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

Yi An; Bo Li; Lei Wang; Chao Zhang; Xiaoli Zhou

doi:10.3934/jimo.2019119

Article Contents

2021, Volume 17, Issue 1: 427-445. Doi: 10.3934/jimo.2019119

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

Received: February 28, 2019

Revised: March 31, 2019

Early access: September 2019

Published: January 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 53C38, 68U05; Secondary: 49K35.

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Figure 1. Calibration board and 3D color laser ranging system

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Figure 2. Pinhole camera model

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Figure 3. Point cloud of the calibration board and its line point clouds

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Figure 4. Calibration images

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Figure 5. Normal vector $ \bar{\mathit{\boldsymbol{n}}}_{j} $ of the calibration board in $ j $th pose

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Figure 6. Line-to-plane constraint

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Figure 7. The plane-to-plane constraint

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Figure 8. Synthetic data generation

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Figure 9. Calibration results with the increasing number of poses

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Figure 10. Calibration results with the increasing noise level

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Figure 11. Calibration results with the number of poses 30 and the noise level 10$ mm $

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Figure 12. 3D color point cloud of the room

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Figure 13. 3D color point cloud of the housing estate

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Table 1. 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

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