# Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions

arXiv: https://arxiv.org/abs/2201.04473 · HTML: https://mlsanity.com/paper/2201.04473/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 12 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator](https://mlsanity.com/paper/1708.03852/) (2017)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Certifiably Optimal Monocular Hand-Eye Calibration](https://mlsanity.com/paper/2005.08298/) (2020)
- [Online Extrinsic Calibration based on Per-Sensor Ego-Motion Using Dual Quaternions](https://mlsanity.com/paper/2101.11440/) (2021)
- [Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion](https://mlsanity.com/paper/1809.03554/) (2018)

## Built on by (most cited first, 2 of 2)

- [Semidefinite Relaxations for Robust Multiview Triangulation](https://mlsanity.com/paper/2301.11431/) (2023)
- [Automated Static Camera Calibration with Intelligent Vehicles](https://mlsanity.com/paper/2304.10814/) (2023)

## Abstract (arXiv)

In this work, we present an approach for monocular hand-eye calibration from per-sensor ego-motion based on dual quaternions. Due to non-metrically scaled translations of monocular odometry, a scaling factor has to be estimated in addition to the rotation and translation calibration. For this, we derive a quadratically constrained quadratic program that allows a combined estimation of all extrinsic calibration parameters. Using dual quaternions leads to low run-times due to their compact representation. Our problem formulation further allows to estimate multiple scalings simultaneously for different sequences of the same sensor setup. Based on our problem formulation, we derive both, a fast local and a globally optimal solving approach. Finally, our algorithms are evaluated and compared to state-of-the-art approaches on simulated and real-world data, e.g., the EuRoC MAV dataset.