## 2 Materials and Methods
### Materials
For a point cloud to point cloud comparison, if the reference cloud is dense enough, the distance to its nearest neighbor is almost as precise as the true distance on the real-world surface. However, the resulting distance is the vector's module, namely, the unsigned distance. To provide signed errors, a local 2.5D triangulation was created from the MMS point cloud (of higher point density), which defines the normal vectors according to each triangular face. Moreover, meshing is also carried out since the distance computation could fail in poor/irregular density clouds. The distance from each point in the ALS cloud is computed to the nearest triangle in the reference mesh (MMS) along its normal vector. This procedure is generally more robust, faster and more accurate than a nearest neighbor procedure, but it is constrained according to the mesh quality. The results of Table 4 and Figure 2 characterize the error data and verify that the error data in the three study cases are non-normal. The check of the normality assumption can be performed by the application of numerical tests or by visual methods (e.g., quantile-quantile plots--Figure 2), in cases where the sample size is very large. In this study, since the sample sizes are less than 5000 points, the robust version [30] of the Jarque-Bera test of normality was employed. The original Jarque-Bera test uses the sum of the squared sample measures of skewness and kurtosis. However, since the sample moments are even more sensitive to outliers than the sample mean, we employ a robust estimator of scale in the denominators of skewness and kurtosis [31]. \begin{table}
\begin{tabular}{c c} \hline
**Sensor** & **Optech Lynx** \\ \hline X,Y position precision & 0.030 m \\ Z position precision & 0.050 m \\ Roll and Pitch & 0.005\({}^{\circ}\) \\ True heading & 0.015\({}^{\circ}\) \\ Measuring principle & Time of Flight (ToF) \\ Maximum range & 200 m \\ Range precision & 8 mm, (1\(\sigma\)) \\ Range accuracy & \(\pm\)10 mm, (1\(\sigma\)) \\ Laser measurement rate & 75–500 kHz \\ Measurement per laser pulse & Up to 4 simultaneous \\ Scan frequency & 80–200 Hz \\ Laser wavelength & 1550 nm (near-infrared) \\ Scanner field of view & 360\({}^{\circ}\) \\ Operating temperature & 10 \({}^{\circ}\)C–40 \({}^{\circ}\)C \\ Angular resolution & 0.001\({}^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Technical characteristics of the mobile mapping system (MMS) Optech Lynx. The key feature of this test is the robust estimation of the dispersion in the skewness and kurtosis instead of using the second-order central moment. The results are outlined in Table 3, where the critical value according to a chi-square distribution and the \(p\)-values of the associated statistics are presented. A visual way to analyze the data normality is the use of the adequate quantile-quantile plot (QQ-plot). A QQ-plot is a probability plot, which is a graphical method for determining if a dataset follows a specific probability model by plotting the empirical distribution function of data with respect to the quantiles of the desired probability distribution (the normal distribution in these examples). If data actually follow a normal distribution, all the points will appear around a straight line. This line assumes that the empirical quantiles are identical to the theoretical ones. If there are points that are far away from the straight line, the data are not normally distributed. Figure 2 shows the QQ-plots for each of the three study cases. To characterize a non-normal sample, robust statistical estimators must be used (Table 4). The robust statistical analysis was selected according to [PERSON] et al. [32]. The adopted values are the median (m) for the measure of the central tendency and the median absolute deviation (MAD) [18; 19] for measure of the dispersion. To provide the thresholds for the positional accuracy assessment, a normalized value of the MAD was employed through the NMAD (NMAD = 1.4826 MAD), as proposed by [PERSON] & Hohle [33].