A Bayesian theory of multi-scale cross-correlation in images

Cross-correlation is a commonly used principle for intensity-based object localization but gives only a single estimate of location. On the other hand, random sampling algorithms can generate an entire probability distribution for object location. That allows the representation of ambiguity, and sequential inference including propagation from coarse to fine scale, and over time. Bayesian cross-correlation is a synthesis of cross-correlation with probabilistic sampling and has required several key developments. The first is the interpretation of correlation matching functions in probabilistic terms, as observation likelihoods. Second, a response-learning procedure has been developed for distributions of filter-bank responses. Lastly, multi-scale processing is achieved, in a Bayesian context, by means of a new algorithm, layered sampling, for which asymptotic properties are derived.