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

Jiayuan Liu; Guohui Wang

doi:10.3788/LOP202259.1615001

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 16 >Page 1615001 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 16, 1615001 (2022)

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

Jiayuan Liu and Guohui Wang^*

Author Affiliations

School of Optoelectronic Engineering, Xi’an Technological University, Xi’an 710021, Shaanxi , China

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DOI: 10.3788/LOP202259.1615001 Cite this Article Set citation alerts

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 Copy Citation Text

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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

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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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 1. Camera 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 2. Camera internal parameters

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 3. Structural parameters of stereo vision system

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 4. 3D coordinates 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 5. Diagonal distance of LED light sources based on stereo vision

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 6. 3D coordinates 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 7. Diagonal distance of LED light sources based on specular reflection method

Parameter	Three-dimensional coordinate error /mm
Parameter	Specular reflection method	Stereo vision method
MAE	6.34	0.63
RMSE	6.65	0.66

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

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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