Maximisation of cross-correlation is a commonly used principle for intensity-based object localization that gives a single estimate of location. However, to facilitate sequential inference (eg over time or scale) and to allow the representation of ambiguity, it is desirable to represent an entire probability distribution for object location. Although the cross-correlation itself (or some function of it) has sometimes been treated as a probability distribution, this is not generally justifiable.
Bayesian correlation achieves a consistent probabilistic treatment by combining several developments. The first is the interpretation of correlation matching functions in probabilistic terms, as observation likelihoods. Second, probability distributions of filter-bank responses are learned from training examples. Inescapably, response-learning also demands statistical modelling of background intensities, and there are links here with image coding and Independent Component Analysis. Lastly, multi-scale processing is achieved, in a Bayesian context, by means of a new algorithm, "layered sampling", for which asymptotic properties are derived.
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