Multi-Camera Calibration of One-Dimensional Calibration Objects Based on Normalization Algorithm

Yanming Quan; Zhenbo Qin; Weishi Li; Rui Zhang

doi:10.3788/AOS201939.0415001

Acta Optica Sinica, Volume. 39, Issue 4, 0415001(2019)

Multi-Camera Calibration of One-Dimensional Calibration Objects Based on Normalization Algorithm

Yanming Quan^1、*, Zhenbo Qin^1,2, Weishi Li², and Rui Zhang²

¹ School of Mechanical & Automotive Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China;

² Intelligent Measurement Team, Guangdong Academy, Hefei University of Technology, Foshan, Guangdong 528137, China

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Figures & Tables(10)

Fig. 1. Schematic of pinhole imaging

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Fig. 2. Schematic of simulation

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Fig. 3. Intrinsic parameters from original and normalized data. (a) Relative error of αk; (b) relative error of βk; (c) relative error of uk; (d) relative error of vk

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Fig. 4. Extrinsic parameters from original and normalized data. (a) Maximum relative error of Euler angle; (b) relative error of translation vector

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Fig. 5. Effect of normalization on condition number

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Fig. 6. Calibration stick

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Fig. 7. Images sampled by camera set. (a) Calibration stick; (b) calibration board

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Table 1. Intrinsic parameters of three simulation cameras
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Table 1. Intrinsic parameters of three simulation cameras
Camera α_k β_k u_k v_k
0 765 762 385 293
1 763 768 410 305
2 760 755 403 307

Table 2. Results of calibration

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Table 2. Results of calibration

Method	Camera	α_k	β_k	u_k	v_k	s_k	Condition number
Proposed method	Left	4880.35	4833.77	1018.66	1009.89	-2.11	4.71×10⁷
	Right	4868.55	4823.98	1023.67	1001.17	2.00
Method in Ref. [10]	Left	4591.12	4675.97	801.73	1194.25	7.18	2.93×10¹⁹
	Right	4565.62	4658.49	979.90	1185.77	2.72
Two-dimensional (2D) method	Left	4640.62	4643.98	984.20	1003.20	0
	Right	4628.86	4630.32	977.77	1042.68	0

Table 3. Results of length measurement
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Table 3. Results of length measurement
Method Difference /mm Standard deviation /mm
AB BC CD AB BC CD
Proposed method 0.19 -0.10 -0.02 0.40 0.72 0.53
Method in Ref. [10] 0.24 0.22 0.19 1.08 2.62 5.33
2D method 0.21 0.03 -0.18 0.66 1.10 1.33

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Yanming Quan, Zhenbo Qin, Weishi Li, Rui Zhang. Multi-Camera Calibration of One-Dimensional Calibration Objects Based on Normalization Algorithm[J]. Acta Optica Sinica, 2019, 39(4): 0415001

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