Three-Dimensional Reconstruction Based on Spatial Geometric Constraints Using Trinocular Multi-Line Laser Galvanometer

Fuping Qin; Guihua Liu; Huiming Huang; Lei Deng; Tao Song; Wencan Ju

doi:10.3788/AOS250699

Acta Optica Sinica, Volume. 45, Issue 15, 1511002(2025)

Three-Dimensional Reconstruction Based on Spatial Geometric Constraints Using Trinocular Multi-Line Laser Galvanometer

Fuping Qin^1,2, Guihua Liu^1,2、*, Huiming Huang^1,2, Lei Deng^1,2, Tao Song^1,2, and Wencan Ju^1,2

¹School of Information and Control Engineering, Southwest University of Science and Technology, Mianyang 621010, Sichuan , China

²Robot Technology Used for Special Environment Key Laboratory of Sichuan Province, Mianyang 621010, Sichuan , China

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Figures & Tables(20)

Fig. 1. Schematic diagram of system reconstruction process

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Fig. 2. Trinocular laser galvanometer system calibration model

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Fig. 3. Trinocular epipolar constraint schematic diagram

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Fig. 4. Trinocular multi-line laser galvanometer system hardware structure

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Fig. 5. Reprojection errors of matched points across three views. (a) Left view error; (b) center view error; (c) right view error

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Fig. 6. Standard target surface and circle center localization with numbering. (a) Standard target pattern; (b) circle center localization and numbering

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Fig. 7. Statistical results of threshold errors. (a) Mean slope error; (b) mean epipolar line distance error; (c) mean 3D distance error; (d) three-view mean projection error

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Fig. 8. Three-view laser center point matching and local mismatching effects. (a) Laser center point matching between the left and middle images; (b) laser center point matching between the left and right images; (c) laser center point matching between the middle and right images

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Fig. 9. Surface reconstruction results of various methods under different laser line numbers. (a) Results of different laser line numbers; (b) method in Ref. [23]; (c) method in Ref. [28]; (d) ours

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Fig. 10. Reconstruction of step standard parts. (a) Standard part object; (b) point cloud of standard part; (c) fitting of different step planes

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Fig. 11. Error analysis of step reconstruction. (a) MAE; (b) RMSE

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Fig. 12. Scanning and reconstruction of a plaster statue. (a) Real object image; (b) reconstructed point cloud; (c) point cloud detail

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Fig. 13. Reconstruction of high reflective cup. (a) Real object image; (b) reconstructed point cloud; (c) point cloud detail

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Fig. 14. Reconstruction of cultural relics. (a) Real object image; (b) front view of point cloud; (c) contour details of point cloud; (d) texture details of point cloud

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Table 1. TGPM calibration and mean reprojection error results for three views

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Table 1. TGPM calibration and mean reprojection error results for three views

System	TGPM	MRE
LC-R	$[\begin{matrix} - 0.00331399 & 4.61988 \times 10^{- 5} & 0.00311108 & 0.997453 \\ 0.000559144 & 0.00426692 & 0.00116522 & - 0.0710443 \\ 9.7039 \times 10^{- 7} & - 8.41904 \times 10^{- 9} & 2.23307 \times 10^{- 6} & - 0.000125174 \end{matrix}]$	0.071695
LR-C	$[\begin{matrix} - 0.00709883 & - 0.000292833 & 0.00415404 & 0.999774 \\ 0.000302525 & 0.00764634 & 0.00252615 & - 0.0178823 \\ 8.26317 \times 10^{- 7} & - 1.92629 \times 10^{- 7} & 4.37013 \times 10^{- 6} & - 2.12664 \times 10^{- 5} \end{matrix}]$	0.053784
CR-L	$[\begin{matrix} 0.0076697 & - 0.000222777 & - 0.00121432 & 0.999789 \\ 0.000240899 & - 0.00739113 & - 0.00178391 & 0.0174077 \\ 7.7714 \times 10^{- 7} & - 1.94405 \times 10^{- 7} & - 4.07259 \times 10^{- 6} & 8.58108 \times 10^{- 5} \end{matrix}]$	0.083056

