Certifiably Optimal Monocular Hand-Eye Calibration
This work addresses the calibration challenge for robotics and computer vision systems using monocular cameras, offering a theoretically sound solution but is incremental as it builds on prior convex optimization methods.
The paper tackles the problem of extrinsic calibration for sensors with unknown scale, such as monocular cameras, by extending a convex optimization approach to provide certifiably globally optimal solutions for hand-eye calibration. It demonstrates optimality and speed through synthetic experiments, with proven tightness and stability under bounded noise.
Correct fusion of data from two sensors is not possible without an accurate estimate of their relative pose, which can be determined through the process of extrinsic calibration. When two or more sensors are capable of producing their own egomotion estimates (i.e., measurements of their trajectories through an environment), the 'hand-eye' formulation of extrinsic calibration can be employed. In this paper, we extend our recent work on a convex optimization approach for hand-eye calibration to the case where one of the sensors cannot observe the scale of its translational motion (e.g., a monocular camera observing an unmapped environment). We prove that our technique is able to provide a certifiably globally optimal solution to both the known- and unknown-scale variants of hand-eye calibration, provided that the measurement noise is bounded. Herein, we focus on the theoretical aspects of the problem, show the tightness and stability of our solution, and demonstrate the optimality and speed of our algorithm through experiments with synthetic data.