3–66, 1995.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    C. Chang and S. Chatterjee. Multiresolution stereo-A Bayesian approach. IEEE International Conference on Pattern Recognition, 1:908–912, 1990.CrossRefGoogle Scholar
  5. [5]
    J.P. Chilès and P. Delfiner. Geostatistics: Modeling Spatial Uncertainty. Wiley and Sons, 1999.Google Scholar
  6. [6]
    I.J. Cox. A maximum likelihood n-camera stereo algorithm. International Conference on Computer Vision and Pattern Recognition, pages 733–739, 1994.Google Scholar
  7. [7]
    F. Dellaert, S. Seitz, S. Thrun, and C. Thorpe. Feature correspondance: A Markov chain Monte Carlo approach. In Advances in Neural Information Processing Systems 13, pages 852–858, 2000.Google Scholar
  8. [8]
    F. Devernay and O. Faugeras. Automatic calibration and removal of distorsions from scenes of structured environments. In Leonid I. Rudin and Simon K. Bramble, editors, Investigate and Trial Image Processing, Proc. SPIE, volume 2567. SPIE, San Diego, CA, 1995.Google Scholar
  9. [9]
    U.R. Dhond and J.K. Aggarwal. Structure from stereo-A review. IEEE Transactions on systems, man and cybernetics, 19(6):1489–1510, 1989.CrossRefMathSciNetGoogle Scholar
  10. [10]
    O. Faugeras. Three-Dimensional Computer Vision. Massachussets Institute of Technology, 1993.Google Scholar
  11. [11]
    D. Forsyth, S. Ioffe, and J. Haddon. Bayesian structure from motion. In International Conference on Computer Vision, volume 1, pages 660–665, 1999.CrossRefGoogle Scholar
  12. [12]
    L. Garcin, X. Descombes, H. Le Men, and J. Zerubia. Building detection by markov object processes. In Proceedings of ICIP’01, Thessalonik, Greece, 2001.Google Scholar
  13. [13]
    S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6):721–741, 1984.zbMATHCrossRefGoogle Scholar
  14. [14]
    W.R. Gilks, S. Richardson, and D.J. Spiegelhalter. Markov Chain Monte Carlo in Practice. Chapman and Hall, 1996.Google Scholar
  15. [15]
    W.K. Hastings. Monte carlo sampling methods using Markov chains and their applications. Biometrika, 57:97–109, 1970.zbMATHCrossRefGoogle Scholar
  16. [16]
    T. Kanade and M. Okutomi. A stereo matching algorithm with an adaptive window: Theory and experiment. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(9), september 1994.Google Scholar
  17. [17]
    R. Mandelbaum, G. Kamberova, and M. Mintz. Stereo depth estimation: a confidence interval approach. In International Conference on Computer Vision, pages 503–509, 1998.Google Scholar
  18. [18]
    S.P. Meyn and R.L. Tweedie. Markov Chains and Stochastic Stability. Springer-Verlag London, 1993.zbMATHGoogle Scholar
  19. [19]
    G.O. Roberts and J.S. Rosenthal. Optimal scaling of discrete approximations to Langevin diffusions. J. Roy. Statist. Soc. Ser. B, 60:255–268, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    J.J. Rodriguez and J.K. Aggarwal. Stochastic analysis of stereo quantization error. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5):467–470, 1990.CrossRefGoogle Scholar
  21. [21]
    J. Sénégas, M. Schmitt, and P. Nonin. Conditional simulations applied to uncertainty assessment in DTMs. In G. Foody and P. Atkinson, editors, Uncertainty in Remote Sensing and GIS. Wiley and Sons, 2002. to appear.Google Scholar
  22. [22]
    R. Stoica, X. Descombes, and J. Zerubia. Road extraction in remote sensed images using a stochastic geometry framework. In Proceedings of MaxEnt’ 00, Gif Sur Yvette, July 8–13, 2000.Google Scholar
  23. [23]
    R. Szeliski. Bayesian Modeling of Uncertainty in Low-level Vision. Kluwer Academic Publishers, 1989.Google Scholar
  24. [24]
    R.L. Tweedie. Markov chains: Structure and applications. In B. N. Shanbhag and C.R. Rao, editors, Handbook of Statistics 19, pages 817–851. Elsevier Amsterdam, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Julien Sénégas
    • 1
    • 2
  1. 1.Centre de GéostatistiqueEcole des Mines de ParisFontainebleau CedexFrance
  2. 2.IstarSophia-Antipolis CedexFrance

Personalised recommendations