Hierarchal Perceptual Organization with the Center-Surround Algorithm

We present a method for imposing hierarchal structure on segmented images using probabilistic context-free gram- mars (PCFGs). The notion of PCFG, which has been used in the past to characterize 1D word strings, is extended to characterize 2D images as well. The inside-outside algo- rithm is then extended to support training, classification, and parsing on images with these extended PCFGs. The soundness and efficiency of these extensions rely on a novel notion of constituency that constrains the allowable ways to partition a parent segment into child subsegments during parsing. We successfully apply our method to the task of classifying natural images and also show that our method can learn the common hierarchal structure in such images, in an unsupervised fashion, from unlabeled training data.