## 2 Materials and Methods
### Materials  
The original dataset corresponds to an ALS flight campaign executed over the city of Avila (Spain). The data were acquired in April 2012 with a Leica ALS50-II sensor with a flying height of 1000 m, resulting in an original ground spacing of approximately 2 points/m\({}^{2}\) over urban and open terrain areas. Different test bed sites in terms of roughness and slope were used to validate the accuracy assessment of the ALS: an urban road stretch covered with asphalt (denoted by infrastructure), a building with variable heights (denoted by urban) and an abrupt natural area with vegetation, slopes and rocks (denoted by natural), (Figure 1a) as well as some point cloud image from ALS (Figure 1b). Reference data were derived [28] by a mobile mapping system (MMS), Optech Lynx, in May 2012, so that no significant changes of the test sites were possible. Although static laser scanning techniques usually provide better quality than MMS, especially if only a single station is required, everything become more complicated when we address large urban, infrastructure and natural areas since static laser technologies require many stations and thus error propagation and processing steps would make these static technologies less efficient. Table 1 presents information characterizing the three areas used (surface, density of LiDAR points, roughness and maximum height difference). More technical specifications about the ALS and MMS equipment are outlined in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Infrastructure** & **Urban** & **Natural** \\ \hline Area (m\({}^{2}\)) & 408.5 & 180.8 & 1772.3 \\ Mean density (points/m\({}^{2}\)) & 1.03 & 3.56 & 2.23 \\ Max height difference (m) & 1.57 & 1.65 & 14.64 \\
90 th percentile Roughness (m) & 0.013 & 0.138 & 0.107 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the three test bed sites. Figure 1: (**a**) Tests bed sites used in the analysis (in red), from left to right: urban (building), infrastructure (road) and natural (hillside). (**b**) point cloud image from airborne laser scanner (ALS). \begin{table}
\begin{tabular}{c c} \hline \hline
**Sensor** & **ALS50\_II SN48** \\ \hline X,Y position precision & 0.320 m \\ Z position precision & 0.120 m \\ Laser pulse rate used & 95.8 KHz \\ Scan field of view (half angle) & 22.50\({}^{\circ}\) \\ Point density (average) & 1.87 m\({}^{2}\) \\ Number of returns & 4 \\ Laser divergence & 0.22 mr \\ Max field of view & 75\({}^{\circ}\) \\ Max rate of acquisition & 120 KHz \\ Wavelength & 1064 nm \\ Standard deviation of GNSS & 0.05 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Technical characteristics of the LIDAR system. Regarding Table 2, there are some components that contribute to the final horizontal (X,Y) and vertical (Z) precision in the actual ALS dataset: (i) errors due to calibration of the GNSS/IMU and the scanner assembly; (ii) errors due to the complexity of the object (i.e., sloping terrains can lead to larger errors in the horizontal and vertical components); (iii) errors due to multipath reflections produced when the laser beam is reflected by another object on the ground before reaching the detector. Regarding planimetric error, it should be noted that the Y coordinate will be mainly affected by the roll angle, whereas the X coordinate will be affected by the pitch angle. Laser parameters (scan angle and range) will directly affect the Y coordinate. The positional accuracy samples of the three study cases (infrastructure, urban and natural) were computed using the open source software CloudCompare [29]. For the three positional accuracy samples, the MMS data were used as the ground truth. In the infrastructure case, the positional accuracy between the MMS and ALS points was computed as Z discrepancies (1D) due to its planar nature. In the other two study cases (urban and natural), the error was computed using the 3D coordinates (3D) since the normal vector of the surfaces does not follow the Z axis.