Multiresolution Random Fields and their Application to Image Analysis

In this paper, a new class of Random Field, defined on a multiresolution array structure, is defined. These combine earlier, tree based models with the more conventional MRF models. The fundamental statistical properties of these models are investigated and it is proved that they can avoid some of the obvious limitations of their predecessors, in terms of modelling realistic image structures. Prediction and estimation from noisy data are then considered and a new procedure: Multiresolution Maximum a Posteriori estimation, is defined. These ideas are then applied to the problem of analysing images containing a number of regions. It is shown that the model forms an excellent basis for the segmentation of such images.