Point Cloud Plane Fitting Algorithm Based on Least Square Median

Fig. 3. Line laser sensor platform, sheet metal parts, and point cloud data. (a) Line laser sensor platform; (b) sheet metal parts and surface point cloud

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Fig. 4. Fitting effect of point cloud on sheet metal surface. (a) Sheet metal part surface point cloud; (b) RANSAC and PCA fitting; (c) LMedS and PCA fitting

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Fig. 5. Desktop point cloud containing sundries such as cups and hats

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Fig. 6. Fitting effect of desktop point cloud with sundries such as cups and hats. (a) Desktop point cloud; (b) RANSAC fitting;(c) LMedS fitting

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Fig. 7. Comparison of fitting results between LMedS and RANSAC. (a) Running time of two algorithms; (b) standard deviation of two algorithms

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Fig. 8. Correct fitting results and fitting results with certain errors of wall point cloud using LMedS. (a) Correct fitting plane; (b) (c) fitting plane with large error

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Fig. 9. Correct fitting results and fitting results with certain errors of point cloud on surface of sheet metal parts using LMedS. (a) Correct fitting plane; (b) fitting plane with large error

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Fig. 10. Correct fitting results and fitting results with certain errors of desktop point cloud using LMedS. (a) Correct fitting plane; (b) fitting plane with large error

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Table 1. P=95%, minimum number of iterations K with minimum number of samples n
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Table 1. P=95%, minimum number of iterations K with minimum number of samples n
n $ε$ ：contaminated data fraction
10% 20% 30% 40% 50%
2 2 3 5 7 11
3 2 4 7 12 22
5 4 8 17 38 95
10 7 27 105 494 3067

Table 2. Comparison of plane parameters of point cloud fitting on wall of St. Gallen Cathedral
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Table 2. Comparison of plane parameters of point cloud fitting on wall of St. Gallen Cathedral
Method Points A B C D σ Time /s
RANSAC 185747 0.0354 0.9993 0.0037 -27.7172 1.0377 1.32
LMedS 185747 0.0325 0.9960 0.0034 -27.7268 0.9398 0.90

Table 3. Comparison of surface point cloud fitting plane parameters of sheet metal parts
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Table 3. Comparison of surface point cloud fitting plane parameters of sheet metal parts
Method Points A B C D σ Time /s
RANSAC 332520 0.0150 0.0128 0.9998 16.8170 0.2877 2.21
LMedS 332520 0.0149 0.0129 0.9998 16.8281 0.3032 1.57

Table 4. Comparison of fitting plane parameters of desktop point cloud including cups, hats, and other sundries
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Table 4. Comparison of fitting plane parameters of desktop point cloud including cups, hats, and other sundries
Method Points A B C D σ Time /s
RANSAC 593334 0.2309 -0.0450 0.9719 1.3150 0.0282 4.40
LMedS 593334 0.2282 -0.0428 0.9726 1.3156 0.0343 2.81

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Yang Wang, Junyuan Wang, Wenhua Du, Nengquan Duan. Point Cloud Plane Fitting Algorithm Based on Least Square Median[J]. Laser & Optoelectronics Progress, 2023, 60(4): 0410019

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Paper Information

Category: Image Processing

Received: Dec. 13, 2021

Accepted: Jan. 5, 2022

Published Online: Feb. 14, 2023

The Author Email: Wang Junyuan (wangjy@nuc.edu.cn)

DOI:10.3788/LOP213208

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. P=95%, minimum number of iterations K with minimum number of samples n

Table 1. P=95%, minimum number of iterations K with minimum number of samples n

Table 2. Comparison of plane parameters of point cloud fitting on wall of St. Gallen Cathedral

Table 2. Comparison of plane parameters of point cloud fitting on wall of St. Gallen Cathedral

Table 3. Comparison of surface point cloud fitting plane parameters of sheet metal parts

Table 3. Comparison of surface point cloud fitting plane parameters of sheet metal parts

Table 4. Comparison of fitting plane parameters of desktop point cloud including cups, hats, and other sundries

Table 4. Comparison of fitting plane parameters of desktop point cloud including cups, hats, and other sundries