High-Precision Calibration Based on Multi-Camera System

Fig. 3. Axis distribution of pixel coordinate system of calibration board. (a) Original drawing; (b) extracting the center of the circle; (c) center sorting

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Fig. 4. Correction of perspective deviation. (a) Before correction; (b) after correction

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Fig. 5. Special calibration board

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Fig. 6. Physical drawing of rear cover laminating module

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Fig. 7. External parameter display after optimization

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Fig. 8. Re-projection error comparison. (a) Schematic diagram of reprojection error of DLT method and proposed method; (b) re-projection error difference curve of DLT method and proposed method

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Table 1. Pixels and mechanical coordinates for calibrating the center of the plate

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Table 1. Pixels and mechanical coordinates for calibrating the center of the plate

Serial number	Camera 1		Camera 2
Serial number	Pixel coordinate /pixel	Mechanical coordinate /mm	Pixel coordinate /pixel	Mechanical coordinate /mm
1	（111.871，-93.072）	（0，0）	（-186.984，-128.707）	（220，0）
2	（258.103，-93.072）	（10，0）	（-60.295，-201.856）	（230，0）
3	（111.873，-209.335）	（0，10）	（-245.119，-229.391）	（220，10）
4	（258.105，-209.335）	（10，10）	（-118.426，-302.548）	（230，10）

Table 2. Comparison of parameters before and after Levenberg-Marquardt algorithm optimization
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Table 2. Comparison of parameters before and after Levenberg-Marquardt algorithm optimization
Internal reference $f_{x}$ $f_{y}$ $γ$ $u_{0}$ $v_{0}$ $a_{1}$ $a_{2}$
Reference initial value 2971.07 2971.07 1296.00 972.00 0 0
After optimization 2976.70 2970.21 0.0005 1390.45 988.32 -0.1572 0.6562

Table 3. Comparison of average re-projection error of camera calibration
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Table 3. Comparison of average re-projection error of camera calibration
Calibration method Re-projection error /pixel
Traditional calibration method 0.02591
Proposed method 0.00866

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Yifan Xiao, Wei Hu. High-Precision Calibration Based on Multi-Camera System[J]. Laser & Optoelectronics Progress, 2023, 60(20): 2015003

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Paper Information

Category: Machine Vision

Received: Oct. 17, 2022

Accepted: Dec. 12, 2022

Published Online: Oct. 13, 2023

The Author Email: Yifan Xiao (897686694@qq.com)

DOI:10.3788/LOP222787

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Pixels and mechanical coordinates for calibrating the center of the plate

Table 1. Pixels and mechanical coordinates for calibrating the center of the plate

Table 2. Comparison of parameters before and after Levenberg-Marquardt algorithm optimization

Table 2. Comparison of parameters before and after Levenberg-Marquardt algorithm optimization

Table 3. Comparison of average re-projection error of camera calibration

Table 3. Comparison of average re-projection error of camera calibration