## 3 Results
### Validation of the Results  
The validation of the results obtained through the proposed methodology has been performed with respect to the clustering that represents the novelty of the work. In detail, the performed validation consists of comparing the clustering results, obtained as described in Section 3.2.3 thanks to DBSCAN algorithm, to the point cloud identified, for the same buildings through a detailed analysis of the PSs. Unfortunately, we do not have the ground truth for the considered areas, i.e., the real match between the points and the clusters, and, in general, it is difficult to find datasets with this information. For this reason, in order to carry out our validation, a ground truth has been built by applying a controlled procedure, performed without the aid of AI algorithms. In detail, the performed procedure is characterized by the following steps: (i) the schematic volumes of the building, obtained from the open-source Regional Technical Numerical Map (CTR) of Lazio Region [51], are reconstructed; (ii) all the PSs intersecting the volumes themselves are selected, considering a buffer of 2.5 m around; (iii) as proposed in Section 3.2.1, the PSs having a \(\delta\) under the \(\delta\) limit used in Area 1 (see Table 1) are neglected. The procedure is schematically represented in Figure 17, with reference to the building 14 of Area 1 (see Figure 18). The grey volume shows the step (i) of the procedure; then, all the PSs in a buffer of 2.5 m from the edges of the building are considered, according to step (ii); finally, the PSs under a red line at \(\delta\) height used in Area 1 (see Table 1) are neglected (step (iii)).  
Figure 17: Target building of the sample Area 1 (no. 14 in Figure 18): building’s volume from CTRR and PSs, with identification of the \(\delta\) limit.  
Due to the effort related to this procedure, it has been repeated only for the buildings in Area 1. A spatial check has been done, as shown in Figure 18 where the floor plan view of the buildings and the selected PSs are represented. Moreover, the rectangles delimiting the clusters obtained through DBSCAN are also reproposed to highlight, on one side, that there is a general good agreement between the buildings' plans geometries (from CTR) and the rectangles delimiting the previous clusters, and, on the other side, that almost in every case, the PSs by the validation procedure are included in them. Only in one case, this is not verified: for building no. 9; in fact, 4 PSs are external to the corresponding rectangle. This means that the proposed algorithm had excluded them from the cluster, while the built ground truth includes them. Moreover, the building footprints under the clusters allow observing that some PSs belonging to building no. 7 were included in the cluster of building 11 since the 11 th rectangle extends to the south side of building no. 7.  
The comparison of the results has been done not only in spatial terms, but also in terms of number of PSs included in each cluster. The number of _ASC_ and _DES_ PSs, and the total number of PSs composing the 19 clusters of Area 1, are reported in Table 2 (results from the proposed methodology) and Table 3 (results for the ground truth). There is a good agreement between the clusters' composition. Indeed, for 17 clusters out of 19, the difference is contained in the 5%, for cluster no. 9 is 8% and for cluster no. 12 is 15%.