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.