Novel camera calibration method based on invariance of collinear points and pole–polar constraint

doi:10.23919/JSEE.2023.000074

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 744-753.doi: 10.23919/JSEE.2023.000074

• CONTROL THEORY AND APPLICATION • Previous Articles

Novel camera calibration method based on invariance of collinear points and pole–polar constraint

Liang WEI¹(), Guiyang ZHANG²(), Ju HUO¹^,*(), Muyao XUE³()

¹ School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China
² School of Mechanical Engineering, Changshu Institute of Technology, Suzhou 215500, China
³ Space Propulsion Technology Research Institute, Shanghai Academy of Spaceflight Technology, Shanghai 201109, China

Received:2021-07-30 Online:2023-06-15 Published:2023-06-30
Contact: Ju HUO E-mail:weiliangts@163.com;gyzhang@cslg.edu.cn;torch@hit.edu.cn;xuemuyao@163.com
About author:
WEI Liang was born in 1993. He received his B.S. degree in packaging engineering from Hebei Agricultural University, Hebei, China, in 2015, and M.S. degree in electric engineering from Harbin Institute of Technology, in 2019. He is pursuing his Ph.D. degree in electrical engineering from Harbin Institute of Technology. His current research interests include optical measurement and camera calibration. E-mail: weiliangts@163.com

ZHANG Guiyang was born in 1990. He received his B.S. degree in detection guidance and control technology from Changchun University of Science and Technology, Jilin, China, in 2014. He received his M.S. and Ph.D. degrees in control science and engineering from Harbin Institute of Technology, in 2016 and 2021, respectively. He is a lecturer in the School of Mechanical Engineering, Changshu Institute of Technology. His current research interests include vision measurement and machine vision. E-mail: gyzhang@cslg.edu.cn

HUO Ju was born in 1977. He received his B.S. and M.S. degrees in electrical engineering, and his Ph.D. degree in control science and engineering from Harbin Institute of Technology, in 1999, 2001, and 2007, respectively. He is a professor and a doctoral supervisor with the Simulation and Control Center, Harbin Institute of Technology. His current research interests include vision measurement and system simulation. E-mail: torch@hit.edu.cn

XUE Muyao was born in 1985. He received his B.S. degree from Harbin Institute of Technology in 2007 and his M.S. degree from Harbin Engineering University in 2011. He is a senior engineer with Space Propulsion Technology, Shanghai Space Propulsion Technology Research Institute. His current research interests include vision measurement and system simulation. E-mail: xuemuyao@163.com
Supported by:
This work was supported by the Aerospace Science and Technology Joint Fund (6141B061505) and the National Natural Science Foundation of China (61473100)

Abstract

Abstract:

To address the eccentric error of circular marks in camera calibration, a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper. Firstly, the centers of the ellipses are extracted, and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points. Subsequently, since the infinite lines passing through the centers of the marks are parallel, the other center projection coordinates are expressed as the solution problem of linear equations. The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed, and the results are utilized as the true image points to achieve the high precision camera calibration. As demonstrated by the simulations and practical experiments, the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks. The relevant results confirm the precision and robustness of the proposed approach.

Key words: camera calibration, cross ratio invariance, infinite lines, eccentricity error compensate

Liang WEI, Guiyang ZHANG, Ju HUO, Muyao XUE. Novel camera calibration method based on invariance of collinear points and pole–polar constraint[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 744-753.

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References 28

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Location accuracy		Gaussian white noise
Location accuracy		$ {\sigma ^{\text{2}}}{\text{ = 0}} $	$ {\sigma ^{\text{2}}}{\text{ = 0}}{\text{.002}} $	$ {\sigma ^{\text{2}}}{\text{ = 0}}{\text{.004}} $
Edge location	Mean error	0.050 1	0.086 7	0.106 4
Edge location	Variance	0.019 8	0.030 7	0.251 2
Fitting center	Coordinate deviation	(0.036 1,0.022 3)	(0.041 4,0.014 2)	(0.054 1,0.012 1)
Fitting center	Distance error	0.042 4	0.043 7	0.055 4

No.	Concentric circle		Circle
1	(257.290 6,194.163 7)	(323.476 4,124.467)	(512.191 6,162.626 9)
2	(271.942 6,250.243)	(167.923 6,465.429 1)	(493.319 5,203.224 7)
3	(264.001,209.842 4)	(104.484 9,407.255 9)	(641.911 8,276.296 5)
4	(271.023 2,238.535 9)	(75.152 5,328.070 5)	(532.757 7,333.176 6)
5	(154.277 3,205.306 3)	(77.085 3,339.652 8)	(496.89,284.526 3)
6	(154.246 5,323.018 9)	(125.408 1,98.222 5)	(495.664 8,195.235 5)
7	(254.684,323.241 9)	(71.091 6,246.484 7)	(582.305 7,341.247 5)
8	(271.209 8,266.330 4)	(335.611 1,151.473 6)	(624.006 5,311.547 3)
9	(251.659 8,185.683 3)	(278.431,68.076 5)	(648.944 3,232.622 3)
10	(256.611 4,193.771 9)	(172.061,58.068 8)	(648.098 7,248.539 1)
11	(265.711 1,297.18)	(280.737 5,69.936 6)	(547.235 5,131.304 5)
12	(239.580 8,343.049 2)	(340.899 7,167.243 1)	(611.235 5,325.248 7)
13	(176.241 6,349.518 3)	(348.717 8,208.216 4)	(640.550 6,280.305 7)
14	(141.679 8,274.278 6)	(172.476 4,467.438 8)	(595.547 3,128.567 3)
15	(164.932,187.213)	(91.644 1,155.172 6)	(646.799 1,203.622 3)
Ellipse center	(208.121 5,259.962 1)	(211.052,259.932 8)	(570.910 1,234.413 2)

Center location	Proposed method	Traditional method
Concentric circle	(205.208 9,260.007 9)	(207.490 1,259.991 4)
Circle	(568.737 4,234.347 4)	(569.448 1,234.332 8)

Parameter	Method
Parameter	Proposed	Traditional
Left camera	$ {f_u} = 3{\text{ }}048.380{\text{ }}3 $	$ {f_u} = 3{\text{ }}082.551{\text{ }}1 $
	$ {f_v} = 3{\text{ }}048.493{\text{ }}5 $	$ {f_v} = 3{\text{ }}082.680{\text{ }}9 $
	$ {u_0} = 833.151{\text{ }}6 $	$ {u_0} = 833.295{\text{ }}2 $
	$ {v_0} = 901.107{\text{ }}7 $	$ {v_0} = 906.220{\text{ }}9 $
Right camera	$ {f_u} = 3{\text{ }}061.098{\text{ }}2 $	$ {f_u} = 3{\text{ }}101.673{\text{ }}6 $
	$ {f_v} = 3{\text{ }}060.632{\text{ }}7 $	$ {f_v} = 3{\text{ }}100.568{\text{ }}6 $
	$ {u_0} = 819.322{\text{ }}2 $	$ {u_0} = 826.158{\text{ }}9 $
	$ {v_0} = 867.025{\text{ }}9 $	$ {v_0} = 875.027{\text{ }}6 $

Parameter	Method
Parameter	Traditional	Proposed
Measuring distance	119.914 7	119.97
Absolute error	0.085 3	0.03

Novel camera calibration method based on invariance of collinear points and pole–polar constraint

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[2]	Meng An*, Zhiguo Jiang, Danpei Zhao. High speed robust image registration and localization using optimized algorithm and its performances evaluation [J]. Journal of Systems Engineering and Electronics, 2010, 21(3): 520-526.