Minimal Solvers for Generalized Pose and Scale Estimation from Two Rays and One Point

Abstract

Estimating the poses of a moving camera with respect to a known 3D map is a key problem in robotics and Augmented Reality applications. Instead of solving for each pose individually, the trajectory can be considered as a generalized camera. Thus, all poses can be jointly estimated by solving a generalized P n P (gP n P) problem. In this paper, we show that the gP n P problem for camera trajectories permits an extremely efficient minimal solution when exploiting the fact that pose tracking allows us to locally triangulate 3D points. We present a problem formulation based on one point-point and two point-ray correspondences that encompasses both the case where the scale of the trajectory is known and where it is unknown. Our formulation leads to closed-form solutions that are orders of magnitude faster to compute than the current state-of-the-art, while resulting in a similar or better pose accuracy.