3D Structure Reconstruction from Point Correspondences between two Perspective Projections

An iterative algorithm for 3D structure reconstruction from two perspective projections is proposed. The basis of the method is the eight-point algorithm (Longuet-Higgins, Nature 293(10), 1981, 133-135; Tsai and Huang, IEEE Trans. PAMI 6, 1984, 13-27). A drawback of the eight-point algorithm is that it requires at least eight point correspondences. Further, there are certain point configurations for which the algorithm fails. For example, the eight corners of a cube on a quadratic surface passing through the focal points of the cameras form such a degenerate configuration. By combining the eight-point algorithm with an SVD (singular value decomposition) characterization of the so-called E-matrix (Faugeras and Maybank, Internat. J. Comput. Vision 4, 1990, 225-246; Huang and Faugeras, IEEE Trans. PAMI 11, 1989, 1310-1312), the proposed iterative algorithm solves the 3D reconstruction problem even from less than eight points. The algorithm is also free from the artificial degeneracy problem inherent to the eight-point algorithm. The iteration in the algorithm takes place only if the configuration is degenerate or violates the SVD characterization due to measurement error. Otherwise the computation is O(N) as in the eight-point algorithm.