# American Institute of Mathematical Sciences

January  2021, 17(1): 427-445. doi: 10.3934/jimo.2019119

## Calibration of a 3D laser rangefinder and a camera based on optimization solution

 a. School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China b. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China c. Information Center, Ministry of Water Resources of China, Beijing 100032, China

* Corresponding author: Lei Wang (Email: wanglei@dlut.edu.cn)

Received  March 2019 Revised  April 2019 Published  September 2019

The calibration of a 3D laser rangefinder (LRF) and a camera is a key technique in the field of computer vision and intelligent robots. This paper proposes a new method for the calibration of a 3D LRF and a camera based on optimization solution. The calibration is achieved by freely moving a checkerboard pattern in front of the camera and the 3D LRF. The images and the 3D point clouds of the checkerboard pattern in various poses are collected by the camera and the 3D LRF respectively. By using the images, the intrinsic parameters and the poses of the checkerboard pattern are obtained. Then, two kinds of geometric constraints, line-to-plane constraints and plane-to-plane constraints, are constructed to solve the extrinsic parameters by linear optimization. Finally, the intrinsic and extrinsic parameters are further refined by global optimization, and are used to compute the geometric mapping relationship between the 3D LRF and the camera. The proposed calibration method is evaluated with both synthetic data and real data. The experimental results show that the proposed calibration method is accurate and robust to noise.

Citation: Yi An, Bo Li, Lei Wang, Chao Zhang, Xiaoli Zhou. Calibration of a 3D laser rangefinder and a camera based on optimization solution. Journal of Industrial & Management Optimization, 2021, 17 (1) : 427-445. doi: 10.3934/jimo.2019119
##### References:

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##### References:
Calibration board and 3D color laser ranging system
Pinhole camera model
Point cloud of the calibration board and its line point clouds
Calibration images
Normal vector $\bar{\mathit{\boldsymbol{n}}}_{j}$ of the calibration board in $j$th pose
Line-to-plane constraint
The plane-to-plane constraint
Synthetic data generation
Calibration results with the increasing number of poses
Calibration results with the increasing noise level
Calibration results with the number of poses 30 and the noise level 10$mm$
3D color point cloud of the room
3D color point cloud of the housing estate
RMS error analysis results (unit: pixel)
 Method Minimum Average Maximum Our Method 1.3571 3.6962 7.2579 Zhang's Method 1.8495 4.7702 8.6392 Ying's Method 1.5946 3.7866 7.4648
 Method Minimum Average Maximum Our Method 1.3571 3.6962 7.2579 Zhang's Method 1.8495 4.7702 8.6392 Ying's Method 1.5946 3.7866 7.4648
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