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

Jing Wang; Liang Wei; Wenhao Xiang; Guiyang Zhang; Ju Huo

doi:10.3788/IRLA20210130

Journals >Infrared and Laser Engineering >Volume 50 >Issue 12 >Page 20210130 > Article

Infrared and Laser Engineering
Vol. 50, Issue 12, 20210130 (2021)

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

Jing Wang¹, Liang Wei¹, Wenhao Xiang², Guiyang Zhang³, and Ju Huo^1、*

Author Affiliations

¹School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China

²Systems Engineering Research Institute, Beijing 100094, China

³School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

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DOI: 10.3788/IRLA20210130 Cite this Article

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 Copy Citation Text

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Fig. 1. Ideal step edge model

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Fig. 2. Grayscale distribution of projected ellipse

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Fig. 3. Two-dimensional representation of edge gray distribution model

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Fig. 4. Spatial circular projection model

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Fig. 5. Projection ellipse fitting algorithm

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Fig. 6. Simulative image

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Fig. 7. Error distribution of =0.002的误差分布

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Fig. 8. Edge and center localization based on improved Zernike moments

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Fig. 9. Acquisition equipment of stereo camera system image

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Fig. 10. Extraction and coding of circular mark points

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Fig. 11. Target image acquisition and center extraction

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Fig. 12. Stereo vision system calibration results

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Fig. 13. Calibration rod

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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 1. Edge location accuracy of simulative image

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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 2. Center location accuracy of simulative image

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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{gathered} R = \left[ {\begin{array}{{20}{c}} {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{array}} \right] \\ T = \left[ {\begin{array}{{20}{c}} {{\rm{ - 363}}{\rm{.001\;5}}}&{{\rm{14}}{\rm{.625\;0}}}&{{\rm{86}}{\rm{.082\;6}}} \end{array}} \right] \\ \end{gathered} $

Table 3. Camera internal parameters and binocular posture relationship

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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

Table 4. Calibration rod measurement accuracy

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