Optical flow by nonlinear relaxation

In this paper, we present a local approach to the computation of raw optical flow fields based on nonlinear relaxation, which is explicitly designed to be coupled with a nonlinear vector filtering technique so as to achieve an effective rejection of the outliers. We derive the approach from a standard linear algorithm—the one-dimensional least squares. This is split down into two steps. First, the linear algorithm is formulated as an iterative procedure, in which image points in a suitable geometric neighborhood are made to interact each other. Second, a nonlinearity term in the elementary interaction between neighbors is added, which depends on the Gaussian interaction of elements of a velocity neighborhood. The results of a comparison with two linear local techniques show clearly the effectiveness of the approach, both in terms of motion boundary preservation and of optical flow field density.