Object Identification in a Bayesian Context Timothy Huang, Stuart Russell Computer Science Division University of California Berkeley, CA 94720, USA {tthuang,russell}@cs.berkeley.edu Abstract Object identification—the task of deciding that two observed objects are in fact one and the same object—is a fundamental requirement for any sit- uated agent that reasons about individuals. Object identity, as represented by the equality operator be- tween 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 bridg- ing 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 prob- ability 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 nat- ural 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 net- work, 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. 1 Introduction 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 indi- viduals. Our aim in this paper is to establish the patterns of reasoning involved in object identification. To avoid pos- sibly empty theorizing, we couple this investigation with a This work was sponsored by JPL’s New Traffic Sensor Technol- ogy program and by California PATH under MOU 152 and 214. real application of economic significance: identification of vehicles in freeway traffic. Each refinement of the theoretical framework is illustrated in the context of this application. We begin with a general introduction to the identification task. Section 2 provides a Bayesian foundation for computing the probability of identity. Section 3 shows how this probability can be expressed in terms of appearance probabilities, and Section 4 describes our implementation. Finally, Section 5 presents experimental results in the application domain. 1.1 Conceptual and theoretical issues The existence of individuals is central to our conceptualization of the world. While object recognition deals with assigning objects to categories, such as 1988 Toyota Celicas or adult humans, object identification deals with recognizing specific individuals, such as one’s car or one’s spouse. One can have specific relations to individuals, such as ownership or mar- riage. Hence, it is often important to be fairly certain about the identity of the particular objects one encounters. Formally speaking, identity is expressed by the equal- ity operator of first-order logic. Having detected an ob- ject C in a parking lot, one might be interested in whether C = MyCar. Because mistaken identity is always a possibil- ity, this becomes a question of the probability of identity: P(C = MyCar all available evidence). There has been little work on this question in AI. 1 The approach we will take (Sec- tion 2) is the standard Bayesian approach: define an event space, assign a prior, condition on the evidence, and identify the events corresponding to the truth of the identity sentence. The key step is the last, and takes the form of an identity criterion. Once we have a formula for the probability of iden- tity, we must find a way to compute it in terms of quantities that are available in the domain model. Section 3 shows that one natural quantity of interest is the appearance probability. This quantity, which covers diverse domain-specific phenom- ena ranging from the effects of motion, pose, and lighting to changes of address of credit applicants, seems to be more nat- ural and usable than the usual division into sensor and motion models, which require calibration against ground truth. 1 In contrast, reasoning about category membership based on ev- idence is the canonical task for probabilistic inference. Proposing that MyCar is just a very small category misses the point.