Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces
Issue No. 01 - January (1984 vol. 6)
Roger Y. Tsai , Coordinated Science Laboratory and the Department of Electrical Engineering, University of Illinois, Urbana, IL 61801; IBM T. J. Watson Research Center, Yorktown Heights, NY 10598.
Thomas S. Huang , Coordinated Science Laboratory and the Department of Electrical Engineering, University of Illinois, Urbana, IL 61801.
Two main results are established in this paper. First, we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces. The seven points should not be traversed by two planes with one plane containing the origin, nor by a cone containing the origin. Second, a set of ``essential parameters'' are introduced which uniquely determine the motion parameters up to a scale factor for the translations, and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points. The actual motion parameters can subsequently be determined by computing the singular value decomposition (SVD) of a 3Ã-3 matrix containing the essential parameters.
T. S. Huang and R. Y. Tsai, "Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 6, no. , pp. 13-27, 1984.