Discrete Wavelet Analysis for Fast Optic Flow Computation

This paper describes a new way to compute the optic flow, based on a discrete wavelet basis analysis. The optic flow is estimated locally by the projection of the differential optic flow equation onto wavelets. The resulting linear systems are small and of fixed size (3-5 equations). They are solved to find out the visual displacement. In this way, we circumvent the classical problems of time aliasing and aperture. Moreover, the coefficients of the systems can be computed with a set of wavelet transforms, and the resolution of these systems is of similar complexity. The algorithm has thus a complexity of only O(N) (if one image of the sequence has N pixels). We show that our approach permits the measurement of illumination changes, making the optic flow computation more robust. A consistency result is also proven, which states that this method provides asymptotically correct flow estimates.