# Certifiably Optimal Monocular Hand-Eye Calibration

arXiv: https://arxiv.org/abs/2005.08298 · HTML: https://mlsanity.com/paper/2005.08298/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2020.

## Built on by (most cited first, 7 of 7)

- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Extrinsic Camera Calibration with Semantic Segmentation](https://mlsanity.com/paper/2208.03949/) (2022)
- [Semidefinite Relaxations for Robust Multiview Triangulation](https://mlsanity.com/paper/2301.11431/) (2023)
- [Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions](https://mlsanity.com/paper/2201.04473/) (2022)
- [Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search](https://mlsanity.com/paper/2207.08350/) (2022)
- [Automated Static Camera Calibration with Intelligent Vehicles](https://mlsanity.com/paper/2304.10814/) (2023)
- [PLS-Calib: A Partial Least Squares Framework for Event Camera and Odometry Calibration under Ground Motion Constraints](https://mlsanity.com/paper/2608.03296/) (2026)

## Abstract (arXiv)

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.