A Maximum-Likelihood Approach for Multiresolution W-Operator Design

The design of W-operators from a set of input/output examples for large windows is a hard problem. From the statistical standpoint, it is hard because of the large number of examples necessary to obtain a good estimate of the joint distribution. From the computational standpoint, as the number of examples grows memory and time requirements can reach a point where it is not feasible to design the operator. This paper introduces a technique for joint distribution estimation in W-operator design. The distribution is represented by a multiresolution pyramidal structure and the mean conditional entropy is proposed as a criterion to choose between distributions induced by different pyramids. Experimental results are presented for maximum-likelihood classifiers designed for the problem of handwritten digits classification. The analysis shows that the technique is interesting from the theoretical point of view and has potential to be applied in computer vision and image processing problems.