# Error Distribution Pattern Analysis of Mobile Laser Scanners for Precise As-Built BIM Generation
## 4 Results
### Error Distribution Patterns in MLS Devices
The standard deviation is measured at 10.8 mm, implying that approximately 68% of the data fall within one standard deviation from the mean, i.e., within the range of 9.2 \(\pm\) 10.8 mm, consistent with the characteristics of a normal distribution illustrated in Figure 9b. As a result, MLS-02 not only exhibits a more biased error pattern but also shows lower data precision compared to MLS-01. The measured overall mean of MLS-03 is -2.1 mm, while the median is -2.0 mm, as shown in Figure 10. This suggests that MLS-03 exhibits a more biased error distribution relative to the reference planes, with a representative offset of -2.1 mm in the inward direction. Compared to MLS-01 and MLS-02, MLS-03 shows an opposite bias pattern. Figure 9c shows that the aggregated error distribution of MLS-03 forms a bell-shaped curve, indicating that a Gaussian distribution reasonably characterizes the pattern. The standard deviation is 9.3 mm, implying that approximately 68% of the data fall within one standard deviation from the mean, i.e., within the range of -2.1 \(\pm\) 9.3 mm, consistent with the characteristics of a normal distribution illustrated in Figure 9c. As a result, MLS-03 exhibits an inward bias pattern opposite to those of MLS-01 and MLS-02, with data precision higher than MLS-02 but lower than MLS-01. Figures 11-13 present the error distribution curves of MLS-01, MLS-02, and MLS-03, respectively. According to Figures 12 and 13, MLS-02 and MLS-03 exhibit consistent error patterns across all columns within each of the four datasets, particularly when considering the entire set of planes. In contrast, the error distribution curve of MLS-01 shows less consistency across planes within individual columns compared to those of MLS-02 and MLS-03. In other words, MLS-01 shows relatively unstable error patterns and point distribution consistency within a single dataset. However, from the perspective of the overall analysis, MLS-01 still demonstrates a clearly biased error distribution, and the  
Figure 10: Box plot of mean errors and median errors for all planes in each MLS device. measured overall mean error is considered sufficient to serve as a correction factor. This aspect is further examined in Section 4.4. As a result, our findings reveal that each MLS device exhibits a unique and consistent biased error distribution pattern relative to the actual surface of the objects. These findings are clearly distinguished from those of previous studies. [PERSON] et al. (2020), who shared a similar objective with our study, measured the dimensions of architectural components such as doors and windows using MLS point clouds. Their study reported that a handheld MLS device exhibited a mean error of 7.8 mm and a standard deviation of 4.3 mm. This mean error was presented as an absolute value, making it difficult to reflect the directional bias, which is the central focus of our study. This limitation is commonly found in other related works, as reviewed in Section 2.1. Meanwhile, [PERSON] and [PERSON] (2020) presented positive and negative dimensional errors for BIM elements generated from an iPad LiDAR device. However, their results represent proportional deviations in overall object size, not the internal error patterns in point clouds that our study aims to investigate. Figure 11: Error distribution curves of MLS-01 at the Column Level. (**a**) Dataset 01—Column A, (**b**) Dataset 01—Column B, (**c**) Dataset 02—Column A, (**d**) Dataset 02—Column B, (**e**) Dataset 03—Column A, (**f**) Dataset 03—Column B. According to Figures 11-13, as well as Appendix A, the mean errors measured from opposing planes were highly similar. This suggests that RMSE minimization during ICP registration balances error across opposing planes. In addition, the plane-level mean errors were consistently distributed within a narrow range, indicating stable error characteristics. If the error distribution had varied significantly in direction across planes within the same dataset, such consistency would not have been observed.