Table 2. Laser center point matching effects of different methods

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Table 2. Laser center point matching effects of different methods

Method	Frame number	$R_{L P M R, L}$ /%	$R_{L P M R, C}$ /%	$R_{L P M R, R}$ /%	R_LPMA /%
Li， et al.^［23］	100	93.99	94.75	86.78	70.29
Li， et al.^［23］	200	93.65	90.63	89.11	65.56
Shao， et al.^［28］	100	89.52	90.07	86.65	88.10
Shao， et al.^［28］	200	77.77	80.56	78.59	76.52
Ours	100	89.09	89.66	82.11	92.57
Ours	200	88.35	86.47	83.97	91.71

Table 3. Mean values of LPMR and LRMA of laser points for each constraint method under different numbers of laser lines

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Table 3. Mean values of LPMR and LRMA of laser points for each constraint method under different numbers of laser lines

Method	Number of laser lines	Frame number	R_LPMR，L /%	R_LPMR，C/%	R_LPMR，R /%	R_LPMA /%
Li， et al. ^［23］	7	200	93.65	90.63	89.11	65.56
	11	200	95.52	91.59	90.29	57.78
	15	200	96.71	90.19	91.16	48.42
Shao， et al. ^［28］	7	200	86.82	84.12	82.55	85.05
	11	200	87.25	83.67	82.38	81.14
	15	200	87.42	81.48	82.39	76.16
Ours	7	200	88.35	86.47	83.97	91.71
	11	200	89.09	85.38	84.13	86.65
	15	200	89.16	83.06	84.04	84.05

Table 4. Seven measurement results of proposed algorithm

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Table 4. Seven measurement results of proposed algorithm

Step number	1	2	3	4	5	6	7
The first step	3.0830	3.0853	3.0918	3.0273	3.0669	3.0474	2.9679
The second step	0.9970	1.0244	1.0273	1.0245	1.0037	0.9786	0.8925
The third step	0.4998	0.5136	0.5167	0.4844	0.5088	0.4897	0.3668
The fourth step	0.3027	0.3044	0.3104	0.2987	0.3114	0.2894	0.2723

Table 5. Step measurement results of different methods

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Table 5. Step measurement results of different methods

Method	Step number	Standard value of step	Average of step measurement	MAE	RMSE
Li， et al.^［23］	The first step	3	3.002750	0.106050	0.106086
	The second step	1	0.912450	0.112950	0.142908
	The third step	0.5	0.484100	0.151800	0.152630
	The fourth step	0.3	0.238050	0.122950	0.137675
Shao， et al.^［28］	The first step	3	2.816267	0.231733	0.259937
	The second step	1	0.802567	0.197433	0.203665
	The third step	0.5	0.489730	0.121267	0.131778
	The fourth step	0.3	0.390733	0.090733	0.111403
Liu， et al.^［21］	The first step	3	2.985675	0.021350	0.022965
	The second step	1	0.938913	0.061088	0.064498
	The third step	0.5	0.494950	0.015100	0.017724
	The fourth step	0.3	0.306388	0.017813	0.019156
Ours	The first step	3	3.052286	0.061457	0.066447
	The second step	1	0.992571	0.030257	0.044686
	The third step	0.5	0.482829	0.028343	0.051593
	The fourth step	0.3	0.284186	0.024071	0.048823

Table 6. Time consumption of each module of algorithm unit: ms
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Table 6. Time consumption of each module of algorithm unit: ms
Module LCE LCSM LCFM Total
Time consumption 3.005 10.235 1.840 15.080

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Fuping Qin, Guihua Liu, Huiming Huang, Lei Deng, Tao Song, Wencan Ju. Three-Dimensional Reconstruction Based on Spatial Geometric Constraints Using Trinocular Multi-Line Laser Galvanometer[J]. Acta Optica Sinica, 2025, 45(15): 1511002

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