Bayesian Tracking with Auxiliary Discrete Processes. Application to Detection and Tracking of Objects with Occlusions

A number of Bayesian tracking models involve auxiliary discrete variables beside the main hidden state of interest. These discrete variables usually follow a Markovian process and interact with the hidden state either via its evolution model or via the observation process, or both. We consider here a general model that encompasses all these situations, and show how Bayesian filtering can be rigorously conducted with it. The resulting approach facilitates easy re-use of existing tracking algorithms designed in the absence of the auxiliary process. In particular we show how particle filters can be obtained based on sampling only in the original state space instead of sampling in the augmented space, as it is usually done. We finally demonstrate how this framework facilitates solutions to the critical problem of appearance and disappearance of targets, either upon scene entering and exiting, or due to temporary occlusions. This is illustrated in the context of color-based tracking with particle filters.