Calibration of an underwater binocular vision system based on the refraction model

Yunpeng Ma; Yaqin Zhou; Chunkuan Wang; Yi Wu; Yang Zou; Shan Zhang

doi:10.1364/AO.448184

Applied Optics
Vol. 61,
Issue 7,
pp. 1675-1686
(2022)
•https://doi.org/10.1364/AO.448184

Calibration of an underwater binocular vision system based on the refraction model

Yunpeng Ma, Yaqin Zhou, Chunkuan Wang, Yi Wu, Yang Zou, and Shan Zhang

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Yunpeng Ma, Yaqin Zhou, Chunkuan Wang, Yi Wu, Yang Zou, and Shan Zhang, "Calibration of an underwater binocular vision system based on the refraction model," Appl. Opt. 61, 1675-1686 (2022)

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Related Topics
Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: November 9, 2021
- Revised Manuscript: January 18, 2022
- Manuscript Accepted: January 23, 2022
- Published: February 24, 2022

Abstract

Underwater measurement based on stereo vision attaches great importance to camera calibration. However, it is challenging to perform accurate calibration due to the significant refraction presented at the interfaces of air and water. To solve this problem, a calibration method for an underwater binocular vision system based on the optimized refractive model is proposed. First, conventional calibration is performed to obtain basic initial camera parameters using checkerboard images collected in the air. Then, an evolutionary multi-objective function is established according to Snell’s law, the refractive light propagation path, and checkerboard geometric relationship. Finally, precise camera parameters and involved refraction parameters are both obtained for underwater target positioning and size measurement by the non-dominated sorting genetic algorithm of the reference point. A group of experiments is performed, and the validity and effectiveness of the proposed calibration algorithm is demonstrated.

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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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Camera Parameters	Left Camera	Right Camera
Internal matrix	$[\begin{matrix} 914 .1437 & - 0 .0143 & 619.2320 \\ 0 & 914 .3417 & 485 .0708 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} 910 .7178 & - 0 .1908 & 654 .2105 \\ 0 & 911 .1071 & 494 .8268 \\ 0 & 0 & 1 \end{matrix}]$
Distortion coefficient	$[\begin{matrix} 0.000262 - 0.00039 0.00041 0.0054 0 \end{matrix}]$	$[\begin{matrix} 0.0336 - 0.0510 - 0.000613 0.000795 0 \end{matrix}]$
Rotation matrix	$[\begin{matrix} 1 .0000 & 0 .00075 & 0 .00630 \\ - 0 .000768 & 1 .0000 & 0 .00306 \\ - 0 .006302 & - 0 .0031 & 1 .0000 \end{matrix}]$
Translation matrix	$[- 100 .658 0.2605 - 0 .3023]$

Camera Parameters	Left Camera	Right Camera
Internal matrix	$[\begin{matrix} 1221 .539 & - 0 .29566 & 615 .089 \\ 0 & 1221 .563 & 482 .603 \\ 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} 1216 .581 & - 0 .16744 & 655 .276 \\ 0 & 1217 .140 & 495 .733 \\ 0 & 0 & 1 \end{matrix}]$
Distortion coefficient	$[\begin{matrix} 0 .4434 0 .06857 - 0 .00205 - 0 .00284 0 \end{matrix}]$	$[\begin{matrix} 0.4554 0.0378 - 0.0018 0.0022 0 \end{matrix}]$
Rotation matrix	$[\begin{matrix} 1 .0000 & 0 .00099 & 0 .00845 \\ - 0 .0010 & 1 .0000 & 0 .00431 \\ - 0 .0085 & - 0 .0043 & 1 .0000 \end{matrix}]$
Translation matrix	$[- 100.7230 0.2403 - 0.3552]$

Refractive Parameter	Parameter Value
$n = (n_{x}, n_{y}, n_{z})$	$[\begin{matrix} 0.0366 & 0 .0833 & 0 .9965 \end{matrix}]$
$d_{l}$	$0.1774 m m$
$d_{r}$	$0 .0883 m m$
$h$	$10.415 m m$

	Method 1	Method 2	Method 3	Method 4	Ours
Distance difference (mean/variance)	4.0926 mm/0.4987 mm	0.3175 mm/0.0983 mm	0.4605 mm/0.0396 mm	0.3623 mm/0.0473 mm	0.2556 mm/0.0308 mm
Position difference (mean/variance)	0.0388 rad/0.0231 rad	0.0142 rad/0.0063 rad	0.0510 rad/0.0016 rad	0.0091 rad/0.0092 rad	0.0059 rad/0.0020 rad
Angle difference (mean/variance)	0.0170 rad/0.0019 rad	0.00003 rad/0.000009 rad	0.0005 rad/0.0001 rad	0.0002 rad/0.00005 rad	0.0002 rad/0.00002 rad

	Method 1	Method 2	Method 3	Method 4	Ours
Distance difference (mean/variance)	0.9705 mm/0.6274 mm	0.5830 mm/0.2205 mm	0.5818 mm/0.3124 mm	0.5059 mm/0.2641 mm	0.3748 mm/0.02377 mm
Position difference (mean/variance)	0.0388 rad/0.0103 rad	0.0224 rad/0.0081 rad	0.0172 rad/0.0086 rad	0.0154 rad/0.0081 rad	0.0132 rad/0.0079 rad
Angle difference (mean/variance)	0.0066 rad/0.0016 rad	0.0021 rad/0.0026 rad	0.0026 rad/0.0026 rad	0.0025 rad/0.0028 rad	0.0023 rad/0.0027 rad

Abstract

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Applied Optics