Omnidirectional stereo vision sensor based on single camera and catoptric system

Fuqiang Zhou, Xinghua Chai, Xin Chen, and Ya Song

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Fuqiang Zhou, Xinghua Chai, Xin Chen, and Ya Song, "Omnidirectional stereo vision sensor based on single camera and catoptric system," Appl. Opt. 55, 6813-6820 (2016)

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Abstract

An omnidirectional stereo vision sensor based on one single camera and catoptric system is proposed. As crucial components, one camera and two pyramid mirrors are used for imaging. The omnidirectional measurement towards different directions in the horizontal field can be performed by four pairs of virtual cameras, with a consummate synchronism and an improved compactness. Moreover, the perspective projection invariance is ensured in the imaging process, which avoids the imaging distortion reflected by the curved mirrors. In this paper, the structure model of the sensor was established and a sensor prototype was designed. The influences of the structural parameters on the field of view and the measurement accuracy were also discussed. In addition, real experiments and analyses were performed to evaluate the performance of the proposed sensor in the measurement application. The results proved the feasibility of the sensor, and exhibited a considerable accuracy in 3D coordinate reconstruction.

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Parameters	Reference $(R - L)$	Area ${(R - L)}_{O}$	Area ${(R - L)}_{R}$	Area ${(R - L)}_{L}$
$(f_{x}, f_{y}) / pixels$	(3619.096, 3612.251)
$(u_{0}, v_{0}) / pixels$	(1294.269, 973.015)
$k_{1}$ , $k_{2}$	0.008743, 0.0559
$R$	$[\begin{matrix} 0.7124 & - 0.0879 & 0.679 \\ 0.0879 & 0.995 & 0.0015 \\ - 0.6953 & - 0.0011 & 0.7091 \end{matrix}]$	$[\begin{matrix} 0.7087 & - 0.0158 & 0.696 \\ 0.0609 & 0.991 & - 0.0158 \\ - 0.6830 & 0.0107 & 0.6904 \end{matrix}]$	$[\begin{matrix} 0.727 & 0.0733 & 0.6754 \\ - 0.0728 & 0.993 & 0.0139 \\ - 0.6861 & - 0.0029 & 0.6814 \end{matrix}]$	$[\begin{matrix} 0.7144 & - 0.0321 & 0.6934 \\ - 0.03287 & 0.986 & - 0.0026 \\ - 0.6719 & 0.0034 & 0.7069 \end{matrix}]$
$T$	(20.533, 0.1542, 5.6671)	(19.445, −0.0964, 6.1602)	(19.719, −0.1283, 5.937)	(20.3145, 0.1204, 5.9518)
$R_{G}$	—	$[\begin{matrix} 0.1996 & 0.7806 & - 0.5916 \\ 0.7179 & 0.2256 & 0.5315 \\ 0.5829 & - 0.5411 & - 0.5543 \end{matrix}]$	$[\begin{matrix} 0.7239 & 0.3918 & 0.3149 \\ - 0.3928 & 0.06524 & 0.7201 \\ 0.3310 & - 0.7135 & 0.3086 \end{matrix}]$	$[\begin{matrix} 0.1060 & - 0.3870 & - 0.9441 \\ 0.3509 & 0.8476 & - 0.3305 \\ 0.9027 & - 0.3211 & 0.1994 \end{matrix}]$
$T_{G}$	—	(−5.0090, 197.46, 4. 3910)	(97.493, 95.227, −3.8460)	(−96.225, 96.715, 4. 0234)
$E_{RP} / pixels$	0.0459	0.0516	0.0503	0.0497

Parameters	Calibration Results using Multiple Image Approach
$(f_{x}, f_{y}) / pixels$	(3615.146, 3617.873)
$(u_{0}, v_{0}) / pixels$	(1293.582, 974.372)
$k_{1}$ , $k_{2}$	0.008965, 0.0578
$E_{RP} / pixels$	0.0157

Parameter	Reference Area $(R - L)$	Area ${(R - L)}_{O}$	Area ${(R - L)}_{R}$	Area ${(R - L)}_{L}$
$E_{M} / mm$	0.04941	0.03930	0.04958	0.04191
	0.04362	0.03851	0.04249	0.05104
	0.04238	0.04136	0.04751	0.04682
	0.04059	0.04901	0.04970	0.04523
	0.03853	0.05034	0.05002	0.04011

Parameters	Reference $(R - L)$	Area ${(R - L)}_{O}$	Area ${(R - L)}_{R}$	Area ${(R - L)}_{L}$
$(f_{x}, f_{y}) / pixels$	(3619.096, 3612.251)
$(u_{0}, v_{0}) / pixels$	(1294.269, 973.015)
$k_{1}$ , $k_{2}$	0.008743, 0.0559
$R$	$[\begin{matrix} 0.7124 & - 0.0879 & 0.679 \\ 0.0879 & 0.995 & 0.0015 \\ - 0.6953 & - 0.0011 & 0.7091 \end{matrix}]$	$[\begin{matrix} 0.7087 & - 0.0158 & 0.696 \\ 0.0609 & 0.991 & - 0.0158 \\ - 0.6830 & 0.0107 & 0.6904 \end{matrix}]$	$[\begin{matrix} 0.727 & 0.0733 & 0.6754 \\ - 0.0728 & 0.993 & 0.0139 \\ - 0.6861 & - 0.0029 & 0.6814 \end{matrix}]$	$[\begin{matrix} 0.7144 & - 0.0321 & 0.6934 \\ - 0.03287 & 0.986 & - 0.0026 \\ - 0.6719 & 0.0034 & 0.7069 \end{matrix}]$
$T$	(20.533, 0.1542, 5.6671)	(19.445, −0.0964, 6.1602)	(19.719, −0.1283, 5.937)	(20.3145, 0.1204, 5.9518)
$R_{G}$	—	$[\begin{matrix} 0.1996 & 0.7806 & - 0.5916 \\ 0.7179 & 0.2256 & 0.5315 \\ 0.5829 & - 0.5411 & - 0.5543 \end{matrix}]$	$[\begin{matrix} 0.7239 & 0.3918 & 0.3149 \\ - 0.3928 & 0.06524 & 0.7201 \\ 0.3310 & - 0.7135 & 0.3086 \end{matrix}]$	$[\begin{matrix} 0.1060 & - 0.3870 & - 0.9441 \\ 0.3509 & 0.8476 & - 0.3305 \\ 0.9027 & - 0.3211 & 0.1994 \end{matrix}]$
$T_{G}$	—	(−5.0090, 197.46, 4. 3910)	(97.493, 95.227, −3.8460)	(−96.225, 96.715, 4. 0234)
$E_{RP} / pixels$	0.0459	0.0516	0.0503	0.0497

Parameters	Calibration Results using Multiple Image Approach
$(f_{x}, f_{y}) / pixels$	(3615.146, 3617.873)
$(u_{0}, v_{0}) / pixels$	(1293.582, 974.372)
$k_{1}$ , $k_{2}$	0.008965, 0.0578
$E_{RP} / pixels$	0.0157

Omnidirectional stereo vision sensor based on single camera and catoptric system

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Equations (21)

Applied Optics