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One of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input. The main way to attack the problem, as with several other problems in science and engineering, is redundancy in the data. Up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene. We present in this paper an algorithm based on multiple frames that employs only the rigidity assumption, is simple and mathematically elegant and, experimentally proves to be a major improvement over the two-frame algorithms. The algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem. One of the side effects of this mean-square method is that the algorithm can have a very descriptive physical interpretation in terms of the “loaded spring model.”

A theory is presented for the computation of three-dimensional motion and structure from dynamic imagery, using only line correspondences. The traditional approach of corresponding microfeatures (interesting points-highlights, corners, high-curvature points, etc.) is reviewed and its shortcomings are discussed. Then, a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views. The theory is compared with previous ones that are based on nonlinear equations and iterative methods.