Second-order polynomial models for background subtraction

This paper is aimed at investigating background subtraction based on second-order polynomial models. Recently, preliminary results suggested that quadratic models hold the potential to yield superior performance in handling common disturbance factors, such as noise, sudden illumination changes and variations of camera parameters, with respect to state-of-the-art background subtraction methods. Therefore, based on the formalization of background subtraction as Bayesian regression of a second-order polynomial model, we propose here a thorough theoretical analysis aimed at identifying a family of suitable models and deriving the closed-form solutions of the associated regression problems. In addition, we present a detailed quantitative experimental evaluation aimed at comparing the different background subtraction algorithms resulting from theoretical analysis, so as to highlight those more favorable in terms of accuracy, speed and speed-accuracy tradeoff.