Camera Calibration Method for Concentric Circle Eccentricity Error Compensation Iteration

Zhenzhen Huang; Xiaomei Huang; Lianyu Zheng; Kejian Liu; Tao Peng; Zhijiang Zhang

doi:10.3788/AOS202242.1912003

Acta Optica Sinica, Volume. 42, Issue 19, 1912003(2022)

Camera Calibration Method for Concentric Circle Eccentricity Error Compensation Iteration

Zhenzhen Huang¹, Xiaomei Huang², Lianyu Zheng³, Kejian Liu⁴, Tao Peng¹, and Zhijiang Zhang^1、*

Author Affiliations

¹Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200444, China

²Shanghai Institute of Astronautical Systems Engineering, Shanghai 201108, China

³Shanghai Satellite Engineering Research Institute, Shanghai 200240, China

⁴Shanghai Aerospace Electronics Research Institute, Shanghai 201108, China

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Figures & Tables(13)

Fig. 1. Concentric circle eccentricity error model and geometric constraint model diagram. (a) Mathematical model of concentric circle eccentricity error; (b) geometric constraint mathematical model

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Fig. 2. Geometric constraint models of distance $\bar{O C}$ and concentric circle center. (a) Geometric constraint relation between distance $\bar{O C}$ and $θ$ ; (b) geometric constraint relation of coordinates near center of concentric circle projection

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Fig. 3. Pseudo-code of camera iterative calibration algorithm based on concentric circle center eccentricity error

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Fig. 4. Comparison of concentric circle eccentricity error compensation

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Fig. 5. Compensation results of eccentricity error for boundary points after adding noise

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Fig. 6. Concentric circle calibration plate pattern

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Fig. 7. Camera calibration of concentric planar target. (a)-(d) Concentric circle target patterns collected; (e) sub-pixel detection effect of concentric circle edge; (f) ordering of concentric circle feature points

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Fig. 8. Camera calibration of concentric planar target

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Fig. 9. Accuracy verification experiment of binocular system. (a) Binocular experimental measurement system; (b) benchmark ruler measurement; (c) binocular system calibration image

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Fig. 10. Error between measured data and standard data of ruler length

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Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods

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Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods

Parameter		Zhang^［5］	Ours
Focal length	$f_{x}$	1462.4185	1464.8232
Focal length	$f_{y}$	1460.5965	1464.3652
Principal point	$u_{0}$	1235.9562	1239.1695
Principal point	$v_{0}$	1042.6918	1039.2509
Distortion	$k_{1}$	0.01660	0.01285
	$k_{2}$	0.01790	0.00208
	$p_{1}$	-0.00021	-0.00092
	$p_{2}$	0.00042	0.00098
	$k_{3}$	-0.00015	-0.00020
$R M S$		0.09	0.03
Uncertainty	$U_{f_{x}}$	1.0860	0.5230
	$U_{f_{y}}$	1.0860	0.4890
	$U_{u_{0}}$	0.6030	0.1560
	$U_{v_{0}}$	0.7820	0.1860
	$U_{k_{1}}$	0.0045	0.0023
	$U_{k_{2}}$	0.0074	0.0030
	$U_{p_{1}}$	0.0013	0.0010
	$U_{p_{2}}$	0.0011	0.0009
	$U_{k_{3}}$	0.0065	0.0060

Table 2. Correction results of binocular camera calibration parameters

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Table 2. Correction results of binocular camera calibration parameters

Parameter	Before compensation		After compensation
Parameter	$L e f t c a m e r a$	$R i g h t c a m e r a$	$L e f t c a m e r a$	$L e f t c a m e r a$
$f_{x}$	1462.128	1459.704	1463.001	1459.795
$f_{y}$	1461.765	1459.610	1462.733	1460.001
$u_{0}$	1238.685	1232.031	1237.231	1232.050
$v_{0}$	1040.992	1047.504	1035.328	1047.042
$k_{1}$	0.01134	0.00890	0.00980	0.00330
$k_{2}$	-0.00082	0.01330	0.01200	0.04180
$p_{1}$	0.000000263	-0.000630000	-0.001000000	-0.000620000
$p_{2}$	0.000900	0.001764	0.000400	0.002200
$k_{3}$	-0.01510	-0.02700	-0.03300	-0.06400
RMS	0.1256	0.1347	0.0321	0.0286
R	［0.001843 0.942010 -0.001980］		［0.005220 0.939200 -0.003200］
$T$	［-460.1710 -0.7764 228.6040］		［-459.2620 -0.7932 227.5350］
RMS	0.1532		0.0426

Table 3. Statistical results of error between measurement data and standard length of base ruler
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Table 3. Statistical results of error between measurement data and standard length of base ruler
Method Zhang's method Yang's method Proposed method
Mean 0.1172 0.0828 0.0239
RMS 0.1240 0.0779 0.0268
Maximum 0.1956 0.1360 0.0450

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Zhenzhen Huang, Xiaomei Huang, Lianyu Zheng, Kejian Liu, Tao Peng, Zhijiang Zhang. Camera Calibration Method for Concentric Circle Eccentricity Error Compensation Iteration[J]. Acta Optica Sinica, 2022, 42(19): 1912003

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Mar. 3, 2022

Accepted: Apr. 15, 2022

Published Online: Oct. 18, 2022

The Author Email: Zhijiang Zhang (zjzhang@staff.shu.edu.cn)

DOI:10.3788/AOS202242.1912003

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods

Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods

Table 2. Correction results of binocular camera calibration parameters

Table 2. Correction results of binocular camera calibration parameters

Table 3. Statistical results of error between measurement data and standard length of base ruler

Table 3. Statistical results of error between measurement data and standard length of base ruler