Motion and Structure of Four Points from One Motion of a Stereo Rig with Unknown Extrinsic Parameters

We describe an analytical method for recovering 3D motion and structure of four or more points from one motion of a stereo rig. The extrinsic parameters are unknown. The motion of the stereo rig is also unknown. Because of the exploitation of information redundancy, the approach gains over the traditional "motion and structure from motion" approach in that less features and less motions are required, and thus more robust estimation of motion and structure can be obtained. Since the constraint on the rotation matrix is not fully exploited in the analytical method, nonlinear minimization can be used to improve the result. We propose to estimate directly the motion and structure by minimizing the difference between the measured positions and the predicted ones in the image plane. Both computer simulated data and real data are used to validate the proposed algorithm, and very promising results are obtained.