Very Robust Direct Solver of the P3P Problem

Abstract

In this paper, we propose a robust and novel direct solver for solving the Perspective-Three-Point (P3P) problem, which is called RP3P by us. Although the P3P has been studied for many years and achieved great success, it still faces the following three limitations at least: (1) The instability of solutions caused by different ordering of vertices, (2) geometric degradation in the singular case, (3) depending on the specific equation solver. The main method of the proposed solver is to use two auxiliary variables to simplify the calculation process. Additionally, the depth of the three-dimension control points is normalized to simplify the process of derivation, and then the depth of three-dimension control points can be obtained in a simple fashion. RP3P does not depend on particular equation solver and has high stability in image noise. Moreover, in “singular cylinder”, even if all other classic direct solutions are seriously degraded, the proposed solution can still obtain reliable solution.