Simple and precise calibration of the line-structured light vision system using a planar target

Zimiao Zhang; Zimiao Zhang; Hao Zhang; Hao Zhang; Yanan Wu; Fumin Zhang; Fumin Zhang

doi:10.1364/JOSAA.485907

Journal of the Optical Society of America A
Vol. 40,
Issue 7,
pp. 1397-1408
(2023)
•https://doi.org/10.1364/JOSAA.485907

Simple and precise calibration of the line-structured light vision system using a planar target

Zimiao Zhang, Hao Zhang, Yanan Wu, and Fumin Zhang

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Zimiao Zhang, Hao Zhang, Yanan Wu, and Fumin Zhang, "Simple and precise calibration of the line-structured light vision system using a planar target," J. Opt. Soc. Am. A 40, 1397-1408 (2023)

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Abstract

When calibrating a line-structured light vision system using a planar target, noise easily affects the solution of the coordinates of light stripe points at the camera coordinate frame. Therefore, the planar target must be placed in the measurement space many times to capture more target images for improving calibration stability and achieving relatively high calibration accuracy. This complicates the calibration process. This paper proposes a calibration method considering the measurement baselines of a planar target. The planar target is placed only two times, and two target images are captured correspondingly. A three-point subset is made up of the two calibration points that form the measurement baseline with the longest 2D projection and any other calibration point. In this way, it is less affected by noise when using the three-point subsets to establish the equations. Then, we use the lengths of the measurement baselines provided by all three-point subsets and their 2D projections to solve the coordinates of light stripe points at the camera coordinate frame more accurately to calibrate the line-structured light vision system. Both the simulation and actual experiment results demonstrate the feasibility of our method. Based on our calibration method, the RMS error is 0.035 mm for length measurement and 0.054 mm for height measurement. Compared with other existing methods, our method needs only two target images. It can also achieve more accurate calibration results than the other methods. In addition, our calibration method increases the applicability of the line-structured light measurement method by reducing the number of target swings.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding author upon reasonable request.

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	Traditional Method Image 1			Image 2			Image 3
$R$	0.9998	−0.0028	0.0180	0.9998	0.0005	0.0190	0.9998	0.0079	0.0157
	0.0032	0.9998	−0.0212	−0.0001	0.9998	−0.0200	−0.0059	0.9923	−0.1234
	−0.0179	0.0212	0.9996	−0.0190	0.0200	0.9996	−0.0166	0.1233	0.9922
$t$	−44.907	−35.853	295.792	−47.524	−34.524	276.189	−45.156	−25.005	285.071
	Image 4			Image 5
$R$	0.9976	0.0080	−0.0692	0.9999	−0.0025	0.0170
	−0.0093	0.9998	−0.0184	0.0009	0.9958	0.0911
	0.0690	0.0190	0.9974	−0.0172	−0.0911	0.9957
$t$	−45.994	−26.563	274.723	−47.481	−35.291	281.946
	Our Method Image 1			Image 2
$R$	0.9998	−0.0028	0.0177	0.9998	0.0004	0.0192
	0.0032	0.9998	−0.0208	−0.0001	0.9998	−0.0200
	−0.0177	0.0209	0.9996	−0.0192	0.0200	0.9996
$t$	−44.910	−35.847	295.774	−47.523	−34.520	276.194

Calibration Method	Light Plane Equation
Traditional method $+$ 2	$2.3086 X_{c} + 0.0130 Y_{c} - Z_{c} + 352.9483 = 0$
Traditional method $+$ 5	$2.3073 X_{c} + 0.0096 Y_{c} - Z_{c} + 353.0165 = 0$
Our method $+$ 2	$2.3137 X_{c} + 0.0131 Y_{c} - Z_{c} + 352.9718 = 0$

