Circuits and systems able to process high quality video in real time are fundamental in nowadays imaging systems. The circuit proposed in the paper, aimed at the robust identification of the background in video streams, implements the improved formulation of the Gaussian Mixture Model (GMM) algorithm that is included in the OpenCV library. An innovative, hardware oriented, formulation of the GMM equations, the use of truncated binary multipliers, and ROM compression techniques allow reduced hardware complexity and increased processing capability. The proposed circuit has been designed having commercial FPGA devices as target and provides speed and logic resources occupation that overcome previously proposed implementations. The circuit, when implemented on Virtex6 or StratixIV, processes more than 45 frame per second in 1080p format and uses few percent of FPGA logic resources.