Object Identification in a Bayesian Context

Object identification—the task of deciding that two observed objects are in fact one and the same object—is a fundamental requirement for any situated agent that reasons about individuals. Object identity, as represented by the equality operator between two terms in predicate calculus, is essentially a first-order concept. Raw sensory observations, on the other hand, are essentially propositional— especially when formulated as evidence in standard probability theory. This paper describes patterns of reasoning that allow identity sentences to be grounded in sensory observations, thereby bridging the gap. We begin by defining a physical event space over which probabilities are defined. We then introduce an identity criterion, which selects those events that correspond to identity between observed objects. From this, we are able to compute the probability that any two objects are the same, given a stream of observations of many objects. We show that the appearance probability, which defines how an object can be expected to appear at subsequent observations given its current appearance, is a natural model for this type of reasoning. We apply the theory to the task of recognizing cars observed by cameras at widely separated sites in a freeway network, with new heuristics to handle the inevitable complexity of matching large numbers of objects and with online learning of appearance probability models. Despite extremely noisy observations, we are able to achieve high levels of performance.