## 3 Experimental Results and Evaluations
### Analysis of the Effect of the Adaptive Cylindrical Neighborhood Definition  
Laser points reflected from a structure of 15 m \(\times\) 10 m \(\times\) 7 m dimensions were, first, simulated for this analysis. The structure had two small objects on the rooftop (e.g., cooling towers of 3.0 m \(\times\) 3.0 m \(\times\) 1.5 m dimensions). The mean point density of the simulated data was 2.24 points/m\({}^{2}\) (\(\sim\)0.67 m point spacing), and the horizontal and vertical accuracies of the laser points were 0.5 m and 0.15 m, respectively. It should be emphasized that the simulated data followed the specifications of the real data acquired from OPTECH ALTM 3100, which was used by [32]. Figure 12a,b show the designed structure for the simulation and the produced laser points on the rooftop of the structure, respectively. Three hundred and forty-five (345) laser points were generated, among which thirty-two (32) points were located on the two small objects, as seen in Figure 12b.  
Based on the simulated laser points, the fitted plane was determined using the neighboring laser points around the target point; then, the surface normal vector of the plane was calculated. For this test, two neighborhood definition approaches, the adaptive cylindrical and spherical ones, were applied. The surface normal vectors calculated from the two approaches were then compared with the true one. Significantly, the components of the true unit normal vector were (0, 0, 1), because the laser points were reflected from the structure's horizontal rooftop. Angle computation between the surface normal vector calculated and the true one was implemented for all of the points in the simulated dataset (refer to Equation (8)):  
\[\theta_{i}=\arccos(\frac{\overrightarrow{\eta}_{i}\bullet\overrightarrow{ \eta}_{t}}{\left|\overrightarrow{v}_{i}\right|\left|\overrightarrow{v}_{t} \right|}) \tag{8}\]  
where \(\overrightarrow{v}_{i}\) is the surface normal vector of the plane determined using the neighboring laser points around the \(i\)-th point, \(\overrightarrow{v}_{t}\) is the true unit normal vector (0, 0, 1), and \(\theta_{i}\) is the angle between the vectors \(\overrightarrow{v}_{i}\) and \(\overrightarrow{v}_{t}\). In the test, the numbers of neighboring points were determined using four different  
Figure 12: (**a**) Shape of a structure on which laser points are projected; and (**b**) the produced laser points on the rooftop of the structure.  
searching radii: 2.0 m, 2.5 m, 3.0 m, and 3.5 m. Figure 13 shows the angles based on the spherical and adaptive cylindrical approaches together with the searching radii. Additionally, Table 1 lists the statistical evaluation data for the angles calculated.  
Figure 13: _Cont._  
Figure 13 shows that the angles provided by the adaptive cylindrical approach are more concentrated than the values provided by the spherical one. Considering Table 1 results, it is also clear that the mean and standard deviation values of the angles were much lower for the adaptive cylindrical method than for the spherical one. Therefore, the adaptive cylindrical method can be considered robust against random noises and outliers in the laser point cloud when compared to those using spherical neighborhoods. In other words, the adaptive cylindrical neighborhood approach increases the homogeneity of the laser point attributes. To see the impact of the neighborhood definition on the segmentation results, the qualitative and qualitative comparison between the results from the spherical and adaptive cylindrical approaches is added in Section 3.3, Segments extracted and evaluations.