Image Modeling Using Gibbs-Markov Random Field and Support Vector Machines Algorithm
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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:58862", author = "Refaat M Mohamed and Ayman El-Baz and Aly A. Farag", title = "Image Modeling Using Gibbs-Markov Random Field and Support Vector Machines Algorithm", abstract = "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 = "Image Modeling, MRF, Parameters Estimation,
SVM Learning.", volume = "1", number = "11", pages = "3555-4", }