In video surveillance, one scene image/frame can be modeled as a superimposition or linear mixture of foreground visual contents and background contents. In the real world, however, the background and foreground are correlated to each other. Therefore, the foreground extraction cannot be well solved by the PCA (principle component analysis) and the ICA (independent component analysis) algorithms. The foreground extraction was modeled as a BSE (blind source extraction) problem. The MSCPE (mean square cross prediction error), one solution of BSE, was generalized to extract desired source signal which was correlated with other source signals. Then MSCPE BSE method was applied to the background subtraction schemes by using the basic model and eigen backgrounds method. Experimental results on artificial video shows the feasibility of MSCPE, and the realworld video experiments demonstrate its effectiveness.