High-precision binocular camera calibration method based on a 3D calibration object

Xiaowen Zhang; Tiegang Lv; Tiegang Lv; Wang Dan; Wang Dan; Zhang Minghao; Zhang Minghao

doi:10.1364/AO.517411

Applied Optics
Vol. 63,
Issue 10,
pp. 2667-2682
(2024)
•https://doi.org/10.1364/AO.517411

High-precision binocular camera calibration method based on a 3D calibration object

Xiaowen Zhang, Tiegang Lv, Wang Dan, and Zhang Minghao

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Xiaowen Zhang, Tiegang Lv, Wang Dan, and Zhang Minghao, "High-precision binocular camera calibration method based on a 3D calibration object," Appl. Opt. 63, 2667-2682 (2024)

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Abstract

A high-precision binocular camera calibration method is proposed to address the issues of poor calibration accuracy and large calibration errors in current practical applications. This method uses a triangular stereo sphere as the calibration object and employs steps, such as ellipse fitting, Cholesky decomposition, homography matrix solution, and nonlinear optimization, to compute the intrinsic and extrinsic parameters, distortion parameters, and relative pose of the binocular camera. Moreover, this method simplifies the correspondences between primitives, enabling simultaneous calibration of multiple viewpoint cameras. This method is also suitable for both binocular cameras consisting of two different structured monocular cameras and those composed of two image sensors within the same structure. Experimental results showed that this method outperforms traditional algorithms in terms of binocular camera calibration accuracy, calibration errors between left and right cameras, and robustness, resulting in a significant improvement in overall algorithm performance.

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Supplementary Material (1)

Name	Description
Code 1	Experimental code

Data availability

Data underlying the results presented in this paper are available as we show in Code 1, Ref. [27].

27. X. W. Zhang, “High-precision binocular camera calibration method based on a 3D calibration object,” figshare, 2024, https://doi.org/10.6084/m9.figshare.25289152.

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Equations (40)

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Method		$K$	$R$	$t$	Distortion Coefficient	Time
SC	$L$	$[\begin{matrix} 1273.64 & 0 & 573.54 \\ 0 & 1279.19 & 482.43 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.031 & - 0.975 & - 0.009 \\ 0.932 & - 0.021 & 0.201 \\ - 0.198 & - 0.004 & 0.984 \end{matrix}]$	$[\begin{matrix} - 53.748 \\ 72.752 \\ 406.472 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.094 & 0.63 & - 0.036 \\ - 0.079 & - 4.872 \end{matrix}] \end{array}$	2.5 s
	$R$	$[\begin{matrix} 1264.78 & 0 & 547.61 \\ 0 & 1250.72 & 446.72 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.030 & - 0.997 & - 0.009 \\ 0.947 & - 0.025 & 0.203 \\ - 0.202 & - 0.006 & 0.963 \end{matrix}]$	$[\begin{matrix} - 50.852 \\ 74.276 \\ 412.963 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.091 & 0.51 & - 0.033 \\ - 0.068 & - 3.953 \end{matrix}] \end{array}$
Zhang	$L$	$[\begin{matrix} 1254.26 & 0 & 543.76 \\ 0 & 1277.93 & 433.23 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.026 & - 0.992 & - 0.009 \\ 0.951 & - 0.022 & 0.201 \\ - 0.202 & - 0.005 & 0.969 \end{matrix}]$	$[\begin{matrix} - 51.052 \\ 71.136 \\ 408.853 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.075 & 0.473 & - 0.031 \\ - 0.064 & - 3.681 \end{matrix}] \end{array}$	5.7 s
	$R$	$[\begin{matrix} 1246.34 & 0 & 528.89 \\ 0 & 1260.59 & 428.40 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.024 & - 0.991 & - 0.009 \\ 0.985 & - 0.024 & 0.201 \\ - 0.201 & - 0.005 & 0.958 \end{matrix}]$	$[\begin{matrix} - 51.078 \\ 71.058 \\ 411.857 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.068 & 0.45 & - 0.029 \\ - 0.065 & - 3.541 \end{matrix}] \end{array}$
Ours	$L$	$[\begin{matrix} 1252.84 & 0 & 523.65 \\ 0 & 1254.79 & 415.64 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.021 & - 0.999 & - 0.009 \\ 0.973 & - 0.023 & 0.201 \\ - 0.201 & - 0.005 & 0.976 \end{matrix}]$	$[\begin{matrix} - 51.013 \\ 70.531 \\ 408.954 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.06 & 0.415 & - 0.024 \\ - 0.056 & - 2.895 \end{matrix}] \end{array}$	3 s
	$R$	$[\begin{matrix} 1248.61 & 0 & 519.16 \\ 0 & 1251.43 & 417.78 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.021 & - 0.998 & - 0.009 \\ 0.983 & - 0.024 & 0.202 \\ - 0.202 & - 0.005 & 0.975 \end{matrix}]$	$[\begin{matrix} - 50.642 \\ 70.357 \\ 409.021 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.052 & 0.315 & - 0.019 \\ - 0.046 & - 2.749 \end{matrix}] \end{array}$

