Computation of instantaneous optical flow using the phase of Fourier components

A technique for computing the instantaneous optical flow of two images is p resented. The velocity at each point in the image can be computed by treati ng a local region as a distinct sub-image which is translating with some ve locity, and by identifying the Fourier components which exhibit the magnitu de and phase changes which are consistent with this velocity. The velocity detection itself is accomplished using a Hough transform. The approach lend s itself to the production of arbitrarily dense optical flow fields and the velocity vectors are computed to sub-pixel accuracy. Image data in a regio n are weighted as a function of its distance from the region centre to redu ce 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 tra nslation. Results are presented for Gaussian weighting functions of three s tandard deviations, each representing increased attenuation of image data t oward the edge of the image. The proposed approach is evaluated using Otte and Nagel's benchmark image sequence [Lecture Notes in Computer Science, Co mputer Vision-ECCV'94, 1994, pp. 51-60], for which ground-truth data are av ailable, and both maximum and RMS errors of velocity magnitude and directio n are computed. (C) 1999 Elsevier Science B.V. All rights reserved.