A method of obtaining the relative positions of four points from three perspective projections

摘要

According to Ullman's Structure-from-Motion Theorem 1, three orthogonal projections of four points in a non-planar configuration uniquely determine their structure, and the relative orientations of the three projections, up to a reflection the image plane. This paper describes a direct method, based on quaternion algebra, for computing the alternative structures, and shows that it can be simply generalized from orthogonal to para-perspective projections, in which the viewing distances are large but finite. This leads on to an iterative method of computing structure from motion in the fully perspective case — a method that makes it possible, in favourable circumstances, to resolve the Necker ambiguity and arrive at an accurate structure after a small number of computational cycles.