Camera optimal projection model identification and calibration method based on the NGO-BA architecture

Qilin Liu; Qilin Liu; Guangyi Dai; Mingli Dong; Peng Sun; Bixi Yan; Jun Wang; Lianqing Zhu; Lianqing Zhu

doi:10.1364/AO.510124

Applied Optics
Vol. 63,
Issue 3,
pp. 793-803
(2024)
•https://doi.org/10.1364/AO.510124

Camera optimal projection model identification and calibration method based on the NGO-BA architecture

Qilin Liu, Guangyi Dai, Mingli Dong, Peng Sun, Bixi Yan, Jun Wang, and Lianqing Zhu

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Qilin Liu, Guangyi Dai, Mingli Dong, Peng Sun, Bixi Yan, Jun Wang, and Lianqing Zhu, "Camera optimal projection model identification and calibration method based on the NGO-BA architecture," Appl. Opt. 63, 793-803 (2024)

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Abstract

In order to bridge the fundamental commonalities between imaging models of camera lenses with different principles and structures, allowing for an accurate description of imaging characteristics across a wide range of field-of-view (FOV), we have proposed a generic camera calibration method on the basis of the projection model optimization strategy. First, in order to cover the current mainstream projection models, piecewise functions for geometric projection models and a polynomial function for the fitting projection model are designed. Then, the corresponding camera multistation self-calibration bundle adjustment (BA) module is developed for various projection models. Further, by integrating the self-calibration BA algorithm into the northern goshawk optimization architecture, iterative optimization is performed on the projection model adjustment parameters, camera interior parameters, camera exterior parameters, and lens distortion parameters until the target reprojection (RP) error reaches the global minimum. The experimental results indicate that the calibration RP root mean square error in this method is 1/20 pixel for a 68° FOV camera, 1/13 pixel for an 84° FOV camera, 1/9 pixel for a 115° FOV camera, 1/9 pixel for a 135° FOV camera, and 1/6 pixel for a 180° FOV camera. This calibration method offers fast and versatile optimization for various projection model types, encompassing a wide range of projection functions. It can efficiently determine the optimal projection model and all imaging parameters for multiple cameras during the calibration process.

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Supplementary Material (1)

Name	Description
Supplement 1	Full Experimental Results

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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 authors upon reasonable request.

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Groups	Flash Unit	Camera	Lens	Focal Length (mm)	Lens Aperture	FOV (deg)	Pixel Size (mm)	CMOS Size (mm)	Image Resolution (pixel)
1	Viltrox JY-670	Nikon D2X	BOWER	20	F3.5	68	0.006	$23.7 \times 15.7$	$4288 \times 2848$
2	Macro Ring	Sony $α 7 R$ II	VILTROX	24	F1.8	84	0.004521	$36 \times 24$	$7952 \times 5304$
3	Lit	Nikon D810	SAMYANG	14	F2.8	115	0.004878	$36 \times 24$	$7360 \times 4912$
4		Sony $α 7 R$ II	LAOWA	9	F5.6	135	0.004521	$36 \times 24$	$7952 \times 5304$
5		Nikon D810	SAMYANG	12	F2.8	180	0.004878	$36 \times 24$	$7360 \times 4912$

Results	Group 1	Group 2	Group 3	Group 4	Group 5
FOV (deg)	68	84	115	135	180
Nominal $f$ (mm)	20	24	14	9	12
Model number	1	1	1	3	4
$q$ value	−1	−1	−0.8546	0.1324	—
Mean error (mm)	$- 2.09 \times 10^{- 7}$	$- 2.89 \times 10^{- 7}$	$- 3.17 \times 10^{- 7}$	$8.53 \times 10^{- 7}$	$- 9.37 \times 10^{- 11}$
RP RMSE (mm)	$2.97 \times 10^{- 4}$	$3.43 \times 10^{- 4}$	$5.25 \times 10^{- 4}$	$4.78 \times 10^{- 4}$	$8.72 \times 10^{- 4}$
RP RMSE (pixel)	1/20.2327	1/13.1909	1/9.3001	1/9.4747	1/5.597
$f$ (mm)	19.59	24.31	14.63	9.24	—
$x_{p}$ (mm)	−0.25	−0.20	0.05	−0.21	−0.17
$y_{p}$ (mm)	0.07	−0.17	0.20	−0.11	−0.05
$k_{1}$	$1.02 \times 10^{- 3}$	$6.67 \times 10^{- 4}$	$- 1.47 \times 10^{- 3}$	$- 3.34 \times 10^{- 3}$	12.39
$k_{2}$	$1.01 \times 10^{- 6}$	$3.64 \times 10^{- 7}$	$1.99 \times 10^{- 6}$	$1.42 \times 10^{- 5}$	0.34
$k_{3}$	$- 5.60 \times 10^{- 10}$	$- 1.58 \times 10^{- 10}$	$- 1.53 \times 10^{- 9}$	$- 3.23 \times 10^{- 8}$	0.40
$k_{4}$	—	—	—	—	−0.29
$k_{5}$	—	—	—	—	0.10
$p_{1}$	$6.09 \times 10^{- 6}$	$- 1.35 \times 10^{- 5}$	$1.46 \times 10^{- 5}$	$- 2.8 \times 10^{- 6}$	$1.05 \times 10^{- 5}$
$p_{2}$	$- 1.16 \times 10^{- 5}$	$6.38 \times 10^{- 7}$	$- 5.25 \times 10^{- 6}$	$- 5.14 \times 10^{- 6}$	$1.71 \times 10^{- 5}$
$b_{1}$	$9.14 \times 10^{- 5}$	$- 1.15 \times 10^{- 4}$	$- 5.02 \times 10^{- 5}$	$- 9.72 \times 10^{- 5}$	$- 1.53 \times 10^{- 5}$
$b_{2}$	$1.13 \times 10^{- 4}$	$- 2.44 \times 10^{- 5}$	$7.53 \times 10^{- 5}$	$1.21 \times 10^{- 5}$	$1.24 \times 10^{- 5}$

