## 3 Results  
The two proposed fully automatic segmentation approaches were tested on two case studies with very different characteristics (e.g., different types of urban development and average point density value of the ALS input data) in order to increase the robustness and completeness of the proposed investigation. First, an ALS data set with reference data made available via the International Society for Photogrammetry and Remote Sensing (ISPRS) web site [27] over downtown Toronto (Canada) was used to evaluate the performance of the two above-described segmentation approaches. This test case contained a mixture of 58 low and high-storey buildings; readers can refer to [26] for a more detailed description of characteristics and technical specifications of this benchmark dataset. Figure 5 shows a visual result of the 3D reconstruction using the proposed segmentation methods. Processing was conducted on a consumer laptop (Intel Core i7, 8G RAM). The average performances over the 58 buildings of the two roof segmentation approaches are shown in Table 1. The region growing segmentation approach exhibited slightly better performances but required a greater computational time than the clustering-based approach. Figure 5: _Cont._A 3D reconstruction of one complex palace, constructed in the 1950s with a total surface of 3690 m\({}^{2}\), located in one of the main squares of the historical center of Matera (see Figure 6a), for which building a celerimetric survey made through a total station is available, was carried out from a LIDAR point cloud (see Figure 6a). This complex building was then manually reconstructed in 3D, as shown in Figure 6b, using commercial software that implements Building Information Modeling (BIM) technology [29]. This manually reconstructed 3D building is considered the gold standard because it is based on detailed survey measurements and, therefore, it can be compared with the outcomes of the two proposed segmentation approaches in order to evaluate their vertex geometry accuracy. Figure 6c,d shows the reconstruction results for the data collected for the building test case in Matera. Processing was conducted on a consumer laptop (Intel Core i7, 8G RAM) and is presented as solid models with simplified facades and faithfully reflected roof structure considering that the aims of these kinds of approaches are to realize an interactive visualization covering large areas. The performance of the two approaches, evaluated as described in Section 2.5, are shown in Table 2. The region growing segmentation approach exhibited slightly better performances but required a greater computational time (two times greater) than the clustering-based approach, similar to the performance in the previously described case study over downtown Toronto. Hence, the region growing approach analysing the LIDAR cloud points one by one can be more efficient to reach the best spatial detail possible but, at the same time, this process is more time-consuming. However, the potential-based method can also yield a stable estimate on the number of clusters and initial cluster centers which are needed for the following fuzzy k-means clustering calculation for an efficient segmentation process, saving computational resources. The better performances of both proposed methodologies on the Matera building with respect to the Toronto case study could be associated with the different quality of input ALS data adopted. This is confirmed by the fact that the minimum value \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Segmentation** & **Average RMSE** & **Average Dist.** & **Average Dist** & **Average Computational** \\
**Approach** & **(m)** & **Mean (m)** & **St. Dev. (m)** & **Time (sec)** \\ \hline Clustering & 3.81 & 3.20 & 2.08 & 17 \\ Region-growing & 2.65 & 2.09 & 1.61 & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average performances of the geometry accuracy on the 58 buildings over downtown Toronto (Canada) of each of the two segmentation approaches compared with the reference data.