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.

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.

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 include 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 (20/spl times/20 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 reveal that 20/spl times/20 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.>