Learning Multiscale Representations of Natural Scenes Using Dirichlet Processes

We develop nonparametric Bayesian models for multiscale representations of images depicting natural scene categories. Individual features or wavelet coefficients are marginally described by Dirichlet process (DP) mixtures, yielding the heavy-tailed marginal distributions characteristic of natural images. Dependencies between features are then captured with a hidden Markov tree, and Markov chain Monte Carlo methods used to learn models whose latent state space grows in complexity as more images are observed. By truncating the potentially infinite set of hidden states, we are able to exploit efficient belief propagation methods when learning these hierarchical Dirichlet process hidden Markov trees (HDP-HMTs) from data. We show that our generative models capture interesting qualitative structure in natural scenes, and more accurately categorize novel images than models which ignore spatial relationships among features.