Spatial random tree grammars for modeling hierarchal structure in images with regions of arbitrary shape

We present a novel probabilistic model for the hierarchal structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for exact computation of likelihoods and MAP estimates and exact EM updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the ML parameters of SRTGs, classify images based on their likelihood and based on the MAP estimate of the associated hierarchal structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchal structure significantly improves upon the performance of a baseline model that lacks such structure.