Stochastic grammars for images on arbitrary graphs

We describe a class of multiscale stochastic processes based on stochastic context-free grammars and called spatial random trees (SRTs) which can be effectively used for modeling multidimensional signals. In addition to modeling images which are sampled on a regular rectangular grid, we generalize this methodology to images defined on arbitrary graph structures. We develop likelihood calculation, MAP estimation, and EM-based parameter estimation algorithms for SRTs. To illustrate these methods, we apply them to classification of natural images using region graphs extracted by a recursive bipartitioning segmentation algorithm.