Method		True Value (mm)	Measured Data (mm)	RE(%)
Zhang	$L$	20.00	19.95	0.25
Zhang	$R$	20.00	19.96	0.2
SC	$L$	20.00	19.93	0.35
SC	$R$	20.00	19.91	0.45
Ours	$L$	20.00	19.98	0.1
Ours	$R$	20.00	19.97	0.15

		Zhang		Ours		SC
		Max–min	75%–25%	Max–min	75%–25%	Max–min	75%–25%
Left camera	$f_{x}$	11.26	6.82	9.65	4.14	16.73	7.37
	$f_{y}$	13.23	9.01	7.06	4.47	23.61	14.31
	$u_{0}$	12.45	7.27	9.13	5.02	15.74	10.05
	$v_{0}$	15.26	9.43	10.08	5.28	19.04	12.72
Right camera	$f_{x}$	15.82	6.38	7.49	4.37	19.75	8.43
	$f_{y}$	13.15	7.72	6.08	4.19	20.36	9.67
	$u_{0}$	14.39	8.11	9.23	6.28	18.21	11.29
	$v_{0}$	16.43	9.84	11.53	7.26	21.46	14.35

Method		$K$	$R$	$t$	Distortion Coefficient	Time
SC	$L$	$[\begin{matrix} 1273.64 & 0 & 573.54 \\ 0 & 1279.19 & 482.43 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.031 & - 0.975 & - 0.009 \\ 0.932 & - 0.021 & 0.201 \\ - 0.198 & - 0.004 & 0.984 \end{matrix}]$	$[\begin{matrix} - 53.748 \\ 72.752 \\ 406.472 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.094 & 0.63 & - 0.036 \\ - 0.079 & - 4.872 \end{matrix}] \end{array}$	2.5 s
	$R$	$[\begin{matrix} 1264.78 & 0 & 547.61 \\ 0 & 1250.72 & 446.72 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.030 & - 0.997 & - 0.009 \\ 0.947 & - 0.025 & 0.203 \\ - 0.202 & - 0.006 & 0.963 \end{matrix}]$	$[\begin{matrix} - 50.852 \\ 74.276 \\ 412.963 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.091 & 0.51 & - 0.033 \\ - 0.068 & - 3.953 \end{matrix}] \end{array}$
Zhang	$L$	$[\begin{matrix} 1254.26 & 0 & 543.76 \\ 0 & 1277.93 & 433.23 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.026 & - 0.992 & - 0.009 \\ 0.951 & - 0.022 & 0.201 \\ - 0.202 & - 0.005 & 0.969 \end{matrix}]$	$[\begin{matrix} - 51.052 \\ 71.136 \\ 408.853 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.075 & 0.473 & - 0.031 \\ - 0.064 & - 3.681 \end{matrix}] \end{array}$	5.7 s
	$R$	$[\begin{matrix} 1246.34 & 0 & 528.89 \\ 0 & 1260.59 & 428.40 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.024 & - 0.991 & - 0.009 \\ 0.985 & - 0.024 & 0.201 \\ - 0.201 & - 0.005 & 0.958 \end{matrix}]$	$[\begin{matrix} - 51.078 \\ 71.058 \\ 411.857 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.068 & 0.45 & - 0.029 \\ - 0.065 & - 3.541 \end{matrix}] \end{array}$
Ours	$L$	$[\begin{matrix} 1252.84 & 0 & 523.65 \\ 0 & 1254.79 & 415.64 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.021 & - 0.999 & - 0.009 \\ 0.973 & - 0.023 & 0.201 \\ - 0.201 & - 0.005 & 0.976 \end{matrix}]$	$[\begin{matrix} - 51.013 \\ 70.531 \\ 408.954 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.06 & 0.415 & - 0.024 \\ - 0.056 & - 2.895 \end{matrix}] \end{array}$	3 s
	$R$	$[\begin{matrix} 1248.61 & 0 & 519.16 \\ 0 & 1251.43 & 417.78 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} - 0.021 & - 0.998 & - 0.009 \\ 0.983 & - 0.024 & 0.202 \\ - 0.202 & - 0.005 & 0.975 \end{matrix}]$	$[\begin{matrix} - 50.642 \\ 70.357 \\ 409.021 \end{matrix}]$	$\begin{array}{l} [\begin{matrix} 0.052 & 0.315 & - 0.019 \\ - 0.046 & - 2.749 \end{matrix}] \end{array}$

Method		True Value (mm)	Measured Data (mm)	RE(%)
Zhang	$L$	20.00	19.95	0.25
Zhang	$R$	20.00	19.96	0.2
SC	$L$	20.00	19.93	0.35
SC	$R$	20.00	19.91	0.45
Ours	$L$	20.00	19.98	0.1
Ours	$R$	20.00	19.97	0.15

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (18)

Tables (3)

Equations (40)

Applied Optics