On a constraint equation for the estimation of displacement rates in image sequences

The commonly used constraint equation for the estimation of optical flow can only be justified by assumptions which are, in general, far too restictive for image sequences of real world scenes. Schunck 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 current contribution derives a constraint equation based on a combination of perspective projection and notions from differential geometry. In addition, it demonstrates the quantitative efforts of taking into account radiometric considerations based on the use of Lambertian reflection properties and isotropic illumination in scene space.