High-precision camera calibration method considering projected circular edge blur and eccentricity error

Locate method	Type of noise
	No noise		White noise( ${\sigma ^{\rm{2}}}$=0.002)		White noise( ${\sigma ^{\rm{2}}}$=0.004)
	Mean error/pixel	Variance/pixel²	Mean error/pixel	Variance/pixel²	Mean error/pixel	Variance/pixel²
Gray moment	0.0666	0.0172	0.0807	0.0232	0.1218	0.1979
Fit method	0.0727	0.0363	0.0821	0.0443	0.3277	0.1843
Zernike moment	0.0501	0.0198	0.0867	0.0307	0.1064	0.2512
Proposed method	0.0469	0.0130	0.0564	0.0312	0.0687	0.0866

Table 2. Center location accuracy of simulative image

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Table 2. Center location accuracy of simulative image

Locate method	Type of noise
	No noise		White noise( ${\sigma ^{\rm{2}}}$=0.002)		White noise( ${\sigma ^{\rm{2}}}$=0.004)
	Fitting center	Error/pixel	Fitting center	Error/pixel	Fitting center	Error/pixel
Gray moment	(256.034,256.025)	0.0422	(256.024,255.951)	0.0546	(256.031,256.056)	0.0640
Fit method	(255.994,256.041)	0.0417	(255.967,256.165)	0.1683	(256.226,256.186)	0.2926
Zernike moment	(255.964,256.022)	0.0414	(255.959,256.014)	0.0430	(255.95,256.012)	0.0511
Proposed method	(256.027,255.991)	0.0289	(256.025,255.979)	0.0326	(256.031,255.986)	0.0339

Table 3. Camera internal parameters and binocular posture relationship

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Table 3. Camera internal parameters and binocular posture relationship

Left camera’s intrinsics	Right camera’s intrinsics	Extrinsics
${f_x} = {\rm{3051}}{\rm{.903\;4}}$${f_y} = {\rm{3051}}{\rm{.349\;0}}$${u_0} = {\rm{836}}{\rm{.169\;0}}$${v_0} = {\rm{910}}{\rm{.385\;3}}$${k_1} = - {\rm{0}}{\rm{.176\;9}}$${k_2} = {\rm{0}}{\rm{.189\;4}}$$s = 0$	${f_x} = {\rm{3\;085}}{\rm{.834\;1}}$${f_y} = {\rm{3\;087}}{\rm{.418\;6}}$${u_0} = {\rm{812}}{\rm{.227\;4}}$${v_0} = {\rm{859}}{\rm{.930\;4}}$${k_1} = - {\rm{0}}{\rm{.182\;0}}$${k_2} = {\rm{0}}{\rm{.375\;9}}$$s = 0$	$ $\begin{matrix} R = [\begin{matrix} 0.965 3 & 0.006 2 & - 0.261 1 \\ - 0.040 2 & 0.991 3 & - 0.125 1 \\ 0.258 1 & 0.131 2 & 0.957 2 \end{matrix}] \\ T = [\begin{matrix} - 363 .001 5 & 14 .625 0 & 86 .082 6 \end{matrix}] \end{matrix}$ $

Table 4. Calibration rod measurement accuracy

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Table 4. Calibration rod measurement accuracy

Method	Fitting center A	Fitting center B	Length/mm	Error/mm
Gray moment	(317.588,−237.967,1250.752)	(−223.332,9.369,1172.507)	599.9098	0.2642
Fit method	(317.607,−237.573,1250.357)	(−223.792,9.302,1173.957)	599.9142	0.2598
Zernike moment	(317.624,−237.219,1251.199)	(−223.726,9.496,1173.864)	599.9240	0.2500
Hough transform	(317.701,−237.186,1250.309)	(−223.912,9.357,1174.357)	599.9147	0.2593
Proposed method	(317.486,−238.568,1249.487)	(−223.325,9.329,1171.598)	599.9968	0.1772

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Jing Wang, Liang Wei, Wenhao Xiang, Guiyang Zhang, Ju Huo. High-precision camera calibration method considering projected circular edge blur and eccentricity error[J]. Infrared and Laser Engineering, 2021, 50(12): 20210130

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