Flexible global calibration of multiple cameras with nonoverlapping fields of view using circular targets

Zheng Gong; Zhen Liu; Guangjun Zhang

doi:10.1364/AO.56.003122

Applied Optics
Vol. 56,
Issue 11,
pp. 3122-3131
(2017)
•https://doi.org/10.1364/AO.56.003122

Flexible global calibration of multiple cameras with nonoverlapping fields of view using circular targets

Zheng Gong, Zhen Liu, and Guangjun Zhang

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Zheng Gong, Zhen Liu, and Guangjun Zhang, "Flexible global calibration of multiple cameras with nonoverlapping fields of view using circular targets," Appl. Opt. 56, 3122-3131 (2017)

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Abstract

Global calibration of multicamera systems is a difficult problem. The key is to find an appropriate calibration target. This paper proposes a flexible method to construct a global calibration target with circular targets. Any object that is to be measured by the system can be used as a calibration target with the help of a hand-held scanner. The calibration method does not need a special calibration target or multiple shots, which makes it flexible in applications. Circular targets pasted on the calibration target are used as features that are captured by cameras. The particle swarm optimization method is employed to correct the eccentricity error in the projection of circular targets. The eccentricity correction method does not need any prior knowledge except the cameras’ intrinsic parameters. A synthetic data experiment was performed to validate the eccentricity correction method, and a physical experiment in a train wheelset inner-side distance measurement system was performed to validate the global calibration method. The measurement accuracy of the system was better than 0.1 mm, and the eccentricity correction method improved the three-dimensional reconstruction accuracy by about 0.1 mm.

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Intrinsic Parameter	$A = [\begin{matrix} 2784 & 660 \\ 2781 & 513 \\ 1 \end{matrix}]$
Rotation Matrix	$R = [\begin{matrix} 0.74461 & - 0.07618 & 0.66314 \\ 0.48480 & 0.74461 & - 0.45883 \\ - 0.45883 & 0.66314 & 0.59138 \end{matrix}]$
Translation Vector	$T = {[\begin{matrix} 30 & 45 & 350 \end{matrix}]}^{T}$

Cameras	Left Camera	Right Camera
Intrinsic Parameters	$f_{x} = 2765.34$ ;	$f_{x} = 2736.43$ ;
	$f_{y} = 2763.06$ ;	$f_{y} = 2732.59$ ;
	$u_{0} = 720.94$ ;	$u_{0} = 689.13$ ;
	$v_{0} = 503.44$ ;	$v_{0} = 541.77$ ;
	$k_{1} = - 0.250$ ;	$k_{1} = - 0.277$ ;
	$k_{2} = 0.268$ .	$k_{2} = 0.371$ .

Parameters	Rotation Matrix	Translation Vector
Initial Parameters	$[\begin{array}{l} - 0.30629 & 0.34694 & 0.88646 \\ - 0.43730 & 0.77586 & - 0.45476 \\ - 0.84555 & - 0.52694 & - 0.08592 \end{array}]$	$[\begin{array}{l} 533.3940 \\ - 236.7133 \\ - 610.9472 \end{array}]$
Corrected Parameters	$[\begin{array}{l} - 0.30612 & 0.34691 & 0.88653 \\ - 0.43732 & 0.77592 & - 0.45463 \\ - 0.84560 & - 0.52687 & - 0.08581 \end{array}]$	$[\begin{array}{l} 533.4287 \\ - 236.6779 \\ - 610.9571 \end{array}]$
Two Planar Targets Method Parameters	$[\begin{array}{l} - 0.30556 & 0.34825 & 0.88620 \\ - 0.43749 & 0.77531 & - 0.45551 \\ - 0.84571 & - 0.52690 & - 0.08455 \end{array}]$	$[\begin{array}{l} 531.8097 \\ - 242.5665 \\ - 608.0804 \end{array}]$

Result of Initial Parameters	Result of Corrected Parameters	Result of Two Planar Targets Method	Reference Value
1355.28 mm	1355.31 mm	1353.52 mm	1355.39 mm

Initial Points	Corrected Points	Distance
(831.43, −404.09, −665.76)	(831.49, −404.02, −665.73)	0.097 mm
(831.52, −404.14, −665.88)	(831.58, −404.06, −665.85)	0.104 mm
(831.57, −404.17,-665.96)	(831.64, −404.09, −665.93)	0.110 mm
(831.67, −404.22, −666.08)	(831.73, −404.14, −666.05)	0.104 mm
(831.83, −404.29, −666.28)	(831.90, −404.22, −666.25)	0.103 mm
(831.93, −404.34, −666.39)	(832.00, −404.26, −666.37)	0.108 mm
(832.01, −404.37, −666.49)	(832.08, −404.29, −666.46)	0.110 mm
(832.12, −404.41, −666.60)	(832.18, −404.33, −666.57)	0.104 mm
(832.21, −404.45, −666.70)	(832.27, −404.37, −666.67)	0.104 mm
(832.31, −404.49, −666.81)	(832.38, −404.41, −666.78)	0.110 mm
Root mean square error		0.105 mm

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Equations (9)

Applied Optics