• Laser & Optoelectronics Progress
  • Vol. 60, Issue 4, 0410019 (2023)
Yang Wang, Junyuan Wang*, Wenhua Du, and Nengquan Duan
Author Affiliations
  • School of Mechanical Engineering, North University of China, Taiyuan 030051, Shanxi, China
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    DOI: 10.3788/LOP213208 Cite this Article Set citation alerts
    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 Copy Citation Text show less
    Point cloud on wall of St. Gallen Cathedral
    Fig. 1. Point cloud on wall of St. Gallen Cathedral
    Fitting effect of point cloud on wall of St. Gallen Cathedral. (a) Wall point cloud; (b) RANSAC and PCA fitting; (c) LMedS and PCA fitting
    Fig. 2. Fitting effect of point cloud on wall of St. Gallen Cathedral. (a) Wall point cloud; (b) RANSAC and PCA fitting; (c) LMedS and PCA fitting
    Line laser sensor platform, sheet metal parts, and point cloud data. (a) Line laser sensor platform; (b) sheet metal parts and surface point cloud
    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
    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
    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
    Desktop point cloud containing sundries such as cups and hats
    Fig. 5. Desktop point cloud containing sundries such as cups and hats
    Fitting effect of desktop point cloud with sundries such as cups and hats. (a) Desktop point cloud; (b) RANSAC fitting;(c) LMedS fitting
    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
    Comparison of fitting results between LMedS and RANSAC. (a) Running time of two algorithms; (b) standard deviation of two algorithms
    Fig. 7. Comparison of fitting results between LMedS and RANSAC. (a) Running time of two algorithms; (b) standard deviation of two algorithms
    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
    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
    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
    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
    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
    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
    nε:contaminated data fraction
    10%20%30%40%50%
    2235711
    32471222
    548173895
    107271054943067
    Table 1. P=95%, minimum number of iterations K with minimum number of samples n
    MethodPointsABCDσTime /s
    RANSAC1857470.03540.99930.0037-27.71721.03771.32
    LMedS1857470.03250.99600.0034-27.72680.93980.90
    Table 2. Comparison of plane parameters of point cloud fitting on wall of St. Gallen Cathedral
    MethodPointsABCDσTime /s
    RANSAC3325200.01500.01280.999816.81700.28772.21
    LMedS3325200.01490.01290.999816.82810.30321.57
    Table 3. Comparison of surface point cloud fitting plane parameters of sheet metal parts
    MethodPointsABCDσTime /s
    RANSAC5933340.2309-0.04500.97191.31500.02824.40
    LMedS5933340.2282-0.04280.97261.31560.03432.81
    Table 4. Comparison of fitting plane parameters of desktop point cloud including cups, hats, and other sundries
    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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