The problem of foreground detection in real-time video surveillance applications is addressed. Proposes is a framework, which is computationally cheap and has low memory requirements. It combines two simple processing blocks, both of which are essentially background subtraction algorithms. The main novelty of the approach is a combination of an autoregressive moving average filter with two background models having different adaptation speeds. The first model, having a lower adaptation speed, models long-term background and detects foreground objects by finding areas in the current frame which significantly differ from the proposed background model. The second model, with a higher adaptation speed, models the short-term background and is responsible for finding regions in the scene with a high foreground object activity. The final foreground detection is built by combining the outputs from these building blocks. The foreground obtained by the long-term modelling block is verified by the output of the short-term modelling block, i.e. only the objects exhibiting significant motion are detected as real foreground objects. The proposed method results in a very good foreground detection performance at a low computational cost.