High-Precision Calibration Method of Binocular Cameras for Large Inclination Targets

Lü Junhao; Qun Lou; Jinyou Xiao; Lihua Wen; Xiao Hou

doi:10.3788/AOS202242.2312002

Acta Optica Sinica, Volume. 42, Issue 23, 2312002(2022)

High-Precision Calibration Method of Binocular Cameras for Large Inclination Targets

Lü Junhao¹, Qun Lou¹, Jinyou Xiao^1、*, Lihua Wen¹, and Xiao Hou²

Author Affiliations

¹School of Astronautics, Northwestern Polytechnical University, Xi′an710072, Shaanxi , China

²The 4th Research Institute, China Aerospace Science and Technology Corporation, Xi′an710025, Shaanxi , China

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Figures & Tables(17)

Fig. 1. Ideal pinhole camera model

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Fig. 2. Ideal target image and inclination target image. (a) Ideal target image; (b) inclination target image

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Fig. 3. Projection error of circular marking points^[19]

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Fig. 4. Detection framework for large inclination targets

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Fig. 5. Target point identification framework. (a) Hybrid edge image; (b) initial linear classification result; (c) recognition result after clustering

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Fig. 6. Clustering detection algorithm for target points

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Fig. 7. Process of solving projection error

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Fig. 8. Ideal target image

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Fig. 9. Simulation images of target inclination change. (a1)-(a5) Target images with roll angles of 5°, 25°, 40°, 55°, and 70°, respectively; (b1)-(b5) target images with pitch angles of 5°, 25°, 40°, 55°, and 70°, respectively

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Fig. 10. Circular detection results of target simulation images. (a) Mean reprojection error of simulated target image detected by three methods with change of roll angle; (b) mean reprojection error of simulated target image detected by three methods with change of pitch angle

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Fig. 11. Experimental calibration pictures of binocular camera

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Fig. 12. Reprojection errors of three calibration experiments. (a) Experiment 1; (b) experiment 2; (c) experiment 3

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Fig. 13. Undetected target images. (a) Experiment 1; (b) experiment 2; (c) experiment 3

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Table 1. Parameter table of simulated target image
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Table 1. Parameter table of simulated target image
Parameter Parameter form Parameter value
$K$ $[\begin{array}{l} f_{x} & 0 & c_{x} \\ 0 & f_{y} & c_{y} \\ 0 & 0 & 1 \end{array}]$ $[\begin{matrix} 9481 & 0 & 615 \\ 0 & 9480 & 468 \\ 0 & 0 & 1 \end{matrix}]$
$D$ $[\begin{matrix} d_{1} & d_{2} \end{matrix}]$ $[\begin{matrix} - 0.0025 & 0.1260 \end{matrix}]$
$T$ $[\begin{matrix} T_{x} & T_{y} & T_{z} \end{matrix}]$ $[\begin{matrix} - 60 & - 45 & 2000 \end{matrix}]$
$R$ $[\begin{array}{l} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{array}]$ $[\begin{array}{l} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Table 2. Experimental setup
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Table 2. Experimental setup
Experiment Camera angle /（°） Baseline /mm
Experiment 1 5.3 164
Experiment 2 15.1 323
Experiment 3 32.0 428

Table 3. Statistics of simulation results

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Table 3. Statistics of simulation results

Method	Error（mean±SD）/pixel	Max inclination angle /（°）	Time consuming /（s·frame^-1）
Centroid extraction	0.085±0.045	45（pitch）	0.8
Edge detection	0.054±0.058	50（pitch）	1.1
Cluster matching（our）	0.015±0.008	>70	5.7

Table 4. Statistics of experimental calibration results

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Table 4. Statistics of experimental calibration results

Method	Experiment	Mean error /pixel	Success rate /%
Centroid extraction	Experiment 1	0.090	70
	Experiment 2	0.092	70
	Experiment 3	0.094	50
Edge detection	Experiment 1	0.059	70
	Experiment 2	0.060	70
	Experiment 3	0.060	50
Cluster matching（our）	Experiment 1	0.035	100
	Experiment 2	0.037	100
	Experiment 3	0.038	90

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Lü Junhao, Qun Lou, Jinyou Xiao, Lihua Wen, Xiao Hou. High-Precision Calibration Method of Binocular Cameras for Large Inclination Targets[J]. Acta Optica Sinica, 2022, 42(23): 2312002

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