Bayesian multi-object estimation from image observations

Analytic characterizations of the posterior distribution of a random finite set of states, conditioned on image observations are derived; under the assumption that the regions of the observation influenced by individual states do not overlap. These results provide tractable means to jointly estimate the number of states and their values in the Bayesian framework. As an application, we develop a multi-object filter suitable for image observations with low signal to noise ratio. A particle implementation of the multi-object filter is proposed and demonstrated via simulations.