Finding degenerate conics by in-plane rotations: A direct perspective-three-point solver

Abstract

The perspective-three-point (P3P) method, which estimates pose of a calibrated camera using three 2D/3D point correspondences, plays a crucial role in various visual pipelines. While most methods directly simplify the problem to a quartic, some contemporary approaches solve by degenerate conics, offering benefits in efficiency, preventing duplicate solutions and correct rate. However, existing degenerate-conic-based methods rely on the indirect framework, which is acknowledged to be less efficient and stable than the direct framework. In addition, they formulate degenerate conics algebraically, lacking clear geometric interpretations. To this end, a direct and degenerate-conic-based P3P method has been proposed in this work, which furthermore provides geometric interpretations to the degenerate conics. Concretely, it demonstrates that the conics undergo degeneration under certain in-plane rotations, angles of which are determined by a cubic. The proposed method is carefully designed to circumvent numerically risky computations and unnecessary computational burdens on recovering geometrically-invalid solutions. Both simulated and real experiments show that it excels in efficiency, noise robustness and correct rate, while avoiding the duplicate solutions commonly encountered in quartic-based methods. Additionally, it has the highest efficiency when combined with RANSAC. Code is at https://github.com/Johnnyzyzy/our_p3p.