Stereo Vision-based Calibration Approach for Position Parameters of LED in Photometric Stereo

Fig. 1. Position calibration system of the LED light source based on stereo vision. (a) Diagram of actual experimental scene; (b) diagram of the LED light source distribution

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Fig. 2. LED light source position parameter calibration system

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Fig. 3. Schematic of the stereo vision simultaneous calibration system

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Fig. 4. Reprojection error of the camera. (a) Camera A; (b) camera B; (c) camera C

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Fig. 5. Reprojection error of binocular stereo vision system. (a) Camera A, B; (b) camera B, C

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Fig. 6. LED light source images captured by the binocular camera. (a) (b) LED light source A captured by left and right cameras; (c) (d) LED light source A‒H captured by left and right cameras

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Fig. 7. LED light source position calibration experiment results. (a) $X_{w} Y_{w}$ direction; (b) $Y_{w} Z_{w}$ direction

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Table 1. Camera parameters
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Table 1. Camera parameters
Camera internal parameter Camera external parameter
$[\begin{matrix} f_{x} & 0 & u_{0} \\ 0 & f_{y} & v_{0} \\ 0 & 0 & 1 \end{matrix}]$ $R = [\begin{matrix} r_{1} & r_{2} & r_{3} \\ r_{4} & r_{5} & r_{6} \\ r_{7} & r_{8} & r_{9} \end{matrix}], T = [\begin{matrix} t_{x} \\ t_{y} \\ t_{z} \end{matrix}]$

Table 2. Camera internal parameters

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Table 2. Camera internal parameters

Camera

Focal length

Principal point

Radial distortion

f_{x}

f_{y}

u_{0}

v_{0}

k_{1}

k_{2}

Camera A

Camera B

Camera C

2225.8629

2394.9793

2407.6362

2227.6786

2396.0596

2407.8217

659.0179

664.5126

632.8595

506.3386

481.5372

467.3357

-0.1104

-0.0825

-0.0824

0.4042

0.3242

0.2748

Table 3. Structural parameters of stereo vision system

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Table 3. Structural parameters of stereo vision system

Binocular camera（A、B）		Binocular camera（B、C）
Rotation matrix	Translation matrix	Rotation matrix	Translation matrix
$[\begin{matrix} - 0.5713 & 0.1159 & - 0.8124 \\ - 0.0985 & 0.9731 & 0.2081 \\ 0.8147 & 0.1989 & - 0.5445 \end{matrix}]$	$[\begin{matrix} - 366.8018 \\ - 253.3272 \\ 1869.4907 \end{matrix}]$	$[\begin{matrix} 0.6894 & 0.0342 & - 0.7236 \\ - 0.0533 & 0.9985 & - 0.0035 \\ 0.7224 & 0.0410 & 0.6902 \end{matrix}]$	$[\begin{matrix} - 1094.9922 \\ 32.2841 \\ 52.5594 \end{matrix}]$

Table 4. 3D coordinates of LED light sources based on stereo vision

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Table 4. 3D coordinates of LED light sources based on stereo vision

LED light source	Calibration value of space 3D coordinate /mm
$A (X, Y, Z)$	$(109.11,9.49, - 18.22)$
$B (X, Y, Z)$	$(81.87, - 56.13, - 18.21)$
$C (X, Y, Z)$	$(17.30, - 82.04, - 19.18)$
$D (X, Y, Z)$	$(- 47.21, - 56.28, - 21.45)$
$E (X, Y, Z)$	$(- 73.91,9.19, - 23.34)$
$F (X, Y, Z)$	$(- 46.95,75.59, - 23.34)$
$G (X, Y, Z)$	$(17.84,101.24, - 22.12)$
$H (X, Y, Z)$	$(82.67,74.91, - 20.19)$

Table 5. Diagonal distance of LED light sources based on stereo vision
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Table 5. Diagonal distance of LED light sources based on stereo vision
Parameter Value
l_AE /mm 183.10
l_BF /mm 184.32
l_CG /mm 183.31
l_DH /mm 184.61

Table 6. 3D coordinates of LED light sources based on specular reflection method

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Table 6. 3D coordinates of LED light sources based on specular reflection method

LED light source	Calibration value of space 3D coordinate /mm
$A (X, Y, Z)$	$(77.14, - 11.78,15.78)$
$B (X, Y, Z)$	$(51.71,46.19,48.42)$
$C (X, Y, Z)$	$(- 7.21,83.08,6.43)$
$D (X, Y, Z)$	$(- 64.47,53.03,30.22)$
$E (X, Y, Z)$	$(- 85.78, - 4.11,107.94)$
$F (X, Y, Z)$	$(- 62.53, - 69.55, - 22.40)$
$G (X, Y, Z)$	$(- 6.23, - 93.71, - 10.28)$
$H (X, Y, Z)$	$(51.01, - 69.85, - 16.61)$

Table 7. Diagonal distance of LED light sources based on specular reflection method
View table
Table 7. Diagonal distance of LED light sources based on specular reflection method
Parameter Value
l_AE /mm 187.34
l_BF /mm 177.38
l_CG /mm 177.58
l_DH /mm 175.01

Table 8. Three-dimensional coordinate error of the LED light source based on specular reflection and stereo vision
View table
Table 8. Three-dimensional coordinate error of the LED light source based on specular reflection and stereo vision
Parameter Three-dimensional coordinate error /mm
Specular reflection method Stereo vision method
MAE 6.34 0.63
RMSE 6.65 0.66

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Jiayuan Liu, Guohui Wang. Stereo Vision-based Calibration Approach for Position Parameters of LED in Photometric Stereo[J]. Laser & Optoelectronics Progress, 2022, 59(16): 1615001

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Paper Information

Category: Machine Vision

Received: May. 26, 2021

Accepted: Jun. 27, 2021

Published Online: Jul. 22, 2022

The Author Email: Guohui Wang (booler@126.com)

DOI:10.3788/LOP202259.1615001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Camera parameters

Table 1. Camera parameters

Table 2. Camera internal parameters

Table 2. Camera internal parameters

Table 3. Structural parameters of stereo vision system

Table 3. Structural parameters of stereo vision system

Table 4. 3D coordinates of LED light sources based on stereo vision

Table 4. 3D coordinates of LED light sources based on stereo vision

Table 5. Diagonal distance of LED light sources based on stereo vision

Table 5. Diagonal distance of LED light sources based on stereo vision

Table 6. 3D coordinates of LED light sources based on specular reflection method

Table 6. 3D coordinates of LED light sources based on specular reflection method

Table 7. Diagonal distance of LED light sources based on specular reflection method

Table 7. Diagonal distance of LED light sources based on specular reflection method

Table 8. Three-dimensional coordinate error of the LED light source based on specular reflection and stereo vision

Table 8. Three-dimensional coordinate error of the LED light source based on specular reflection and stereo vision