Fast Certifiable Algorithm for the Absolute Pose Estimation of a Camera

SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1415-1432, September 2024.
Abstract.Estimating the absolute pose of a camera given a set of [math] points and their observations is known as the resectioning or Perspective-n-Point (PnP) problem. It is at the core of most computer vision applications and it can be stated as an instance of three-dimensional registration with point-line distances, making the error quadratic in the unknown pose. The PnP problem, though, is nonconvex due to the constraints associated with the rotation, and iterative algorithms may get trapped into any suboptimal solutions without notice. This work proposes an efficient certification algorithm for central and noncentral cameras that either confirms the optimality of a solution or is inconclusive. We exploit different sets of constraints for the rotation to assess their performance in terms of certification. Two of the formulations lack the Linear Independence Constraint Qualification (LICQ) while one of them has more constraints than variables. This hinders the usage of the “standard” procedure which estimates the Lagrange multipliers in closed-form. To overcome that, we formulate the certification as an eigenvalue optimization and solve it through a line-search method. Our evaluation on synthetic and real data shows that minimal formulations certify most solutions (more than [math] on real data) whereas redundant formulations are able to certify all of them and even random problem instances. The proposed algorithm runs in microseconds for all these formulations.