On functionals with greyvalue-controlled smoothness terms for determining optical flow

The modification by H.H. Nagel (1987) of the approach developed by B.K.P. Horn and B.G. Schunck (1981) for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation. Applying this scheme to three constraint equations reported in the literature, as a special case, a generalization of Nagel's approach is obtained. An existence and uniqueness result of solutions under very general conditions that, in turn, ensures the applicability of standard techniques to compute an approximate solution is presented.