Bayesian Object Matching with Hierarchical Priors and Markov Chain Monte Carlo

Abstract

Abstract We present an object matching system where Bayesian inference is used for estimating the probability distribution of object feature locations in a digital image. The representation of the object contains two parts: the likelihood part which defines the probability of perceiving a pixel image corresponding to the object detail, and a hierarchical prior part which defines the distributions of the feature locations relative to the other features. In this study the objects are human faces. The likelihood part is based on Gabor filters, which are a type of optimal bandpass digital filters. A distortion-tolerant measure of feature similarity is produced by performing statistical analysis on the filter response vectors, and the actual likelihood of observing an image detail given the feature location is computed by analyzing the distribution of the similarities. The prior part defines a priori distributions for the relative locations of the features, which correspond to their average locations on the object. The prior is hierarchical in nature, that is, a hyperprior is set for the width of the prior distribution, which allows the system to automatically determine the feature location variance appropriate for the image at hand. The object matching is carried out as Bayesian inference: the goal is to find the posterior probability distribution of the possible matches given the image and the hierarchical prior. Markov Chain Monte Carlo methods, especially Gibbs sampling, are used to draw samples from the posterior distributions of the feature locations, allowing simple estimation of the essential distribution statistics.