A Method for Extracting 3D Axis and Cross-Sections of Tunnel Point Cloud

Fig. 3. Comparison of fitting accuracy. (a) Boundary lines with different degrees of deviation; (b) root mean square error of fitting with different components as independent variable

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Fig. 4. Sketch of 3D axis points extraction

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Fig. 5. Solving normal vector of cross-section by infinitesimal method

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Fig. 6. Experimental data. (a) Data Ⅰ; (b) data Ⅱ; (c) data Ⅲ

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Fig. 7. Comparison of boundary points extracted by two methods. (a) Our method; (b) traditional method

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Fig. 8. Comparison of horizontal 2D midline extracted by two methods. (a) Our method; (b) method in Ref. [4]

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Fig. 9. Extraction of 3D central axis and cross-section of two sets of data. (a) Data Ⅰ; (b) data Ⅱ

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Fig. 10. Top view of two cross-sections with the same inner diameter and different longitudinal slopes

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Fig. 11. Sketch of cross-section extraction error

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Table 1. Main setting parameters
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Table 1. Main setting parameters
Parameter Value
$(θ_{m i n}, θ_{m a x})$ （160°， 200°）
$R e_{m a x}$ /cm 1.0
$d_{m a x}$ $2 \cdot R e$
$R a_{m i n}$ 80%
l /cm 0.1
e /cm 2.5

Table 2. Comparison of extraction results of two methods
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Table 2. Comparison of extraction results of two methods
Method Data Ⅰ Data Ⅱ Data Ⅲ
Time /s number Time /s number Time /s number
Our method 4.6 5154 4.2 2527 0.9 928
Traditional method 25.6 6351 26.0 4987 5.4 1090

Table 3. Comparison of extraction errors between two methods
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Table 3. Comparison of extraction errors between two methods
Error Our method Ref.［4］
$σ$ 2.7 177.1
$E_{m a x}$ 4.5 571.8
$E_{m i n}$ 0.3 0.004
$E_{m e a n}$ 2.4 72.6

Table 4. Analysis of the accuracy of tunnel cross-sections extraction

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Table 4. Analysis of the accuracy of tunnel cross-sections extraction

f	$\|a o\|$	Section 1			Section 2			Section 3			$\bar{\|a b\|}$ /mm
f	$\|a o\|$	$\|b o\|$ /mm	$\|a b\|$ /mm	ε /%	$\|b o\|$ /mm	$\|a b\|$ /mm	ε /%	$\|b o\|$ /mm	$\|a b\|$ /mm	ε /%	$\bar{\|a b\|}$ /mm
0	0.00	0.11	0.11	/	0.10	0.10	/	0.11	0.11	/	0.11
1%	50.00	49.39	0.61	1.22	49.32	0.68	1.36	49.74	0.26	0.52	0.52
2%	100.00	98.04	1.96	1.96	98.10	1.90	1.90	98.15	1.85	1.85	1.90
3%	150.00	146.42	3.58	2.39	146.40	3.60	2.40	146.46	3.54	2.36	3.57
4%	200.00	195.81	4.19	2.10	195.96	4.04	2.02	195.96	4.04	2.02	4.09
5%	250.00	242.40	7.60	3.04	242.35	7.65	3.06	242.47	7.53	3.01	7.59

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Dong Jing, Guangyu Zhang, Rufei Liu, Minye Wang. A Method for Extracting 3D Axis and Cross-Sections of Tunnel Point Cloud[J]. Laser & Optoelectronics Progress, 2022, 59(8): 0828006

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