Entropy estimates for simple random fields

We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient.