Computation of optical flow using basis functions

Abstract

The issues governing the computation of optical flow in image sequences are addressed. The trade-off between accuracy versus computation cost is shown to be dependent on the redundancy of the image representation. This dependency is highlighted by reformulating Horn's (1986) algorithm, making explicit use of the approximations to the continuous basis functions underlying the discrete representation. The computation cost of estimating optical flow, for a fixed error tolerance, is shown to be a minimum for images resampled at twice the Nyquist rate. The issues of derivative calculation and multiresolution representation are also briefly discussed in terms of basis functions and information encoding. A multiresolution basis function formulation of Horn's algorithm is shown to lead to large improvements in dealing with high frequencies and large displacements.