A Local Algorithm for the Computation of Image Velocity via Constructive Interference of Global Fourier Components

Abstract

A novel Fourier-based technique for local motion detection from image sequences is proposed. In this method, the instantaneous velocities of local image points are inferred directly from the global 3D Fourier components of the image sequence. This is done by selecting those velocities for which the superposition of the corresponding Fourier gratings leads to constructive interference at the image point. Hence, image velocities can be assigned locally even though position is computed from the phases and amplitudes of global Fourier components (spanning the whole image sequence) that have been filtered based on the motion-constraint equation, reducing certain aperture effects typically arising from windowing in other methods. Regularization is introduced for sequences having smooth flow fields. Aperture effects and their effect on optic-flow regularization are investigated in this context. The algorithm is tested on both synthetic and real image sequences and the results are compared to those of other local methods. Finally, we show that other motion features, i.e. motion direction, can be computed using the same algorithmic framework without requiring an intermediate representation of local velocity, which is an important characteristic of the proposed method.