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 (20×20 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 reveals that 20×20 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