Dynamic Trees for unsupervised segmentation and matching of image regions.

We present a probabilistic framework--namely, multiscale generative models known as Dynamic Trees (DT)--for unsupervised image segmentation and subsequent matching of segmented regions in a given set of images. Beyond these novel applications of DTs, we propose important additions for this modeling paradigm. First, we introduce a novel DT architecture, where multilayered observable data are incorporated at all scales of the model. Second, we derive a novel probabilistic inference algorithm for DTs--Structured Variational Approximation (SVA)--which explicitly accounts for the statistical dependence of node positions and model structure in the approximate posterior distribution, thereby relaxing poorly justified independence assumptions in previous work. Finally, we propose a similarity measure for matching dynamic-tree models, representing segmented image regions, across images. Our results for several data sets show that DTs are capable of capturing important component-subcomponent relationships among objects and their parts, and that DTs perform well in segmenting images into plausible pixel clusters. We demonstrate the significantly improved properties of the SVA algorithm--both in terms of substantially faster convergence rates and larger approximate posteriors for the inferred models--when compared with competing inference algorithms. Furthermore, results on unsupervised object recognition demonstrate the viability of the proposed similarity measure for matching dynamic-structure statistical models.