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Image Modeling Using Gibbs-Markov Random Field and Support Vector Machines Algorithm

Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag


This paper introduces a novel approach to estimate the clique potentials of Gibbs Markov random field (GMRF) models using the Support Vector Machines (SVM) algorithm and the Mean Field (MF) theory. The proposed approach is based on modeling the potential function associated with each clique shape of the GMRF model as a Gaussian-shaped kernel. In turn, the energy function of the GMRF will be in the form of a weighted sum of Gaussian kernels. This formulation of the GMRF model urges the use of the SVM with the Mean Field theory applied for its learning for estimating the energy function. The approach has been tested on synthetic texture images and is shown to provide satisfactory results in retrieving the synthesizing parameters.

Keywords: parameters estimation, MRF, Image Modeling, SVM Learning

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[1] B. Julesz, "Visual Pattern Discrimination," IEEE Transactions on Information Theory, Vol. IT-8, pp. 84-97, 1962.
[2] D. Marr, "Analyzing Natural Images: A Computational Theory of Texture Vision, "Cold Spring Harbor Symposium, Quantitave Biology., Vol. 40, pp. 647-662, 1976.
[3] S. Geman and D. Geman, "Stochastic relaxation, Gibbs Distribution, and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine intelligence, Vol. 6, pp. 721-741, 1984.
[4] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice System," Journal of Royal Statistical Society, Ser. B, Vol. 36, pp. 192- 236, 1974.
[5] J. Besag, "Efficiency of Pseudolikelihood Estimation for Simple Gaussian Fields," Biometrika, Vol. 64, pp. 616- 618, 1977.
[6] H. Derin and H. Elliott, "Modeling and Segmentation of Noisy and Texture Images Using Gibbs Random Fields," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 9, pp. 39-55, 1987.
[7] R. Kashyap and R. Chellappa, "Estimation and Choice of Neighbors in Spatial Interaction Models of Images," IEEE Transactions on Information Theory, Vol. 29, pp. 60-72, 1983.
[8] V. Vapnik, The Nature of Statistical Learning Theory. 2nd Edition, Springer: New York, 2001.
[9] Refaat M. Mohamed and Aly A. Farag, "Mean Field Theory for Density Estimation Using Support Vector Machines," Seventh International Conference on Information Fusion, Stockholm, July, 2004, pp. 495-501.
[10] E. Ising, Zetischrift Physiks, Vol. 31, pp.253, 1925.
[11] A.K.Jain, and R.C.Dubes, "Random Field Models in Image Analysis," Journal of Applied Statistics, Vol. 16, No. 2, 1989.