The robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision. This paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images, and an algorithm consistent with that framework. Our framework is based on a scale-based separation of the image intensity information and the process of measuring motion. The large-scale intensity information is first used to obtain rough estimates of image motion, which are then refined by using intensity information at smaller scales. The estimates are in the form of displacement (or velocity) vectors for pixels and are accompanied by a direction-dependent confidence measure. A smoothness constraint is employed to propagate measurements with high confidence to neighboring areas where the confidences are low. At all levels, the computations are pixel-parallel, uniform across the image, and based on information from a small neighborhood of a pixel. Results of applying our algorithm to pairs of real images are included. In addition to our own matching algorithm, we also show that two different hierarchical gradient-based algorithms are consistent with our framework.
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