Random field models in image analysis

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but...

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  J. Berkson Maximum Likelihood and Minimum x 2 Estimates of the Logistic Function , 1955 .

[3]  C. K. Chow,et al.  A Recognition Method Using Neighbor Dependence , 1962, IRE Trans. Electron. Comput..

[4]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[5]  Laveen N. Kanal,et al.  Classification of binary random patterns , 1965, IEEE Trans. Inf. Theory.

[6]  Phil Brodatz,et al.  Textures: A Photographic Album for Artists and Designers , 1966 .

[7]  Josef Raviv,et al.  Decision making in Markov chains applied to the problem of pattern recognition , 1967, IEEE Trans. Inf. Theory.

[8]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[9]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[10]  J. Besag Statistical Analysis of Non-Lattice Data , 1975 .

[11]  Allen R. Hanson,et al.  Context in word recognition , 1976, Pattern Recognition.

[12]  D. K. Pickard A curious binary lattice process , 1977, Journal of Applied Probability.

[13]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[14]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[15]  J. Besag Efficiency of pseudolikelihood estimation for simple Gaussian fields , 1977 .

[16]  Hideyuki Tamura,et al.  Textural Features Corresponding to Visual Perception , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Godfried T. Toussaint,et al.  The use of context in pattern recognition , 1978, Pattern Recognit..

[18]  Olivier D. Faugeras,et al.  Visual Discrimination of Stochastic Texture Fields , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Azriel Rosenfeld,et al.  Mosaic Models for Textures , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[21]  Peter J. Diggle,et al.  On parameter estimation and goodness-of-fit testing for spatial point patterns , 1979 .

[22]  R. Kashyap Univariate and multivariate random field models for images , 1980 .

[23]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[24]  Laveen N. Kanal,et al.  Markov mesh models , 1980 .

[25]  D. K. Pickard,et al.  Unilateral Markov fields , 1980, Advances in Applied Probability.

[26]  M. Hassner,et al.  The use of Markov Random Fields as models of texture , 1980 .

[27]  James W. Modestino,et al.  Texture Discrimination Based Upon an Assumed Stochastic Texture Model , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Stephen B. Vardeman,et al.  Contextual classification of multispectral image data , 1981, Pattern Recognit..

[29]  A.K. Jain,et al.  Advances in mathematical models for image processing , 1981, Proceedings of the IEEE.

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

[31]  Steven W. Zucker,et al.  On the Foundations of Relaxation Labeling Processes , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[33]  Robert M. Haralick,et al.  Decision Making in Context , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[35]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

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

[37]  Rangasami L. Kashyap,et al.  Characterization and estimation of two-dimensional ARMA models , 1984, IEEE Trans. Inf. Theory.

[38]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Donald Geman,et al.  Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[41]  John Haslett,et al.  Maximum likelihood discriminant analysis on the plane using a Markovian model of spatial context , 1985, Pattern Recognit..

[42]  Anil K. Jain,et al.  A spatial filtering approach to texture analysis , 1985, Pattern Recognit. Lett..

[43]  Luc Van Gool,et al.  Texture analysis Anno 1983 , 1985, Comput. Vis. Graph. Image Process..

[44]  Alex Pentland,et al.  Shading into Texture , 1984, Artif. Intell..

[45]  J. Besag On the Statistical Analysis of Dirty Pictures , 1986 .

[46]  Fernand S. Cohen,et al.  Markov random fields for image modelling and analysis , 1986 .

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

[48]  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.

[49]  Christopher M. Brown,et al.  Probabilistic Information Fusion for Multi-Modal Image Segmentation , 1987, IJCAI.

[50]  James M. Keller,et al.  Characteristics of Natural Scenes Related to the Fractal Dimension , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[51]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[52]  G. Horgan,et al.  Linear models in spatial discriminant analysis , 1987 .

[53]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[54]  John W. Woods,et al.  Image Estimation Using Doubly Stochastic Gaussian Random Field Models , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[55]  John W. Woods,et al.  On the relationship of the Markov mesh to the NSHP Markov chain , 1987, Pattern Recognit. Lett..

[56]  Anil K. Jain,et al.  Bootstrap Techniques for Error Estimation , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[57]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[58]  D. K. Pickard Inference for Discrete Markov Fields: The Simplest Nontrivial Case , 1987 .

[59]  Jonas Gårding Properties of fractal intensity surfaces , 1988, Pattern Recognit. Lett..

[60]  Rama Chellappa,et al.  Stochastic and deterministic algorithms for MAP texture segmentation , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[61]  Kanti V. Mardia,et al.  A Spatial Thresholding Method for Image Segmentation , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[62]  E. Weinstein,et al.  The cascade EM algorithm , 1988, Proc. IEEE.

[63]  Robert M. Hodgson,et al.  Texture Measures for Carpet Wear Assessment , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[64]  Charles A. Bouman,et al.  Segmentation of textured images using a multiple resolution approach , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[65]  P. A. Devijver,et al.  Real-time restoration and segmentation algorithms for hidden Markov mesh random fields image models , 1988 .

[66]  Kanti V. Mardia,et al.  Spatial Classification Using Fuzzy Membership Models , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[67]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[68]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[69]  Chaur-Chin Chen,et al.  Experiments in filtering discrete Markov random fields to textures , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[70]  Basilis Gidas,et al.  A Renormalization Group Approach to Image Processing Problems , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[71]  James M. Keller,et al.  Texture description and segmentation through fractal geometry , 1989, Comput. Vis. Graph. Image Process..

[72]  Anil K. Jain,et al.  Segmentation of Document Images , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[73]  R. Chellappa Two-Dimensional Discrete Gaussian Markov Random Field Models for Image Processing , 1989 .