## 2 Materials and Methods
### Proposed Methodology
#### 2.3.1 Buildings Identification through DBSCAN Algorithm  
This section explains how the existing buildings can be identified starting from the ascending and descending datasets of PSs (merged in order to maximize the PSs density), by means of an AI algorithm based on DBSCAN and improved through additional conditions derived by engineering considerations. Other than isolated buildings, in urbanized areas, it is very common to find two or more buildings, with a common wall or separated by a seismic joint, only. It is worth noting that the proposed approach does not allow to distinguish single units but, in the abovementioned cases, the structural aggregate is considered as a single \"building\". The flowchart presented in Figure 3 describes the building identification through the DBSCAN algorithm. With respect to the flowchart shown in Figure 3, the first step of the procedure regards the selection of the PSs by topography (red continue box). It is worth noting that the PSs distribution is usually very heterogeneous in an urban zone: the buildings generally have good reflective properties, so it is very common to detect a density of PSs falling on them. In the areas between buildings, indeed, the PSs are most likely relative to the ground, so, for the purposes of this work, they represent noise and have to be neglected. For this reason, particular attention has to be given to the height of the PSs, \(\delta\). The value of \(\delta\) under which all the PSs are considered to be on the ground surface, is estimated. For the choice of this value, the distribution of the frequency of \(\delta\) for the dataset of the examined area is observed. Figure 2: Flowchart of the proposed methodology. In particular, attention is paid on the \(\delta\) value that shows a first decrease of frequency with respect to the previous one. All the PSs, which have \(\delta\) values less than the value identified as the upper limit, are supposed to be at the ground level and shall be discarded. The ground level is considered to have a topography given by the \(\delta\) mean value of all the discarded PSs. An additional vertical error of \(\pm\) 2 m is considered, corresponding to about one standard deviation, as specified in Section 2.1. The latter, summed to \(\delta\) associated to the ground PSs, led to the definition of the value under which all the PSs are neglected for the clustering. Moreover, since the one-floor point positioning can show an overlap with the ground points (because of the mentioned possible errors of positioning), an additional \(\delta\) can be considered, equal to the height of the one-floor buildings (e.g., 3.00-3.50 m, based on the engineering judgment of the user). This limit of the approach will be discussed in Section 4. The clusters constituted by the one-floor buildings could be identified by implementing a second cluster after the first above-described one, by opportunely setting the cut on \(\delta\) and the other parameters described herein. Once the first noise cut is done through the topographic considerations, the clustering algorithm DBSCAN can be implemented (red dashed box of the flowchart in Figure 3). As described in Section 2.2, the DBSCAN needs the setting of the two hyperparameters: _eps_ distance and _minPoints_. The optimal value for neighborhood radius _eps_ is generally determined through an approach consisting in plotting the mean of the distances between each point and its \(k\)th nearest neighbor, sorted in ascending order, where \(k\) is generally equal to _minPoints_[43; 44]. Then, the optimal value for _eps_ corresponds to the point of maximum curvature of the obtained graph. In this work, to have a better estimation based on the observation of the domain, _eps_ has been evaluated for different values of \(k\), ranging in the interval \([k_{inf},k_{sup}]\), where the boundaries are related to the PSs density of the examined area, obtained by dividing the number of PSs for the corresponding area occupied by buildings.