This paper presents a novel scheme for extracting a still background occluded by a number of foreground objects, moving in different directions and velocities in a video sequence, such that every background pixel is exposed in at least one of the frames. Each identified foreground object is decomposed into blocks. The proposed scheme is able to efficiently estimate, for each foreground block, a source frame from which the occluded background pixels can be extracted. The pixels of the identified source frames are used to populate the co-located occluded pixels in the initial frame. The efficacy and the simplicity of the algorithm lie in its capacity to recover the background directly from the estimated source frames instead of performing a foreground-background classification for every frame. The proposed algorithm is robust to variations in lighting and is effective in removing both rigid and deformable foreground objects. Simulation results are presented to illustrate the performance of the proposed scheme.