Camera calibration method using synthetic speckle pattern with an improved gray wolf optimizer algorithm

Xiaosong Shu; Xiaosong Shu; Xiaosong Shu; Tengfei Bao; Tengfei Bao; Tengfei Bao; Yuhan Hu; Yuhan Hu; Yuhan Hu; Yangtao Li; Yangtao Li; Yangtao Li; Kang Zhang; Kang Zhang; Kang Zhang

doi:10.1364/AO.444593

Applied Optics
Vol. 60,
Issue 34,
pp. 10477-10489
(2021)
•https://doi.org/10.1364/AO.444593

Camera calibration method using synthetic speckle pattern with an improved gray wolf optimizer algorithm

Xiaosong Shu, Tengfei Bao, Yuhan Hu, Yangtao Li, and Kang Zhang

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Xiaosong Shu, Tengfei Bao, Yuhan Hu, Yangtao Li, and Kang Zhang, "Camera calibration method using synthetic speckle pattern with an improved gray wolf optimizer algorithm," Appl. Opt. 60, 10477-10489 (2021)

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- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: September 28, 2021
- Revised Manuscript: November 1, 2021
- Manuscript Accepted: November 1, 2021
- Published: November 22, 2021

Abstract

Camera calibration is essential for various vision-based 3D metrological techniques. In this paper, a novel camera calibration method, to the best of our knowledge, combining synthetic speckle pattern and an improved gray wolf optimizer algorithm is presented. The synthetic speckle pattern serves as the calibration target. The particle swarm algorithm-based digital image correlation is employed to achieve matches among 3D control points and 2D image points; then the improved gray wolf optimizer algorithm is used to calculate the camera parameters. For verification, simulated and real tests are conducted. Through the analysis of calibration results, the proposed method performs better and is more stable than other calibration targets. Research on the influence of camera pose and optimization algorithm is conducted, showing that the improved gray wolf optimizer algorithm performs better than other benchmark algorithms. The camera parameters can be obtained through one captured image when the speckle patterns are added in the portion of the camera sensor.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Checkerboard Pattern		Circular Pattern		Speckle Pattern
Parameters	Measured	Variance	Measured	Variance	Measured	Variance
$K = (0.2, 300, 0, 0, 0)$	25035.71	20.7	24967.82	37.1	25024.19	8.03
$3000 \times 3000$	25029.89	19.8	25042.36	41.6	25007.16	8.15
$f_{x} (p i x e l s)$	1506.255	10.4	1507.022	19.3	1503.543	1.928
$f_{y} (p i x e l s)$	1493.599	10.7	1481.912	18.6	1502.511	3.074
$c_{x} (p i x e l s)$	0.1902	0.27	0.2443	0.19	0.2112	0.16
$c_{y} (p i x e l s)$	318.938	20.2	285.5	28.5	305.5	12.3

Pattern	$f_{x}$	$f_{y}$	$f_{x}$	$f_{y}$	$γ$	$c_{x}$	$c_{y}$	$k_{1}$	$k_{2}$	$k_{3}$	Error
No.1	16855.4	16792.4	0.6263	1223.9	1025.1	1.440	−86.57	−0.0079	−0.0002	−0.6071	0.0507
No.2	17090.4	17014.4	0.5151	1224.0	1025.1	1.418	−86.88	−0.0071	−0.0016	−0.5962	0.0515
No.3	16996.4	16928.7	0.5290	1223.9	1025.2	1.534	−92.23	−0.0083	−0.0007	−0.6482	0.0515
No.4	16933.8	16854.0	0.3968	1224.0	1025.2	1.234	−75.32	−0.0031	−0.0026	−0.5312	0.0512
No.5	17247.9	17194.7	0.6158	1223.8	1025.2	1.395	−87.98	−0.0061	−0.0007	−0.6001	0.0507
No.6	17370.3	17290.8	0.3590	1224.0	1025.1	1.513	−101.6	−0.0062	−0.0018	−0.6906	0.0508
Averaged	17082.4	17012.5	0.5070	1224.0	1025.2	1.422	−88.43	−0.0064	−0.0012	−0.6122	0.0510
Variance	195.63	195.57	0.1101	0.082	0.055	0.107	8.55	0.0018	0.0008	0.0537

