title: Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces.
abstract: 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 3×3 matrix containing the essential parameters.
authors.affiliation: 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.
authors.forename: R Y
authors.initials: RY
authors.lastname: Tsai
authors.forename: T S
authors.initials: TS
authors.lastname: Huang