Reducing Gross Errors of Perspective 3-point Pose Computation

Abstract

As three is the minimum number of points required to compute position and orientation in 3D space, perspective 3-point methods have been widely used for 6DOF pose computation. However, perspective 3-point methods suffer from numerical instability and multiple-solution problems, which are intrinsic problems, independent of computation methods. Many scientists have performed theoretical analysis to identify the unstable regions and classify multiple solutions. However, there have not been many studies on practical issues of avoiding multiple-solutions problem in real-time tracking. In this paper, we performed intensive experiments on perspective 3-point methods in order to obtain insights on the behaviors of multiple solutions. We discovered that the unstable region is in a cone shape, and the ambiguous multiple-solution region is in a tetrahedron shape when measurement noise is involved. Based on the results, techniques are suggested for avoiding unstable and ambiguous regions, selecting combinations of three points, and choosing the best candidate among multiple solutions.