Pattern	$(λ_{1}, λ_{2})$	$(λ_{1}, λ_{2})$	$f_{x}$	$f_{y}$	$γ$	$c_{x}$	$c_{y}$	$k_{1}$	$k_{2}$	$k_{3}$	Error
Speckle	16865.4	16802.4	0.5303	1223.9	1025.1	1.420	−84.57	−0.0069	−0.0002	−0.6371	0.0473
Checkerboard	17030.6	16957.3	1.1131	1224.2	1025.0	1.395	−80.36	−0.0051	−0.0008	−0.5877	0.0647

Algorithm	Population Size	Max Iteration	Parameters	Stopping Criteria
SA	None	200	$p_{1}$	Max iteration
NR	None	200	None	Max iteration
LM	None	200	$p_{2}$	Max iteration
GA	100	200	$Δ f = 0.07$	Max iteration
PSO	100	200	$λ = 0.001$	Max iteration
GS	None	None	None	None
GWO	100	200	$(C_{1}, C_{2}) = (0.6, 0.001)$	Max iteration
Proposed	100	200	$(C_{1}, C_{2}) = (0.5, 0.5)$	Max iteration

Algorithm	$(f_{x}, f_{y})$	$(f_{x}, f_{y})$	$f_{x}$	$f_{y}$	$γ$	$c_{x}$	$c_{y}$	$k_{1}$	$k_{2}$	$k_{3}$	Error
SA	16751.0	16688.9	0.8074	1224.8	1023.2	0.983	−44.32	−0.0067	−0.0002	−0.441	0.0496
NR	16838.5	16776.2	0.5951	1225.0	1025.4	1.059	−51.15	−0.0057	−0.0001	−0.493	0.0487
LM	16871.3	16808.0	0.5726	1224.6	1025.3	1.321	−77.80	−0.0080	−0.0002	−0.442	0.0481
GS	16829.2	16765.7	0.4448	1224.5	1023.7	1.484	−86.62	−0.0077	−0.0002	−0.329	0.0499
PSO	16940.3	16877.2	0.6408	1224.6	1026.3	1.413	−81.47	−0.0074	−0.0001	−0.645	0.0497
GA	16970.3	16907	0.3578	1223.1	1025.6	1.374	−69.85	−0.0094	−0.0001	−0.569	0.0486
GWO	16855.6	16793.8	0.5633	1224.0	1025.2	1.521	−91.55	−0.0083	−0.0002	−0.650	0.0475
Proposed	16855.4	16792.4	0.5293	1223.9	1025.1	1.440	−86.57	−0.0079	−0.0002	−0.607	0.0462

Camera Pose	$p_{1}$	$p_{2}$	$f_{x}$	$f_{y}$	$γ$	$c_{x}$	$c_{y}$	$k_{1}$	$k_{2}$	$k_{3}$	Error
Third	16845.6	16786.2	0.6415	1227.2	1023.1	1.344	−71.42	−0.0055	−0.0001	−0.711	0.0508
Ninth	16940.3	16877.2	0.5362	1224.6	1026.3	1.413	−81.47	−0.0074	−0.0001	−0.645	0.0473
Sixteenth	16781.7	16719.1	0.6813	1231.7	1023.1	1.229	−69.93	−0.0081	−0.0003	−0.510	0.0487
Averaged	16855.9	16794.2	0.620	1227.8	1024.2	1.329	−74.27	−0.0070	−0.0002	−0.622	0.0489
Variance	79.80	79.35	0.075	3.59	1.848	0.093	6.28	0.0013	0.0001	0.102	0.0018

Camera	#1		#2		#3		#4		#5		#6
Pose	X	Y	X	Y	X	Y	X	Y	X	Y	X	Y
Third	−16.5	−211.4	49.3	−0.1	63.6	260.6	204.1	−113.2	549.7	−50.2	269.0	199.7
Ninth	−16.7	−210.8	49.8	−0.1	63.8	261.1	204.6	−112.6	550.1	−50.1	269.3	200.2
Sixteenth	−17.1	−211.5	49.6	−0.1	63.1	260.9	203.8	−113.2	549.3	−50.5	268.8	200.0
Measured	−17.0	−211.0	50.0	0.0	63.0	261.0	204.0	−113.0	550.0	−50.0	269.0	200.0

Abstract

Data Availability

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Tables (10)

Equations (13)

Applied Optics