This paper describes a region based approach to computing dense estimates of 2-D motion fields in image sequences. By dense we mean that we would like to have an estimate of the motion at each pixel location at any point in the sequence. We adopt a two-component model of local motion - the change between corresponding regions in adjacent frames is assumed to be caused by the presence of either a single motion or two separate motions. Moreover, we assume that the global motion field can be described by a set of such regions selected from a quadtree tessellation, i.e. blocks at different spatial resolutions. The estimation scheme for the model therefore consists of two components: a local estimator to determine the single or two-component motion field; and a global component to determine the set of regions. We employ partial correlation combined with an MRF segmentation scheme to do the former and a classic hierarchical selection process for the latter. Experiments on real sequences illustrate that the scheme is effective.