Certifiably Optimal Monocular Hand-Eye Calibration

TL;DR

This paper introduces a convex optimization method for monocular hand-eye calibration that guarantees globally optimal solutions even when the scale of translation is unknown, with proven stability and efficiency.

Contribution

It extends previous convex calibration techniques to handle monocular sensors with unknown translation scale, providing certifiable global optimality and theoretical guarantees.

Findings

Proves the method's global optimality under bounded noise.

Demonstrates the algorithm's stability and speed with synthetic data.

Shows the tightness of the convex relaxation in calibration scenarios.

Abstract

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.