# Error Distribution Pattern Analysis of Mobile Laser Scanners for Precise As-Built BIM Generation
## 4 Results
### Sensitivity Analysis of Random Doversampling  
The proposed analysis method employs the random option of the subsampling tool in the open-source software CloudCompare. To evaluate the sensitivity of random down  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Title 2**} & \multicolumn{2}{c}{**Title 3**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**Column A**} & \multicolumn{2}{c}{**Column B**} \\ \cline{3-6}
**MLS Point Clouds** & \multicolumn{2}{c}{**Individual**} & \multicolumn{2}{c}{**Total**} & \multicolumn{2}{c}{**Individual**} & \multicolumn{2}{c}{**Total**} \\  & & **Plane** & **(Four** & **Planes**)** & **Plane** & **(Four** & **Planes**)** \\ \hline \multirow{3}{*}{MLS-01} & 01 & 13,000 & 52,000 & 9000 & 36,000 \\  & 02 & 25,000 & 10,0000 & 13,900 & 55,600 \\  & 03 & 20,993 & 83,972 & 13,994 & 55,976 \\ \hline \multirow{3}{*}{MLS-02} & 01 & 20,000 & 80,000 & 8995 & 35,980 \\  & 02 & 16,000 & 64,000 & 13,000 & 52,000 \\ \cline{1-1}  & 03 & 23,000 & 92,000 & 15,000 & 60,000 \\ \cline{1-1}  & 04 & 18,000 & 72,000 & 11,000 & 44,000 \\ \hline \multirow{3}{*}{MLS-03} & 01 & 28,000 & 112,000 & 18,000 & 72,000 \\ \cline{1-1}  & 02 & 32,000 & 128,000 & 21,000 & 84,000 \\ \cline{1-1}  & 03 & 28,000 & 112,000 & 13,000 & 52,000 \\ \cline{1-1}  & 04 & 21,000 & 84,000 & 10,000 & 40,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The number of points in each Column used for analysis.  
Figure 7: Examples of extracted Columns in MLS point clouds and results of plane segmentation. (**a**) MLS-01, (**b**) MLS-02, (**c**) MLS-03.  
sampling, one plane was selected for each MLS device. The selected planes correspond those with the lowest sampling ratios among the datasets acquired by each MLS device. Specifically, Plane 02 of Column A in Dataset 01 was selected for MLS-01, Plane 02 of Column A in Dataset 02 for MLS-02, and Plane 01 of Column A in Dataset 01 for MLS-03. The respective sampling ratios were 0.10, 0.14, and 0.15.  
For each selected plane, random downsampling was performed 30 times, and sensitivity was analyzed based on the coordinate values in the direction normal to the plane, which was the primary focus of the analysis. Two indicators were used for comparison: the relative variation of the mean \((\Delta\mu)\) and relative variation of the standard deviation \((\Delta\sigma)\), as defined in Equations (4) and (5). In addition, a one-way ANOVA test was conducted. The null hypothesis was that there is statistically significant difference in mean values between the raw and sampled groups. The ANOVA results with _p_-value above 0.05 support the conclusion that the mean geometry of the raw point cloud remains statistically unaffected by the random downsampling process.  
\[\Delta\mu=\frac{\left|\mu_{sampling}-\mu_{raw}\right|}{\left|\mu_{raw}\right|} \tag{4}\]  
\[\Delta\sigma=\frac{\left|\sigma_{sampling}-\sigma_{raw}\right|}{\left|\sigma_ {raw}\right|} \tag{5}\]  
As a result of the analysis, the maximum relative variations in mean and standard deviation were \(\Delta\mu=0.007\%\) and \(\Delta\sigma=1.131\%\), respectively. For MLS-02, they were \(\Delta\mu=0.008\%\), and \(\Delta\sigma=1.076\%\), and for MLS-03, \(\Delta\mu=0.003\%\) and \(\Delta\sigma=0.819\%\). All maximum \(\Delta\mu\) values remained below 0.01%, and all maximum \(\Delta\sigma\) values below 1.2%. Additionally, the ANOVA results yield _p_-values of 0.727 for MLS-01, 0.281 for MLS-02, and 0.532 for MLS-03, indicating that none of the differences were statistically significant (_p_ > 0.05). The overall sensitivity analysis results are summarized in Table 3.  
Therefore, the random downsampling applied in this study preserves the distributional characteristics of the raw point clouds at the plane level and maintains the integrity of the internal error distribution patterns.