# Error Distribution Pattern Analysis of Mobile Laser Scanners for Precise As-Built BIM Generation
## 4 Results
### Error Distribution Patterns in MLS Devices  
In this section, the experimental results derived from the complete dataset were presented. A total of 88 planes were analyzed, and the analysis was primarily based on the mean and standard deviation values of the C2M distances measured on each plane. As previously mentioned, the mean C2M distance for each plane represents the central value of the error distribution pattern, while the standard deviation reflects the relative accuracy. Eighty-eight planes were analyzed using the proposed analysis method. Figure 8 presents representative results organized at the Column level. According to Figure 8, each MLS device exhibits distinct error distribution patterns and shows biases relative to the reference planes. MLS-01 appears to have more outer points than inner points, while MLS-02 exhibits this tendency more prominently. In contrast, MLS-03 shows a slightly greater number of inner points compared to other MLS devices. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**MLS** & **Dataset** & **Column** & **Plane** & **Max \(\Delta\mu\)** & **Max \(\Delta\sigma\)** & _p_**-Value** \\ \hline
01 & 01 & A & 02 & 0.007\% & 1.131\% & 0.727 \\
02 & 02 & A & 02 & 0.008\% & 1.076\% & 0.281 \\
03 & 01 & A & 01 & 0.003\% & 0.819\% & 0.532 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sensitivity analysis of random downsampling. To obtain a representative overall mean and Gaussian distribution for each MLS device, the C2M distance measurements of all points acquired from the analyzed planes were aggregated. Based on these aggregated data, the overall mean and corresponding histograms were generated for each MLS device as shown in Figure 9. Figure 10 shows a box plot generated from the mean error values of each MLS device. Table 4 presents overall mean and standard deviation for each MLS device. Based on these results, the error distribution patterns of each MLS device can be summarized as follows:  
The measured overall mean of MLS-01 is 4.3 mm, while the median is 4.4 mm, as shown in Figure 10. This suggests that MLS-01 exhibits a biased error distribution pattern relative to the reference planes, with a representative offset of 4.3 mm. Additionally, Figure 9a shows that the aggregated error distribution of MLS-01 forms a bell-shaped curve, indicating that a Gaussian distribution effectively characterizes the pattern. The standard deviation is measured at 7.6 mm, implying that approximately 68% of the data fall within one standard deviation from the mean, i.e., within the range of 4.3 \(\pm\) 7.6 mm, consistent with the characteristics of a normal distribution illustrated in Figure 9a. The measured overall mean and median of MLS-02 are both 9.2 mm, as shown in Figure 10. This suggests that MLS-02 exhibits a more biased error distribution pattern \begin{table}
\begin{tabular}{c c c} \hline \hline
**MLS Type** & **Mean Error (mm)** & **Standard Deviation (mm)** \\ \hline MLS-01 & 4.3 & 7.6 \\ MLS-02 & 9.2 & 10.8 \\ MLS-03 & \(-\)2.0 & 9.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Overall mean error and standard deviation for each MLS device. Figure 8: Top view of the representative column for each MLS device. Red points indicate outward deviations, and blue points indicate inward deviations relative to the reference surface. (**a**) MLS-01, (**b**) MLS-02, (**c**) MLS-03. Figure 9: Fitted Gaussian curves and histograms of C2M errors by MLS device. (**a**) MLS-01, (**b**) MLS-02, (**c**) MLS-03. relative to the reference planes, with a representative offset of 9.2 mm. Compared to MLS-01, MLS-02 shows a greater degree of bias. Figure 9b illustrates that the aggregated error distribution of MLS-02 forms a bell-shaped curve, indicating that a Gaussian distribution reasonably characterizes the pattern.