Improved Generative Models for Continuous Image Features through Tree-structured Non-parametric Distributions

Density estimation arises in a wide range of vision problems and methods which can deal with high dimensional image features are of great importance. While in principle a nonparametric distribution can be estimated for the full feature distribution using Parzen windows technique, the amount of data to make these estimates accurate is usually either unattainable or unmanageable. Consequently, most modelers resort to parametric models such as mixtures of Gaussians (or other more complicated parametric forms) or make independence assumptions about the features. Such assumptions could be detrimental to the performance of vision systems since realistically, image features have neither a simple parametric form, nor are they independent. In this paper, we revive non-parametric models for image feature distributions by finding the best tree-structured graphical model (using the Chow-Liu algorithm) for our data, and estimating non-parametric distributions over the oneand two-node marginals necessary to define the graph. This procedure has the appealing property that, if the tree-structured model represents the true conditional independence relations for the features, then our estimated joint distribution converges rapidly to the true distribution of the data. Even when this is not true, it converges to the best possible tree-structured model for the original distribution. We illustrate the effectiveness of this technique on simulated data and a real-world plankton classification problem.