Modelling Joint Probabilities of Patterns in Natural Images

Considering a small image region and specifying a joint probability distribution which describes the likelihood of finding a specific pattern in this image region, arithmetic coding can provide an optimum code that reaches the Shannon limit for the given probability distribution. Data compression is thus reduced to estimating joint probability distributions of patterns. This paper demonstrates how the fact that the patterns are part of a natural image, can be converted into a priori constraints for the probability distribution. These constraints can improve the quality of an estimated joint probability distribution, thus leading to better data compression factors. 1 Introduction In 1948 Shannon [1] gave a clear recipe how to transmit information in a most compact form. For a set of patterns this recipe would roughly take the following form: ffl Determine the probability P of each pattern. ffl Assign a distinct code consisting of \Gamma log 2 (P ) bits to each pattern. Shannon's theo..