Camera-LiDAR Extrinsic Calibration using Constrained Optimization with Circle Placement

Abstract

We proposes a method to address LiDAR's sparse point cloud (see (a)) by Generating a Probability Distribution and utilizing the Lagrangian-Multipliers (see (b)) of a known target circle placement to extract more accurate features.

Framework

Getting Started

• Example: '3 target poses with 30 LiDAR scans' calibration scenario.

1.Requirements

1.1 Setup

• Our code is tested on Ubuntu 20.04 64-bit with ROS Noetic
  • Ubuntu 20.04
  • ROS Noetic
  • Python 3.8
  • Scipy 1.10.1

1.2 Calibration Board

• We use a planar board with four circular hole placed on rectangular shaped.

1.3 Calibration data

• Sample calibration data was captured in GAZEBO Simulation (velo2cam)
  • LiDAR: 64-channel LiDAR with Gauss noise 0.03m
  • Camera: 1280 x 720 resolution and 69 degree FOV with Gauss noise 0.03m

2. LiDAR

2.1 Capture point cloud

• Sample LiDAR point cloud: 1/1.npy

2.2 LiDAR featrues

• Check the number of poses & LiDAR scan iterations

python3 ./src/vlp_features.py

3. Camera

3.1 Capture images

• Sample camera image: file_001.png

3.2 Camera intrinsic parameters

• We use the ground truth intrinisc parameters of GAZEBO.
• In real-world, it can be estimated using OpenCV (zhang's method)

3.3 Camera features

• The camera features are extracted using the (lvt2calib).

4. 3D Point-to-Point Alignment

• Check the camera & LiDAR features path

python3 ./src/alignment.py

5. Reprojection

• Check the extrinisc parameters path

python3 ./src/reprojection.py

• Reprojection results

Contact

• For any questions, please contact to us at kdh2769@khu.ac.kr or github Issues

Thanks

[1] J. Beltr ́an, C. Guindel, A. de la Escalera, and F. Garc ́ıa, “Automatic extrinsic calibration method for lidar and camera sensor setups,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 10, pp. 17 677–17 689, 2022

[2] J. Zhang, Y. Liu, M. Wen, Y. Yue, H. Zhang, and D. Wang, “L2v2t2 calib: Automatic and unified extrinsic calibration toolbox for different 3d lidar, visual camera and thermal camera,” in 2023 IEEE Intelligent Vehicles Symposium (IV). IEEE, 2023, pp. 1–7

Citation

Please consider citing this work if you use our code in your research:

@ARTICLE{10778314,
  author={Kim, Daeho and Shin, Seunghui and Hwang, Hyoseok},
  journal={IEEE Robotics and Automation Letters}, 
  title={Camera-LiDAR Extrinsic Calibration Using Constrained Optimization With Circle Placement}, 
  year={2025},
  volume={10},
  number={2},
  pages={883-890},
  keywords={Calibration;Laser radar;Point cloud compression;Three-dimensional displays;Cameras;Image edge detection;Feature extraction;Accuracy;Sensor phenomena and characterization;Sensor fusion;Calibration and identification;sensor fusion;intelligent transportation systems},
  doi={10.1109/LRA.2024.3512253}
}