Dynamic scene analysis and the 8-point algorithm

Some extended versions of the 8-point algorithm of H.C. Longuet-Higgins (1981, 1984) are presented. First, the algorithm is extended to (not necessarily rigid) affine transformations. Differentiable transformations are also discussed. Second, the solution of all the affine transformations for the 8-point algorithm, given any point correspondences, is shown to have dimension 9-r, where r is the rank of given point configuration. It is argued that degenerate cases considered by Longuet-Higgins are covered by present extended version