A Bayesian approach to object identification
There are many real world domains where an agent can observe the world state only partially and intermittently, using noisy sensors. Merely keeping track of the objects present in such a system is non-trivial. The problem may be complicated further if the system dynamics are not fully known or unpredictable, so that some on-line learning is necessary. I have been working on a principled approach to state estinaation and prediction under these realistic conditions. So far, I have focused mostly on object identification, deciding if some newly observed object is the same as a previously observed one. The work has been applied to the surveillance of a large metropolitan freeway system. The vehicles are observed through scattered cameras, and both the viewing and traffic conditions are highly variable. The general approach is based on a probabilistic formulation of the domain. The conditional independence and variable density distribution assumptions are made explicit, so the domain can be expressed as a dynamic probabilistic network (DPN). The right assumptions can simplify the problem considerably, although care must be taken to make them realistic. As an example, consider the traffic surveillance domain. There, we can assume that certain observations are dependent on the sensor where they are made, and the object generating them, but not directly dependent on what happens at other sensors. Color, for example, is constant for each vehicle, and the way it appears at each observation site depends on the characteristics of that site. The introduction of hidden variables representing such features of objects in the system enables us to remove many intersensor dependencies. As a result, we can use small, local probability models. We learn model parameters using the Expectation Maximazation (EM) algorithm. Unfortunately, inference in large, complex problems will remain intractable even if the probabilistic network is simplified. The correspondence between observations and objects is unknown, and so inference in the system should involve summing over all the possibilities. Since the number of possible observation-object assignments is exponential in the number of objects, solving such a summation exactly is a #P problem. Our solu-