On a constraint equation for the estimation of displacement ratesin image sequences

The commonly used constraint equation Δg^Tu+g_t=0 for the estimation of optical flow can only be justified by assumptions that are, in general, far too restrictive for image sequences of real world scenes. B.G. Schunck (1985, 86) recently argued that a constraint equation for the estimation of what he called image flow has to include a term containing the divergence of this image flow without presenting, however, a stringent derivation based on perspective projection from 3-D scene space. The present author derives a constraint equation based on a combination of perspective projection and notions from differential geometry. In addition, he demonstrates the quantitive effects of taking into account radiometric considerations based on the use of Lambertian reflection properties and isotropic illumination in scene space