Maximizing entropy of pickard random fields for 2×2 binary constraints

This paper considers the problem of maximizing the entropy of two-dimensional (2D) Pickard Random Fields (PRF) subject to constraints. We consider binary Pickard Random Fields, which provides a 2D causal finite context model and use it to define stationary probabilities for 2×2 squares, thus allowing us to calculate the entropy of the field. All possible binary 2×2 constraints are considered and all constraints are categorized into groups according to their properties. For constraints which can be modeled by a PRF approach and with positive entropy, we characterize and provide statistics of the maximum PRF entropy. As examples, we consider the well known hard square constraint along with a few other constraints.