Optimal search in Hough parameter hyperspace for estimation of complex motion in image sequences

The paper is a contribution to the theory of multiparameter motion estimation using the Hough transform technique and its main feature is the analytic development of closed-form solutions for the optimal estimation strategy. Motion estimation in image sequences using the Hough transform is reviewed. Various motion models are considered offering a more realistic portrayal of camera and scene motion compared with the purely translational models adopted by standardised video coding algorithms. Since the computational complexity arising from the use of such sophisticated models is prohibitive, standard optimisation techniques are used for the search of minima of the motion estimation error function in the Hough parameter hyperspace. In contrast to previously published work, second-order Taylor expansions of the error function are considered. By taking into account such second-order terms the optimal iterative step for a gradient search in the Hough parameter hyperspace is determined for all the motion models of interest. For a purely translational model it is demonstrated that the analysis provides a similar estimate to that of the well-known Netravali and Robbins algorithm. For more complex motion models it is shown that the computation of the optimal solution involves modest complexity.