Labeling Irregular Graphs with Belief Propagation

  • Ifeoma Nwogu
  • Jason J. Corso
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4958)


This paper proposes a statistical approach to labeling images using a more natural graphical structure than the pixel grid (or some uniform derivation of it such as square patches of pixels). Typically, low-level vision estimations based on graphical models work on the regular pixel lattice (with a known clique structure and neighborhood). We move away from this regular lattice to more meaningful statistics on which the graphical model, specifically the Markov network is defined. We create the irregular graph based on superpixels, which results in significantly fewer nodes and more natural neighborhood relationships between the nodes of the graph. Superpixels are a local, coherent grouping of pixels which preserves most of the structure necessary for segmentation. Their use reduces the complexity of the inferences made from the graphs with little or no loss of accuracy. Belief propagation (BP) is then used to efficiently find a local maximum of the posterior probability for this Markov network. We apply this statistical inference to finding (labeling) documents in a cluttered room (under moderately different lighting conditions).


Gaussian Mixture Model Belief Propagation Markov Random Field Synthetic Image Label Image 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cao, H., Govindaraju, V.: Handwritten carbon form preprocessing based on markov random field. In: Proc. IEEE Conf. Comput. Vision And Pattern Recogniton (2007)Google Scholar
  2. 2.
    Corso, J.J., Sharon, E., Yuille, A.L.: Multilevel Segmentation and Integrated Bayesian Model Classification with an Application to Brain Tumor Segmentation. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006, Part II. LNCS, vol. 4191, pp. 790–798. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Duncan, R., Qian, J., Zhu, B.: Polynomial time algorithms for three-label point labeling. In: Wang, J. (ed.) COCOON 2001. LNCS, vol. 2108, p. 191. Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Felzenszwalb, P., Huttenlocher, D.: Efficient belief propagation for early vision. In: Proc. IEEE Conf. Comput. Vision And Pattern Recogn. (2004)Google Scholar
  5. 5.
    Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. International Journal of Computer Vision 40(1), 25–47 (2000)zbMATHCrossRefGoogle Scholar
  6. 6.
    Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)zbMATHCrossRefGoogle Scholar
  7. 7.
    Luo, B., Hancock, E.R.: Structural graph matching using the em algorithm and singular value decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1120–1136 (2001)CrossRefGoogle Scholar
  8. 8.
    Mori, G., Ren, X., Efros, A.A., Malik, J.: Recovering human body configurations: Combining segmentation and recognition. In: Proc. IEEE Conf. Comput. Vision And Pattern Recogn., vol. 2, pp. 326–333 (2004)Google Scholar
  9. 9.
    Murphy, K.P., Weiss, Y., Jordan, M.I.: Loopy belief propagation for approximate inference: An empirical study. In: Proceedings of Uncertainty in AI, pp. 467–475 (1999)Google Scholar
  10. 10.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)Google Scholar
  11. 11.
    Ren, X., Fowlkes, C.C., Malik, J.: Scale-invariant contour completion using conditional random fields. In: Proc. 10th Int’l. Conf. Computer Vision, vol. 2, pp. 1214–1221 (2005)Google Scholar
  12. 12.
    Sharon, E., Brandt, A., Basri, R.: Segmentation and boundary detection using multiscale intensity measurements. In: Proc. IEEE Conf. Comput. Vision And Pattern Recogn., vol. 1, pp. 469–476 (2001)Google Scholar
  13. 13.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  14. 14.
    Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M.F., Rother, C.: A comparative study of energy minimization methods for markov random fields. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 16–29. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Tappen, M.F., Russell, B.C., Freeman, W.T.: Efficient graphical models for processing images. In: Proc. IEEE Conf. Comput. Vision And Pattern Recogniton, pp. 673–680 (2004)Google Scholar
  16. 16.
    Yu, S., Shi, J.: Segmentation with pairwise attraction and repulsion. In: Proceedings of the 8th IEEE IInternational Conference on Computer Vision (ICCV 2001) (July 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ifeoma Nwogu
    • 1
  • Jason J. Corso
    • 1
  1. 1.Department of Computer Science and EngineeringState University of New York at BuffaloBuffalo

Personalised recommendations