## 2 Materials and Methods
### Precision and Accuracy Evaluation  
To evaluate the accuracy of the Leica P40 reference cloud, we created an additional 21 control points (CPs) georeferenced using the total station (see Figure 7 for the placement of these CPs). The accuracy was expressed as the root mean square deviation (_RMSD_) between these points and the closest surface of a triangular network created from the nearest 15 points from the Leica P40 point cloud:  
Figure 5: The cloud obtained using the GeoSLAM Zeb Horizon scanner colored according to the intensity of the reflected signal. Figure 6: An example of the targets used as GCPs for the transformation of the GeoSLAM point cloud into the Czech georeferencing system. (**a**) Black and white scan; (**b**) the target color-coded according to the reflection intensities. \[RMSD=\sqrt{\frac{\sum_{i=1}^{n}d_{i}^{2}}{n}} \tag{1}\]  
where \(d\) is the minimum distance between the tested point (be it a control point or a point from a cloud) and the surface of a local TIN network created from the reference cloud (Leica P40), and \(n\) is the number of points in the tested cloud. Further, the accuracy of the transformation of both GeoSLAM clouds into the Czech coordinate system using high-reflection targets for further comparisons was evaluated using root mean square error (\(RMSE\)), defined as:  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(e_{x_{i}}^{2}+e_{y_{i}}^{2}+e_{z_{i}}^{2} \right)}{3n}} \tag{2}\]  
where \(e_{x}\), \(e_{y}\), and \(e_{z}\) are coordinate corrections of GCPs in the GeoSLAM cloud after its transformation into the Czech coordinate system from the same points georeferenced using the total station, and n is the number of points. For further processing, the data were cropped and cleaned to capture solely the bridge structure. Leica P40 (reference) data were cropped to capture a slightly larger area to prevent any issues with evaluation on the edges of the cloud. If any part of the bridge was not captured in the reference data (e.g., due to obstruction by vegetation), it was also removed from the GeoSLAM data. Further evaluation was performed in two main stages:  
1. Evaluation of the overall agreement by comparing the Zeb Horizon cloud with the reference cloud from the Leica P40 1. Absolute comparison (includes the effect of inaccuracy in the determination of GCPs) 2. Relative comparison (comparison of shape and size--after ICP transformation of the whole GeoSLAM cloud on the reference cloud)
2. Local profile-by-profile evaluation for determining local deformations 1. Absolute (overall profile location, showing local systematic errors) 2. Relative (determination of local deformation and local accuracy)  
Figure 7: Locations of control points on the bridge (red dots). _RMSD_ (Equation (1)) was used as the accuracy parameter for all cloud comparisons. In view of the fact that Zeb Horizon clouds suffer from relatively high noise (with a maximum variance of 10-12 cm on a planar surface), it seems pertinent to smooth the data out. The Moving Least Squares (MLS) smoothing method seems to be a suitable way for such denoising [34] before further use. For this reason, the whole comparison was performed twice--separately for the original data and for data smoothed using this method. The clouds were processed and compared in the freely available software CloudCompare ver. 2.12.4. The Compute cloud/cloud distance function based on creating a local triangular network from the 15 nearest points (Local modeling tab, Local model option--2D1/2 Triangulation) was used for cloud comparison. The \"Smooth using MLS function\" (in the Plugins/PCL wrapper menu, according to [34]) command with the neighborhood size (search radius) set to 0.15 m, Polynomial Order 2 and Squared Gaussian Parameter 0.0009 (corresponding to a standard length measurement of 0.03 m) were used for smoothing. The clouds produced in this way were called GeoSLAM 1-MLS and GeoSLAM 2-MLS, respectively. The Fine Registration ICP function (Tools/Registration menu) was used for the ICP transformation of the clouds.