Global vision measurements of object position and orientation with non-coplanar feature points determined by point optimization in camera coordinate system

Guan Xu; Anqi Zheng; Xiaotao Li; Jian Su

doi:10.1364/AO.56.000105

Applied Optics
Vol. 56,
Issue 1,
pp. 105-114
(2017)
•https://doi.org/10.1364/AO.56.000105

Global vision measurements of object position and orientation with non-coplanar feature points determined by point optimization in camera coordinate system

Guan Xu, Anqi Zheng, Xiaotao Li, and Jian Su

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Guan Xu, Anqi Zheng, Xiaotao Li, and Jian Su, "Global vision measurements of object position and orientation with non-coplanar feature points determined by point optimization in camera coordinate system," Appl. Opt. 56, 105-114 (2017)

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Abstract

Vision-based measurement of object position and orientation is an attractive goal in theoretical and applied measurement research. A target with a vertex is designed as the bridge among the world, the camera, and the image coordinate systems. The optimization function, to minimize the differences between the point derived from the image coordinate system and the point derived from the world coordinate system, is constructed in the camera coordinate system to obtain the rotation matrix and the translation vector of the target. Then the 3D coordinates of the non-coplanar feature points on the object are captured by the target in the camera coordinate system. Six parameters of the object position and orientation are achieved by the decomposition (RQ decomposition) of the projection matrix of the feature points on the object into a product of an upper triangular matrix and an orthogonal matrix. The absolute translation of the measured object is presented to evaluate the measurement accuracy in the comparison experiments. The results demonstrate that the method is capable of measuring the position and the orientation with relatively high accuracy and noise immunity.

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			$E_{k}$ , mm
No.	Method		$L = 10 mm$	$L = 20 mm$	$L = 30 mm$	$L = 40 mm$
1	CCS	Min.	−0.18	0.23	−0.45	−0.86
		Max.	0.27	0.30	0.93	3.47
		Mean	−0.02	0.72	0.19	1.25
		Var.	0.13	0.22	0.40	1.05
	ICS	Min.	0.39	0.42	0.35	0.39
		Max.	0.93	0.76	1.62	3.40
		Mean	0.61	0.59	0.93	1.88
		Var.	0.15	0.10	0.34	0.88
2	CCS	Min.	−0.49	−0.10	−0.69	−1.82
		Max.	−0.16	0.32	0.39	1.30
		Mean	0.08	0.10	0.35	0.41
		Var.	0.08	0.11	0.28	0.85
	ICS	Min.	−0.06	−0.74	−1.61	−3.13
		Max.	0.35	−0.45	−0.53	0.54
		Mean	0.21	0.61	1.14	1.09
		Var.	0.08	0.07	0.26	1.22
3	CCS	Min.	0.17	−0.59	−1.36	0.46
		Max.	0.47	−0.26	0.42	2.40
		Mean	0.33	0.44	0.87	1.25
		Var.	0.89	0.95	0.12	0.22
	ICS	Min.	0.20	0.36	−1.39	0.28
		Max.	0.54	0.78	−0.35	2.73
		Mean	0.40	0.53	−0.97	1.66
		Var.	0.10	0.12	0.26	0.75
4	CCS	Min.	−0.28	−0.58	0.44	−1.40
		Max.	0.13	−0.10	1.26	3.19
		Mean	0.09	0.39	0.79	0.83
		Var.	0.10	0.12	0.27	1.11
	ICS	Min.	−0.53	−0.67	−1.71	−0.98
		Max.	−0.18	0.17	−0.87	2.30
		Mean	0.33	0.41	1.15	1.07
		Var.	0.09	0.12	0.21	0.85

			$E_{k}$ , mm
No.	Method	Noise Level, $\times 10^{- 3}$	$L = 10 mm$	$L = 20 mm$	$L = 30 mm$	$L = 40 mm$
1	CCS	1	0.03	0.05	0.08	0.10
		2	0.06	0.19	0.19	0.30
		3	0.15	0.37	0.27	0.31
		4	0.22	0.44	0.30	0.52
		5	0.38	0.46	0.49	0.59
	ICS	1	0.04	0.06	0.15	0.13
		2	0.06	0.30	0.23	0.31
		3	0.23	0.51	0.49	0.71
		4	0.23	0.58	0.44	0.75
		5	0.43	0.60	0.63	0.90
2	CCS	1	0.10	0.07	0.08	0.13
		2	0.10	0.18	0.33	0.21
		3	0.12	0.33	0.32	0.35
		4	0.11	0.23	0.33	0.32
		5	0.15	0.28	0.54	0.49
	ICS	1	0.10	0.11	0.21	0.41
		2	0.12	0.24	0.49	0.44
		3	0.15	0.29	0.38	0.51
		4	0.12	0.28	0.74	0.50
		5	0.15	0.39	0.75	0.46
3	CCS	1	0.03	0.10	0.15	0.10
		2	0.06	0.19	0.46	0.17
		3	0.15	0.35	0.48	0.29
		4	0.15	0.30	0.94	0.36
		5	0.45	0.53	0.94	0.48
	ICS	1	0.04	0.48	0.19	0.13
		2	0.07	0.20	0.51	0.18
		3	0.19	0.28	0.93	0.27
		4	0.38	0.47	1.09	0.48
		5	0.52	0.58	1.42	0.94
4	CCS	1	0.04	0.09	0.08	0.13
		2	0.08	0.15	0.28	0.20
		3	0.15	0.16	0.57	0.37
		4	0.18	0.29	0.74	0.70
		5	0.27	0.36	0.70	0.76
	ICS	1	0.32	0.08	0.15	0.26
		2	0.60	0.29	0.38	0.27
		3	0.18	0.35	0.44	0.38
		4	0.29	0.43	0.68	0.42
		5	0.42	0.64	0.81	0.66

