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 cond itional Markov fields and small samples, We establish that the least s quare (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 cas e. The performance of this estimator when applied to textured images o f real surfaces is poor if small boxes are used (20 x 20 or less). We investigate the nature of this problem by comparing the behavior predi cted by the rigorous theory to the one that has been experimentally ob served, Our analysis reveals that 20 x 20 samples contain enough infor mation 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 tex tured images of many real surfaces. A more general model that exploits more efficiently the information contained in small samples is also s uggested.