Model	Results	Group 1 (68°)	Group 2 (84°)	Group 3 (115°)	Group 4 (135°)	Group 5 (180°)
Pinhole model	Mean error (mm)	$- 1.96 \times 10^{- 7}$	$1.08 \times 10^{- 6}$	$- 1.46 \times 10^{- 6}$	$1.72 \times 10^{- 7}$	$1.30 \times 10^{- 5}$
	RP RMSE (mm)	$3.48 \times 10^{- 4}$	$6.68 \times 10^{- 4}$	$8.23 \times 10^{- 4}$	$3.97 \times 10^{- 3}$	$6.00 \times 10^{- 3}$
	RP RMSE (pixel)	1/17.2238	1/6.771	1/5.9247	1/1.1389	1/0.8124
NGO-BA optimal model	Mean error (mm)	$- 2.09 \times 10^{- 7}$	$- 2.89 \times 10^{- 7}$	$- 3.17 \times 10^{- 7}$	$8.53 \times 10^{- 7}$	$- 9.37 \times 10^{- 11}$
	RP RMSE (mm)	$2.97 \times 10^{- 4}$	$3.43 \times 10^{- 4}$	$5.25 \times 10^{- 4}$	$4.78 \times 10^{- 4}$	$8.72 \times 10^{- 4}$
	RP RMSE (pixel)	1/20.2327	1/13.1909	1/9.3001	1/9.4747	1/5.597

Groups	Flash Unit	Camera	Lens	Focal Length (mm)	Lens Aperture	FOV (deg)	Pixel Size (mm)	CMOS Size (mm)	Image Resolution (pixel)
1	Viltrox JY-670	Nikon D2X	BOWER	20	F3.5	68	0.006	$23.7 \times 15.7$	$4288 \times 2848$
2	Macro Ring	Sony $α 7 R$ II	VILTROX	24	F1.8	84	0.004521	$36 \times 24$	$7952 \times 5304$
3	Lit	Nikon D810	SAMYANG	14	F2.8	115	0.004878	$36 \times 24$	$7360 \times 4912$
4		Sony $α 7 R$ II	LAOWA	9	F5.6	135	0.004521	$36 \times 24$	$7952 \times 5304$
5		Nikon D810	SAMYANG	12	F2.8	180	0.004878	$36 \times 24$	$7360 \times 4912$

Results	Group 1	Group 2	Group 3	Group 4	Group 5
FOV (deg)	68	84	115	135	180
Nominal $f$ (mm)	20	24	14	9	12
Model number	1	1	1	3	4
$q$ value	−1	−1	−0.8546	0.1324	—
Mean error (mm)	$- 2.09 \times 10^{- 7}$	$- 2.89 \times 10^{- 7}$	$- 3.17 \times 10^{- 7}$	$8.53 \times 10^{- 7}$	$- 9.37 \times 10^{- 11}$
RP RMSE (mm)	$2.97 \times 10^{- 4}$	$3.43 \times 10^{- 4}$	$5.25 \times 10^{- 4}$	$4.78 \times 10^{- 4}$	$8.72 \times 10^{- 4}$
RP RMSE (pixel)	1/20.2327	1/13.1909	1/9.3001	1/9.4747	1/5.597
$f$ (mm)	19.59	24.31	14.63	9.24	—
$x_{p}$ (mm)	−0.25	−0.20	0.05	−0.21	−0.17
$y_{p}$ (mm)	0.07	−0.17	0.20	−0.11	−0.05
$k_{1}$	$1.02 \times 10^{- 3}$	$6.67 \times 10^{- 4}$	$- 1.47 \times 10^{- 3}$	$- 3.34 \times 10^{- 3}$	12.39
$k_{2}$	$1.01 \times 10^{- 6}$	$3.64 \times 10^{- 7}$	$1.99 \times 10^{- 6}$	$1.42 \times 10^{- 5}$	0.34
$k_{3}$	$- 5.60 \times 10^{- 10}$	$- 1.58 \times 10^{- 10}$	$- 1.53 \times 10^{- 9}$	$- 3.23 \times 10^{- 8}$	0.40
$k_{4}$	—	—	—	—	−0.29
$k_{5}$	—	—	—	—	0.10
$p_{1}$	$6.09 \times 10^{- 6}$	$- 1.35 \times 10^{- 5}$	$1.46 \times 10^{- 5}$	$- 2.8 \times 10^{- 6}$	$1.05 \times 10^{- 5}$
$p_{2}$	$- 1.16 \times 10^{- 5}$	$6.38 \times 10^{- 7}$	$- 5.25 \times 10^{- 6}$	$- 5.14 \times 10^{- 6}$	$1.71 \times 10^{- 5}$
$b_{1}$	$9.14 \times 10^{- 5}$	$- 1.15 \times 10^{- 4}$	$- 5.02 \times 10^{- 5}$	$- 9.72 \times 10^{- 5}$	$- 1.53 \times 10^{- 5}$
$b_{2}$	$1.13 \times 10^{- 4}$	$- 2.44 \times 10^{- 5}$	$7.53 \times 10^{- 5}$	$1.21 \times 10^{- 5}$	$1.24 \times 10^{- 5}$

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (7)

Tables (3)

Equations (18)

Applied Optics