Determining motion of image curves from local pattern changes

Abstract

The instantaneous velocity field along a curve satisfies a differential equation. Given the velocity at one point of the curve and the dilatation at every point, the correct velocity field can be obtained by integrating local intensity pattern changes. Usually one has no information about the dilatation of the curve. We therefore apply a minimum dilatation principle yielding the correct velocity field in the case of a nonelastic motion and a two-dimensional rigid motion with expansion. The velocity field can be calculated by applying a propagation algorithm which does not involve iterations and which allows the use of parallel techniques to implement it. In the tests we used natural images with artificially generated motion.