Feature extraction for texture discrimination via random field models with random spatial interaction

In this paper, we attack the problem of distinguishing textured images of real surfaces using small samples. We first analyze experimental data that results from applying ordinary conditional Markov fields. In the face of the disappointing performance of these models, we introduce a random field with spatial interaction that is itself a random variable (usually referred to as a random field in a random environment). For this class of models, we establish the power spectrum and the autocorrelation function as well-defined quantities, and we devise a scheme for the estimation of related parameters. The new set of features that resulted from this approach was applied to real images. Accurate discrimination was observed even for boxes of size 10x16.

[1]  Glenn Healey,et al.  Limitations of Markov random fields as models of textured images of real surfaces , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[3]  Jürg Fröhlich,et al.  Improved perturbation expansion for disordered systems: Beating Griffiths singularities , 1984 .

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

[5]  Alberto Berretti Some properties of random Ising models , 1985 .

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

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

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

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

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

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

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

[13]  A. Klein,et al.  Who is Afraid of Griffiths’ Singularities? , 1994 .

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

[15]  Colin J. Thompson,et al.  Mathematical Statistical Mechanics , 1972 .

[16]  E. Olivieri,et al.  Some rigorous results on the phase diagram of the dilute Ising model , 1983 .

[17]  Rama Chellappa,et al.  Unsupervised Texture Segmentation Using Markov Random Field Models , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  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.

[19]  Glenn Healey,et al.  An analytical and experimental study of the performance of Markov random fields applied to textured images using small samples , 1996, IEEE Trans. Image Process..

[20]  Robert B. Griffiths,et al.  Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet , 1969 .

[21]  Rama Chellappa,et al.  Stochastic and deterministic networks for texture segmentation , 1990, IEEE Trans. Acoust. Speech Signal Process..

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

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

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