In this paper, a new class of Random Field, defined on a multi-resolution array structure, is described. Some of the fundamental statistical properties of the model are established. Estimation from noisy data is then considered and a new procedure: Multi-resolution Maximum a Posteriori estimation, is defined. These ideas are then applied to the problem of segmenting images containing a number of regions. Implementation of the Bayesian approach is based on a multi-resolution form of Gibbs sampling. It is shown that the model forms an excellent basis for the segmentation of such images, which works with no a priori information on the number or sizes of the regions.