Advertisement

Entropy Controlled Gauss-Markov Random Measure Field Models for Early Vision

  • Mariano Rivera
  • Omar Ocegueda
  • Jose L. Marroquin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)

Abstract

We present a computationally efficient segmentation–restoration method, based on a probabilistic formulation, for the joint estimation of the label map (segmentation) and the parameters of the feature generator models (restoration). Our algorithm computes an estimation of the posterior marginal probability distributions of the label field based on a Gauss Markov Random Measure Field model. Our proposal introduces an explicit entropy control for the estimated posterior marginals, therefore it improves the parameter estimation step. If the model parameters are given, our algorithm computes the posterior marginals as the global minimizers of a quadratic, linearly constrained energy function; therefore, one can compute very efficiently the optimal (Maximizer of the Posterior Marginals or MPM) estimator for multi–class segmentation problems. Moreover, a good estimation of the posterior marginals allows one to compute estimators different from the MPM for restoration problems, denoising and optical flow computation. Experiments demonstrate better performance over other state of the art segmentation approaches.

Keywords

Markov Random Field Markov Chain Monte Carlo Method Early Vision Posterior Marginal Distribution Markov Random Field 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Birchfield, S., Tomasi, C.: Multiway cut for stereo and motion with slanted surfaces. In: ICCV, pp. 489–495 (1999)Google Scholar
  2. 2.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE–PAMI 23, 1222–1239 (2001)Google Scholar
  3. 3.
    Boykov, Y., Jolly, M.-P.: Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In: ICCV, vol. I, pp. 105–112 (2001)Google Scholar
  4. 4.
    Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39, 1–38 (1977)Google Scholar
  5. 5.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. John Wiley & Sons, Inc, New York (2001)zbMATHGoogle Scholar
  6. 6.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and Bayesian restoration of images. IEEE–PAMI 6, 721–741 (1984)zbMATHGoogle Scholar
  7. 7.
    Greig, D., Porteous, B., Seheult, A.: Exact maximum a posteriori estimation for binary images. J. R. Statist. Soc. B 51, 271–279 (1989)Google Scholar
  8. 8.
    Jain, A.K., Dubes, R.C.: Algorithm for Clustering Data. Prentice Hall, Englewood Cliffs (1998)Google Scholar
  9. 9.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 65–81. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Li, S.Z.: Markov Random Field Modeling in Image Analysis. Springer, Tokyo (2001)zbMATHGoogle Scholar
  11. 11.
    Marroquin, J., Mitter, S., Poggio, T.: Probabilistic solution of ill–posed problems in computational vision. J. Am. Stat. Asoc. 82, 76–89 (1987)zbMATHCrossRefGoogle Scholar
  12. 12.
    Marroquin, J.L., Botello, S., Calderon, F., Vemuri, B.C.: The MPM-MAP algorithm for image segmentation. ICPR (2000)Google Scholar
  13. 13.
    Marroquin, J.L., Velazco, F., Rivera, M., Nakamura, M.: Gauss-Markov Measure Field Models for Low-Level Vision. IEEE–PAMI 23, 337–348 (2001)Google Scholar
  14. 14.
    Marroquin, J.L., Arce, E., Botello, S.: Hidden Markov Measure Field Models for Image Segmentation. IEEE–PAMI 25, 1380–1387 (2003)Google Scholar
  15. 15.
    Neal, R., Barry, R.: A vew of the EM algorithm that justifies incremental, sparse, and others variants. In: Jordan, M. (ed.) Learning in Graphical Models, pp. 355–368. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  16. 16.
    Nocedal, J., Wright, S.: Numerical Optimization. Springer Series in Operational Resarch. Springer, New York (1999)zbMATHCrossRefGoogle Scholar
  17. 17.
    Picher, O., Teuner, A., Hosticka, B.: An unsupervised texture segmentation algorithm with feature space reduction and knowledge feedback. IEEE Trans. Image Process. 7, 53–61 (1998)CrossRefGoogle Scholar
  18. 18.
    Rivera, M., Gee, J.C.: Image segmentation by flexible models based on robust regularized networks. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 621–634. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Rivera, M., Gee, J.C.: Two-level MRF models for image restoration and segmentation. BMVC 2, 809–818 (2004)Google Scholar
  20. 20.
    Tsai, J.Z., Willsky, A.: Expectation-Maximization Algorithms for Image Processing Using Multiscale Methods and Mean Field Theory, with Applications to Laser Radar Range Profiling and Segmentation. Opt. Engineering 40(7), 1287–1301 (2001)CrossRefGoogle Scholar
  21. 21.
    Tu, Z., Zhu, S.C., Shum, H.Y.: Image Segmentation by Data Driven Markov Chain Monte Carlo. In: ICCV, pp. 131–138 (2001)Google Scholar
  22. 22.
    Weiss, Y., Adelson, E.H.: A unified mixture framework for motion segmentation: incorporating spatial coherence and estimating the number of models. In: CVPR, pp. 321–326 (1996)Google Scholar
  23. 23.
    Wu, Z., Leaby, R.: An optimal graph theoretical approach to data clustering: Theory and its applications to image segmentation. IEEE–PAMI 11, 1101–1113 (1993)Google Scholar
  24. 24.
    Zhang, J.: The mean field theory in EM procedures for Markov random fields. IEEE Trans. Signal Processing 40, 2570–2583 (1992)zbMATHCrossRefGoogle Scholar
  25. 25.
    Tsai, A., Zhang, J., Wilsky, A.: Multiscale Methods and Mean Field Theory in EM Procedures for Image Processing. In: Eight IEEE Digital Signal Processing Workshop (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mariano Rivera
    • 1
  • Omar Ocegueda
    • 1
  • Jose L. Marroquin
    • 1
  1. 1.Centro de Investigacion en Matematicas A.C.GuanajuatoMexico

Personalised recommendations