The Σ-∆ background estimation is a simple non linear method of background subtraction based on comparison and elementary increment/decrement. We propose here some elements of justification of this method with respect to statistical estimation, compared to other re-cursive methods: exponential smoothing, Gaussian estimation. We point out the relation between the Σ-∆ estimation and a probabilistic model: the Zipf law. A new algorithm is proposed for computing the back-ground/foreground classification as the pixel-level part of a motion detection algorithm. Comparative results and computational advantages of the method are commented.