Sufficient conditions for double or unique solution of motion and structure

Several sufficient conditions are presented for a double or unique solution of the problem of motion and structure from two monocular images. It is shown that: five correspondences of points that do not lie on two lines in the image plane suffice to determine a pure rotation uniquely; six correspondences of points that do not lie on two lines in the image plane and do not correspond to space points lying on a specific quadric surface suffice to determine a motion with nonzero translation uniquely; each Maybank quadric can sustain at most two physically acceptable motion solutions and surface interpretations, provided that a sufficient number of correspondences are present; in the plane motion case, six correspondences of points that do not lie on a quadric curve in the image plane will only admit the true motion and structure and their duals as solutions. Several properties of the essential matrix T×R and the plane motion matrix R+TN^T, both of which are frequently used in the motion and structure estimation problem, are listed