Simultaneous Motion Detection and Background Reconstruction with a Mixed-State Conditional Markov Random Field

We consider the problem of motion detection by background subtraction. An accurate estimation of the background is only possible if we locate the moving objects; meanwhile, a correct motion detection is achieved if we have a good available background model. This work proposes a new direction in the way such problems are considered. The main idea is to formulate this class of problem as a joint decision-estimation unique step. The goal is to exploit the way two processes interact, even if they are of a dissimilar nature (symbolic-continuous), by means of a recently introduced framework called mixed-state Markov random fields. In this paper, we will describe the theory behind such a novel statistical framework, that subsequently will allows us to formulate the specific joint problem of motion detection and background reconstruction. Experiments on real sequences and comparisons with existing methods will give a significant support to our approach. Further implications for video sequence inpainting will be also discussed.