# UAV-Based Evaluation of Rockfall Hazard in the Cultural Heritage Area of Kipinas Monastery, Greece
## 2 Methods and Data
### Structural Analysis  
For each sub-region of the point cloud, a supervised automated analysis was performed with the open-source DSE (Discontinuity Set Extractor) software (developed by [66]). This approach, proposed by [66], calculates the normal vector for each point and its \"_knm_\" closest neighbor points. The visual representation of this procedure is via their corresponding poles in a stereographic projection. Then, statistical analysis was carried out for these poles, providing the stereogram and enabling the extraction of the principal discontinuity sets.  
Specifically, the PCA (Principal Component Analysis) algorithm was used to calculate these normal vectors and a tolerance (\(n\)) test was performed in order to define if each set of points could be considered as a candidate of a planar area, or as non-planar and be discarded. Afterwards, in order to estimate the principal orientation, the Kernel Density Estimation [67] was used. The density function was estimated automatically, and with a manual identification of the peaks of the most represented orientations, the number and the orientation of principal planes was determined. Consequently, a discontinuity set was assigned to each input point from point cloud, enabling that way the isolation of all the co-belonging points to a specific set. Then, a spatial cluster analysis was performed with the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm. This resulted in clusters of points, belonging to the same set, forming plane continuous surfaces which, hence, could be considered as planes, so that the automatic calculation of planes' equations (spacing [66] and persistence [68]) was enabled.  
In this particular analysis, the used parameters for all 4 sub-regions were the same. Specifically, for the calculation of the normal vectors of each point and its corresponding poles, two parameters were defined; the number of nearest neighbors (\(knm=30\)) and the tolerance for the coplanarity test (\(n=0.2\)). For the calculation of the density of the poles, the number of bins for the kernel density estimation (\(nbins=64\)) and the minimum angle between normal vectors of discontinuity sets (\(\varphi=20^{\circ}\)) were determined. Then, for the assignment of a discontinuity set to each point, the parameter that was imported was the minimum angle between the normal vector of a discontinuity set and the normal vector of the point (\(cone=30^{\circ}\)). Lastly, for the cluster analysis, an assumption was made about all  
Figure 4: The segmented initial point cloud, in four (4) areas; U1: blue, U2: green, U3: yellow and U4: red.  
Figure 6: (**a**) Stereographic projections of the DSE-derived discontinuity sets for U1 and (**b**) the visual interpretation of the four (4) main sets in the 3D point cloud.  
Figure 7: (**a**) Stereographic projections of the DSE-derived discontinuity sets for U2 and (**b**) the visual interpretation of the four (4) main sets in the 3D point cloud.  
It is important to underline that three of them comprise major joint sets (J\({}_{1}\), J\({}_{2}\) and J\({}_{3}\)) and one (1) the bedding (B).