A robust multiscale B-spline function decomposition for estimating motion transparency

Motion transparency phenomena in image sequences are frequent, but classical methods of motion estimation are unable to deal with them. This paper describes a method for estimating optical flow by a generalization of the brightness constancy assumption to additive transparencies. The brightness constancy assumption is obtained by setting constant velocity fields during three images of a sequence. Thus, by a Taylor development to its second order, we reach an extension of the optical flow constraint equation. Since the equation is nonlinear, the Levenberg-Marquardt algorithm is used. In order to suppress the unavoidable aperture problem, a global model based on B-spline basis functions is applied with the aim of constraining optical flows. This description of motion allows us to work on a coarse to fine estimation of artificial image sequences that shows good convergence properties. It is also applied to natural image sequences.