CvxPnPL: A unified convex solution to the absolute pose estimation problem from point and line correspondences

Sérgio Agostinho, João Gomes, Alessio Del Bue

Abstract: We present a novel certifiable convex method to estimate 3D pose from mixed combinations of 2D–3D point and line correspondences, the Perspective-n-Points-and-Lines problem. We merge the contributions of each point and line into a unified Quadratically Constrained Quadratic Problem and then relax it into a Semidefinite Program through Shor’s relaxation. In this way, we jointly handle mixed configurations of points and lines in a single computational framework. Furthermore, the proposed relaxation allows us to recover a finite number of solutions under ambiguous configurations. In such cases, the 3D pose candidates are found by further enforcing geometric constraints on the solution space and then retrieving such poses from the intersections of multiple quadrics. Experiments provide results in line with the best performing state-of-the-art methods while providing the flexibility of solving for an arbitrary number of points and lines, while the convex formulation provides a framework for a posteriori validation of globally optimal solutions.