Two-Dimensional Discrete Gaussian Markov Random Field Models for Image Processing

This paper is concerned with a systematic exposition of the usefulness of two-dimensional (2-D) discrete Gaussian Markov random field (GMRF) models for image processing applications. Specifically, we discuss the following topics; notion of Markovianity on a plane, statistical inference in GMRF models, and their applications in several image related problems such as, image synthesis, texture classification, segmentation and image restoration.

[1]  Yu. A. Rosanov On Gaussian Fields with Given Conditional Distributions , 1967 .

[2]  John W. Woods,et al.  Two-dimensional discrete Markovian fields , 1972, IEEE Trans. Inf. Theory.

[3]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[4]  J. Besag,et al.  On the estimation and testing of spatial interaction in Gaussian lattice processes , 1975 .

[5]  Azriel Rosenfeld,et al.  A Comparative Study of Texture Measures for Terrain Classification , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Anil K. Jain A Fast Karhunen-Loeve Transform for Digital Restoration of Images Degraded by White and Colored Noise , 1977, IEEE Transactions on Computers.

[7]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[8]  Rangasami L. Kashyap,et al.  Optimal feature selection and decision rules in classification problems with time series , 1978, IEEE Trans. Inf. Theory.

[9]  R.M. Haralick,et al.  Statistical and structural approaches to texture , 1979, Proceedings of the IEEE.

[10]  Olivier D. Faugeras,et al.  Decorrelation Methods of Texture Feature Extraction , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  M. Ekstrom,et al.  Multidimensional spectral factorization and unilateral autoregressive models , 1980 .

[12]  R. L. Kashyap,et al.  Analysis and Synthesis of Image Patterns by Spatial Interaction Models , 1981 .

[13]  R. Chellappa,et al.  Digital image restoration using spatial interaction models , 1982 .

[14]  Charles W. Therrien,et al.  An estimation-theoretic approach to terrain image segmentation , 1983, Comput. Vis. Graph. Image Process..

[15]  Anil K. Jain,et al.  Markov Random Field Texture Models , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  R. Chellappa,et al.  On two-dimensional Markov spectral estimation , 1983 .

[17]  Rama Chellappa,et al.  Estimation and choice of neighbors in spatial-interaction models of images , 1983, IEEE Trans. Inf. Theory.

[18]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Rama Chellappa,et al.  Texture synthesis and compression using Gaussian-Markov random field models , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[20]  Rama Chellappa,et al.  Classification of textures using Gaussian Markov random fields , 1985, IEEE Trans. Acoust. Speech Signal Process..

[21]  Rama Chellappa,et al.  A model-based approach for estimation of two-dimensional maximum entropy power spectra , 1985, IEEE Trans. Inf. Theory.

[22]  H. Derin,et al.  Segmentation of textured images using Gibbs random fields , 1986 .

[23]  B. Ripley Statistics, images, and pattern recognition , 1986 .

[24]  David B. Cooper,et al.  Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.