Combining two computational algorithms for analysing optical flow

Two algorithms for recovering motion parameters from an optical flow field are considered in the special case of the optical flow field arising from two planes moving rigidly together relative to a camera. The first algorithm is based on a least-squares error function defined on the unit sphere of possible directions of the translational velocity. The second algorithm is based on algebraic constraints imposed on the direction of the translational velocity which are obtained from the spatial derivatives of the optical flow field to first order. Each algorithm is closely associated with a linear constraint on the direction of the translational velocity. The linear constraint associated with the second algorithm provides a simple method for locating the intersection of the two planes giving rise to the optical flow field. The situations in which the two linear constraints differs significantly (and hence provide a stable method of determining the translational velocity) are discussed. The stability of the linear constraints is checked using computer-generated optical flow fields