An analytical and experimental study of the performance of Markov random fields applied to textured images using small samples

We investigate to what extent textures can be distinguished using conditional Markov fields and small samples. We establish that the least square (LS) estimator is the only reasonable choice for this task, and we prove its asymptotic consistency and normality for a general class of random fields that includes Gaussian Markov fields as a special case. The performance of this estimator when applied to textured images of real surfaces is poor if small boxes are used (20x20 or less). We investigate the nature of this problem by comparing the behavior predicted by the rigorous theory to the one that has been experimentally observed. Our analysis reveals that 20x20 samples contain enough information to distinguish between the textures in our experiments and that the poor performance mentioned above should be attributed to the fact that conditional Markov fields do not provide accurate models for textured images of many real surfaces. A more general model that exploits more efficiently the information contained in small samples is also suggested.

[1]  Julius T. Tou,et al.  Pictorial feature extraction and recognition via image modeling , 1980 .

[2]  David B. Cooper,et al.  Bayesian Clustering for Unsupervised Estimation of Surface and Texture Models , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

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

[4]  G. Healey,et al.  New directions in texture modeling using random fields with random spatial interaction , 1995, Proceedings of the Workshop on Physics-Based Modeling in Computer Vision.

[5]  Glenn Healey,et al.  Use of invariants for recognition of three-dimensional color textures , 1994 .

[6]  J. Woods.  Markov image modeling , 1976 .

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

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

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

[10]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

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

[12]  F. S. Cohen,et al.  Classification of Rotated and Scaled Textured Images Using Gaussian Markov Random Field Models , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Glenn Healey,et al.  Feature extraction for texture discrimination via random field models with random spatial interaction , 1996, IEEE Trans. Image Process..

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

[15]  Rangasami L. Kashyap,et al.  Image data compression using autoregressive time series models , 1979, Pattern Recognit..

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

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

[18]  A. Jain,et al.  Partial differential equations and finite-difference methods in image processing, part 1: Image representation , 1977 .

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