A Three-Frame Algorithm for Estimating Two-Component Image Motion

A fundamental assumption made in formulating opticalow algorithms is that motion at any point in an image can be represented as a single pattern component undergoing a simple translation: even complex motion will appear as a uniform displacement when viewed through a su ciently small window. This assumption fails for a number of situations that commonly occur in real world images. For example, transparent surfaces moving past one another yield two motion components at a point. More important, it fails along the boundary between two di erently moving image regions. Even local motion analysis must be performed within a window of nite size. This window contains two motion components when it falls on a motion boundary. We propose an alternative formulation of the local motion assumption in which there may be two distinct patterns undergoing coherent (e.g., a ne) motion within a given local analysis region. We then present an algorithm for the analysis of two-component motion in which tracking and nulling mechanisms applied to three consecutive image frames separate and estimate the individual components. Precise results are obtained even for components that di er only slightly in velocity, and for a faint component in the presence of a dominant, masking, component. We demonstrate that the algorithm provides precise motion estimates for a set of elementary two-motion con gurations, and show that it is robust in the presence of noise. Permanent address: Dept. of Computer Science, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.