Certifiable planar relative pose estimation with gravity prior

In this work we propose a certifiable solver for the relative pose problem between two calibrated cameras under the assumptions that the unknown 3D points lay on an unknown plane and the axis of rotation is given, e.g. by an IMU. The problem is stated in terms of the rotation, translation and plane parameters and solved iteratively by an on-manifold optimization. Since the problem is nonconvex, we then try to certify this solution as the global optimum. For that, we leverage four different definitions for the search space that provide us with different certification capabilities. Since the formulations lack the Linear Independence Constraint Qualification and two of them have more constraints than variables, we cannot derive a closed-form certifier. Instead, we leverage the iterative algorithm proposed in our previous work Garcia-Salguero and Gonzalez-Jimenez (2023) that does not assume any condition on the problem formulation. Our evaluation on synthetic and real data shows that the smaller formulations are enough to certify most of the solutions, whereas the redundant ones certify all of them, including problem instances with highly noisy data. Code can be found in https://github.com/mergarsal.