Computation of instantaneous optical flow using the phase of Fourier components

Abstract

A technique for computing the instantaneous optical flow of two images is presented. The velocity at each point in the image can be computed by treating a local region as a distinct sub-image which is translating with some velocity, and by identifying the Fourier components which exhibit the magnitude and phase changes which are consistent with this velocity. The velocity detection itself is accomplished using a Hough transform. The approach lends itself to the production of arbitrarily dense optical flow fields and the velocity vectors are computed to sub-pixel accuracy. Image data in a region are weighted as a function of its distance from the region centre to reduce the impact of `edge effects' caused by the entry and exit of visual data at the region boundary, thereby violating the assumption of pure image translation. Results are presented for Gaussian weighting functions of three standard deviations, each representing increased attenuation of image data toward the edge of the image. The proposed approach is evaluated using Otte and Nagel's benchmark image sequence [Lecture Notes in Computer Science, Computer Vision—ECCV'94, 1994, pp. 51–60], for which ground-truth data are available, and both maximum and RMS errors of velocity magnitude and direct?ion are computed.