Accurate calibration for fringe projection profilometry based on an improved subpixel mapping with local gray distribution

Bin Liu; Bin Liu; Xinxin He; Chunliu Wang; Sen Wang; Guanhao Wu; Guanhao Wu

doi:10.1364/JOSAA.501765

Journal of the Optical Society of America A
Vol. 40,
Issue 12,
pp. 2164-2176
(2023)
•https://doi.org/10.1364/JOSAA.501765

Accurate calibration for fringe projection profilometry based on an improved subpixel mapping with local gray distribution

Bin Liu, Xinxin He, Chunliu Wang, Sen Wang, and Guanhao Wu

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Bin Liu, Xinxin He, Chunliu Wang, Sen Wang, and Guanhao Wu, "Accurate calibration for fringe projection profilometry based on an improved subpixel mapping with local gray distribution," J. Opt. Soc. Am. A 40, 2164-2176 (2023)

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Abstract

Fringe projection profilometry is an efficient and accurate technique for three-dimensional (3D) measurement to calibrate a camera and projector setup. The feature centers of circles on a calibration board are extracted on the camera image plane and mapped to the projector image plane during the calibration procedure. The accuracy of the mapping between camera pixels and projector pixels is crucial to the calibration accuracy, which directly affects the measurement precision of the system. In this paper, we investigate an improved subpixel mapping with local gray distribution from the camera to the projector. The mapped pixels and their gray values are regarded as a set of 3D grayscale space points. The subpixel coordinates of the feature centers on the projector image plane are obtained by directly processing the 3D points. The entire procedure retains the subpixel precision. Calibration experiments were designed to verify the feasibility of our calibration method, which was compared to three existing methods. The reprojection errors and object-space errors were used to evaluate the calibration accuracy of the methods. Additionally, measurement experiments of displacement and in-plane distance were employed to verify the calibration results of the methods. Compared to the three existing methods, we believe our method can improve the calibration accuracy for fringe projection profilometry.

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Data availability

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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Methods	Conventional Method	Li et al.’s Method	Huang et al.’s Method	Deng et al.’s Method	Our Proposed Method
X axis	[−0.894, 2.990]	[−0.509, 1.163]	[−0.573, 0.612]	[−0.530 1.413]	[−0.264, 0.330]
Y axis	[−0.704, 0.623]	[−0.356, 0.615]	[−0.386, 0.462]	[−0.310 0.332]	[−0.237, 0.251]
X-std	0.315	0.168	0.110	0.148	0.075
Y-std	0.268	0.102	0.095	0.081	0.066
Mean error	0.368	0.159	0.121	0.125	0.087

		Conventional Method		Li et al.’s Method		Huang et al.’s Method		Deng et al.’s Method		Our Proposed Method
Planes	$d_{r e a l}$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$
5–4	4	3.933	0.067	3.942	0.058	3.937	0.063	3.941	0.059	3.952	0.048
4–3	4	3.938	0.062	3.934	0.067	3.945	0.055	3.933	0.067	3.943	0.057
3–2	4	3.932	0.068	3.939	0.061	3.937	0.063	3.940	0.060	3.941	0.059
2–1	4	3.949	0.051	3.951	0.049	3.952	0.048	3.951	0.049	3.955	0.045
${s t d}_{Δ d}$		0.0078		0.0075		0.0073		0.0074		0.0068

	Conventional Method		Li et al.’s Method		Huang et al.’s Method		Deng et al.’s Method		Our Proposed Method
Poses	$X$ (mm)	$Y$ (mm)	$X$ (mm)	$Y$ (mm)	$X$ (mm)	$Y$ (mm)	$X$ (mm)	$Y$ (mm)	$X$ (mm)	$Y$ (mm)
1	14.880	14.847	14.895	14.936	14.903	14.931	14.943	14.955	14.955	14.958
2	14.846	14.898	14.907	14.875	14.963	14.881	14.897	14.907	14.907	14.893
3	14.915	14.944	14.935	14.925	14.943	14.932	14.962	14.915	14.997	14.960
Mean error	0.120	0.104	0.088	0.088	0.064	0.085	0.066	0.074	0.047	0.063

Methods	Conventional Method	Li et al.’s Method	Huang et al.’s Method	Deng et al.’s Method	Our Proposed Method
X axis	[−0.894, 2.990]	[−0.509, 1.163]	[−0.573, 0.612]	[−0.530 1.413]	[−0.264, 0.330]
Y axis	[−0.704, 0.623]	[−0.356, 0.615]	[−0.386, 0.462]	[−0.310 0.332]	[−0.237, 0.251]
X-std	0.315	0.168	0.110	0.148	0.075
Y-std	0.268	0.102	0.095	0.081	0.066
Mean error	0.368	0.159	0.121	0.125	0.087

		Conventional Method		Li et al.’s Method		Huang et al.’s Method		Deng et al.’s Method		Our Proposed Method
Planes	$d_{r e a l}$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$	$d$	$Δ d$
5–4	4	3.933	0.067	3.942	0.058	3.937	0.063	3.941	0.059	3.952	0.048
4–3	4	3.938	0.062	3.934	0.067	3.945	0.055	3.933	0.067	3.943	0.057
3–2	4	3.932	0.068	3.939	0.061	3.937	0.063	3.940	0.060	3.941	0.059
2–1	4	3.949	0.051	3.951	0.049	3.952	0.048	3.951	0.049	3.955	0.045
${s t d}_{Δ d}$		0.0078		0.0075		0.0073		0.0074		0.0068

Abstract

Data availability

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Tables (4)

Equations (19)

Journal of the Optical Society of America A