Optical flow estimation using forward-backward constraint equation

This article introduces the estimation of the optical flow, based on the combination of forward and backward constraint motion equations. Among all the existing techniques allowing the retrieval of the motion, many methods start from the assumption of recorded image brightness dependency after displacement. This dependency spans a derivative formulation, so called motion constraint equation, based on the spatial transformation. In this framework, for fixed temporal positions, the motion of a rigid object can be described by a forward and backward exploitation of the motion constraint equation, for the same spatial position. This setting in equation enables us to establish a new relation called a forward-backward optical flow equation.