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.
This work was partially supported by CONACYT, Mexico (grants 40722 and 46270).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Birchfield, S., Tomasi, C.: Multiway cut for stereo and motion with slanted surfaces. In: ICCV, pp. 489–495 (1999)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE–PAMI 23, 1222–1239 (2001)
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)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39, 1–38 (1977)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. John Wiley & Sons, Inc, New York (2001)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and Bayesian restoration of images. IEEE–PAMI 6, 721–741 (1984)
Greig, D., Porteous, B., Seheult, A.: Exact maximum a posteriori estimation for binary images. J. R. Statist. Soc. B 51, 271–279 (1989)
Jain, A.K., Dubes, R.C.: Algorithm for Clustering Data. Prentice Hall, Englewood Cliffs (1998)
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)
Li, S.Z.: Markov Random Field Modeling in Image Analysis. Springer, Tokyo (2001)
Marroquin, J., Mitter, S., Poggio, T.: Probabilistic solution of ill–posed problems in computational vision. J. Am. Stat. Asoc. 82, 76–89 (1987)
Marroquin, J.L., Botello, S., Calderon, F., Vemuri, B.C.: The MPM-MAP algorithm for image segmentation. ICPR (2000)
Marroquin, J.L., Velazco, F., Rivera, M., Nakamura, M.: Gauss-Markov Measure Field Models for Low-Level Vision. IEEE–PAMI 23, 337–348 (2001)
Marroquin, J.L., Arce, E., Botello, S.: Hidden Markov Measure Field Models for Image Segmentation. IEEE–PAMI 25, 1380–1387 (2003)
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)
Nocedal, J., Wright, S.: Numerical Optimization. Springer Series in Operational Resarch. Springer, New York (1999)
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)
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)
Rivera, M., Gee, J.C.: Two-level MRF models for image restoration and segmentation. BMVC 2, 809–818 (2004)
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)
Tu, Z., Zhu, S.C., Shum, H.Y.: Image Segmentation by Data Driven Markov Chain Monte Carlo. In: ICCV, pp. 131–138 (2001)
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)
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)
Zhang, J.: The mean field theory in EM procedures for Markov random fields. IEEE Trans. Signal Processing 40, 2570–2583 (1992)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rivera, M., Ocegueda, O., Marroquin, J.L. (2005). Entropy Controlled Gauss-Markov Random Measure Field Models for Early Vision. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_12
Download citation
DOI: https://doi.org/10.1007/11567646_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
Online ISBN: 978-3-540-32109-5
eBook Packages: Computer ScienceComputer Science (R0)