			$E_{k}$ , mm
No.	Method		$L = 10 mm$	$L = 20 mm$	$L = 30 mm$	$L = 40 mm$
1	CCS	Min.	−0.18	0.23	−0.45	−0.86
		Max.	0.27	0.30	0.93	3.47
		Mean	−0.02	0.72	0.19	1.25
		Var.	0.13	0.22	0.40	1.05
	ICS	Min.	0.39	0.42	0.35	0.39
		Max.	0.93	0.76	1.62	3.40
		Mean	0.61	0.59	0.93	1.88
		Var.	0.15	0.10	0.34	0.88
2	CCS	Min.	−0.49	−0.10	−0.69	−1.82
		Max.	−0.16	0.32	0.39	1.30
		Mean	0.08	0.10	0.35	0.41
		Var.	0.08	0.11	0.28	0.85
	ICS	Min.	−0.06	−0.74	−1.61	−3.13
		Max.	0.35	−0.45	−0.53	0.54
		Mean	0.21	0.61	1.14	1.09
		Var.	0.08	0.07	0.26	1.22
3	CCS	Min.	0.17	−0.59	−1.36	0.46
		Max.	0.47	−0.26	0.42	2.40
		Mean	0.33	0.44	0.87	1.25
		Var.	0.89	0.95	0.12	0.22
	ICS	Min.	0.20	0.36	−1.39	0.28
		Max.	0.54	0.78	−0.35	2.73
		Mean	0.40	0.53	−0.97	1.66
		Var.	0.10	0.12	0.26	0.75
4	CCS	Min.	−0.28	−0.58	0.44	−1.40
		Max.	0.13	−0.10	1.26	3.19
		Mean	0.09	0.39	0.79	0.83
		Var.	0.10	0.12	0.27	1.11
	ICS	Min.	−0.53	−0.67	−1.71	−0.98
		Max.	−0.18	0.17	−0.87	2.30
		Mean	0.33	0.41	1.15	1.07
		Var.	0.09	0.12	0.21	0.85

			$E_{k}$ , mm
No.	Method	Noise Level, $\times 10^{- 3}$	$L = 10 mm$	$L = 20 mm$	$L = 30 mm$	$L = 40 mm$
1	CCS	1	0.03	0.05	0.08	0.10
		2	0.06	0.19	0.19	0.30
		3	0.15	0.37	0.27	0.31
		4	0.22	0.44	0.30	0.52
		5	0.38	0.46	0.49	0.59
	ICS	1	0.04	0.06	0.15	0.13
		2	0.06	0.30	0.23	0.31
		3	0.23	0.51	0.49	0.71
		4	0.23	0.58	0.44	0.75
		5	0.43	0.60	0.63	0.90
2	CCS	1	0.10	0.07	0.08	0.13
		2	0.10	0.18	0.33	0.21
		3	0.12	0.33	0.32	0.35
		4	0.11	0.23	0.33	0.32
		5	0.15	0.28	0.54	0.49
	ICS	1	0.10	0.11	0.21	0.41
		2	0.12	0.24	0.49	0.44
		3	0.15	0.29	0.38	0.51
		4	0.12	0.28	0.74	0.50
		5	0.15	0.39	0.75	0.46
3	CCS	1	0.03	0.10	0.15	0.10
		2	0.06	0.19	0.46	0.17
		3	0.15	0.35	0.48	0.29
		4	0.15	0.30	0.94	0.36
		5	0.45	0.53	0.94	0.48
	ICS	1	0.04	0.48	0.19	0.13
		2	0.07	0.20	0.51	0.18
		3	0.19	0.28	0.93	0.27
		4	0.38	0.47	1.09	0.48
		5	0.52	0.58	1.42	0.94
4	CCS	1	0.04	0.09	0.08	0.13
		2	0.08	0.15	0.28	0.20
		3	0.15	0.16	0.57	0.37
		4	0.18	0.29	0.74	0.70
		5	0.27	0.36	0.70	0.76
	ICS	1	0.32	0.08	0.15	0.26
		2	0.60	0.29	0.38	0.27
		3	0.18	0.35	0.44	0.38
		4	0.29	0.43	0.68	0.42
		5	0.42	0.64	0.81	0.66

Abstract

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Figures (6)

Tables (2)

Equations (16)

Applied Optics