Position	Traditional Method $+$ 2	Traditional Method $+$ 5	Our Method $+$ 2
1	$Q_{1}$ (−9.95, −11.40, 292.90) $Q_{2}$ (−9.51, 8.44, 294.43)	$Q_{1}$ (−9.88, −11.41, 293.14) $Q_{2}$ (−9.66, 8.51, 294.02)	$Q_{1}$ (−9.95, −11.40, 292.90) $Q_{2}$ (−9.58, 8.52, 294.21)
2	$Q_{1}$ (−10.11, −3.28, 292.55) $Q_{2}$ (−9.51, 16.52, 294.52)	$Q_{1}$ (−10.26, −3.19, 292.14) $Q_{2}$ (−9.36, 16.63, 294.99)	$Q_{1}$ (−10.26, −3.11, 292.12) $Q_{2}$ (−9.36, 16.63, 294.96)
3	$Q_{1}$ (−10.03, −11.64, 292.67) $Q_{2}$ (−9.51, 8.19, 294.43)	$Q_{1}$ (−9.88, −11.74, 293.14) $Q_{2}$ (−9.66, 8.18, 294.02)	$Q_{1}$ (−9.95, −11.73, 292.89) $Q_{2}$ (−9.58, 8.18, 294.21)
4	$Q_{1}$ (−9.88, −13.98, 293.09) $Q_{2}$ (−9.66, 5.93, 293.96)	$Q_{1}$ (−9.95, −13.97, 292.89) $Q_{2}$ (−9.58, 5.94, 294.21)	$Q_{1}$ (−10.33, −13.75, 291.78) $Q_{2}$ (−9.35, 5.95, 294.85)
5	$Q_{1}$ (−9.96, −3.20, 292.99) $Q_{2}$ (−9.43, 16.62, 294.75)	$Q_{1}$ (−9.88, −3.20, 293.21) $Q_{2}$ (−9.51, 16.69, 294.54)	$Q_{1}$ (−9.96, −3.20, 292.99) $Q_{2}$ (−9.51, 16.69, 294.54)
6	$Q_{1}$ (−10.33, −5.25, 291.88) $Q_{2}$ (−8.66, −14.14, 296.95)	$Q_{1}$ (−10.33, −5.25, 291.88) $Q_{2}$ (−8.74, 14.04, 296.73)	$Q_{1}$ (−10.33, −5.25, 291.88) $Q_{2}$ (−8.66, 14.05, 296.95)
7	$Q_{1}$ (−9.74, 10.83, 293.81) $Q_{2}$ (−9.59, 30.76, 294.48)	$Q_{1}$ (−10.11, 11.04, 292.72) $Q_{2}$ (−9.36, 30.83, 295.14)	$Q_{1}$ (−10.11, 11.04, 292.72) $Q_{2}$ (−9.36,30.91, 295.14)
8	$Q_{1}$ (−10.19, 10.04, 292.49) $Q_{2}$ (−9.21, 29.70, 295.57)	$Q_{1}$ (−9.96, 9.90, 293.14) $Q_{2}$ (−9.36, 29.74, 295.12)	$Q_{1}$ (−10.11, 9.96, 292.71) $Q_{2}$ (−9.21, 29.70, 295.57)
9	$Q_{1}$ (−10.11, −2.53, 292.57) $Q_{2}$ (−9.51, 17.27, 294.54)	$Q_{1}$ (−9.88, −2.71, 293.22) $Q_{2}$ (−9.51, 17.19, 294.54)	$Q_{1}$ (−10.03, −2.62, 292.78) $Q_{2}$ (−9.51, 17.27, 294.54)
10	$Q_{1}$ (−10.18, 0.53, 292.38) $Q_{2}$ (−9.36, 20.22, 295.02)	$Q_{1}$ (−10.18, 0.44, 292.38) $Q_{2}$ (−9.36, 20.30, 295.02)	$Q_{1}$ (−10.18, 0.53, 292.38) $Q_{2}$ (−9.36, 20.30, 295.02)

	Traditional Method $+$ 2			Traditional Method $+$ 5			Our Method $+$ 2
Position	$l s$	$l m$	$Δ l$	$l s$	$l m$	$Δ l$	$l s$	$l m$	$Δ l$
1	20.000	19.905	−0.095	20.000	19.942	−0.058	20.000	19.964	−0.036
2	20.000	19.907	−0.093	20.000	20.048	0.048	20.000	19.964	−0.036
3	20.000	19.914	−0.086	20.000	19.941	−0.059	20.000	19.963	−0.037
4	20.000	19.930	−0.070	20.000	19.953	−0.047	20.000	19.961	−0.039
5	20.000	19.905	−0.095	20.000	19.940	−0.060	20.000	19.955	−0.045
6	20.000	20.111	0.111	20.000	19.959	−0.041	20.000	20.030	0.030
7	20.000	19.940	−0.060	20.000	19.950	−0.050	20.000	20.033	0.033
8	20.000	19.928	−0.072	20.000	19.955	−0.045	20.000	19.967	−0.033
9	20.000	19.915	−0.085	20.000	19.943	−0.057	20.000	19.977	−0.023
10	20.000	19.887	−0.113	20.000	20.052	0.052	20.000	19.970	−0.030
RMS error			0.090			0.052			0.035

	Traditional Method $+$ 2			Traditional Method $+$ 5			Our Method $+$ 2
Position	$h s$	$h m$	$Δ h$	$h s$	$h m$	$Δ h$	$h s$	$h m$	$Δ h$
1	9.000	8.929	−0.071	9.000	8.947	−0.053	9.000	8.953	−0.047
2	9.000	9.061	0.061	9.000	9.052	0.052	9.000	9.050	0.050
3	9.000	9.079	0.079	9.000	9.068	0.068	9.000	9.052	0.052
4	9.000	9.073	0.073	9.000	9.059	0.059	9.000	9.053	0.053
5	9.000	9.077	0.077	9.000	9.067	0.067	9.000	9.058	0.058
6	9.000	9.064	0.064	9.000	9.062	0.062	9.000	9.054	0.054
7	9.000	9.084	0.084	9.000	9.070	0.070	9.000	9.056	0.056
8	9.000	9.080	0.080	9.000	9.068	0.068	9.000	9.059	0.059
9	9.000	9.078	0.078	9.000	9.058	0.058	9.000	9.053	0.053
10	9.000	9.084	0.084	9.000	9.079	0.079	9.000	9.062	0.062
RMS error			0.075			0.064			0.054

Abstract

Data availability

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Figures (18)

Tables (5)

Equations (15)

Journal of the Optical Society of America A