## 3 Experimental Results and Evaluations
### Segments Extracted and Evaluations
Overall, the mean value of centroid difference was 0.25 m, and the angle difference was less than 1\({}^{\circ}\), as can be seen in Table 14. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Patch**} & **Precision-Manual** & **Precision-Auto** & **Precision** & **Centroid** & **Angle Difference** \\  & **(m)** & **(m)** & **Difference (m)** & **Difference (m)** & **(Degree)** \\ \hline P1 & 0.005 & 0.027 & 0.022 & 0.098 & 0.179 \\ P2 & 0.002 & 0.004 & 0.002 & 0.104 & 0.011 \\ P3 & 0.009 & N.A. & N.A. & N.A. & N.A. \\ P4 & 0.001 & 0.001 & 0.000 & 0.023 & 0.008 \\ P5 & 0.004 & N.A. & N.A. & N.A. & N.A. \\ P6 & 0.002 & 0.011 & 0.009 & 0.205 & 4.072 \\ P7 & 0.002 & N.A. & N.A. & N.A. & N.A. \\ P8 & 0.002 & N.A. & N.A. & N.A. & N.A. \\ P9 & 0.001 & N.A. & N.A. & N.A. & N.A. \\ P10 & 0.001 & N.A. & N.A. & N.A. & N.A. \\ Mean & 0.003 & N.A. & N.A. & N.A. & N.A. \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Plane fitting precision, plane fitting precision difference, centroid difference, and angle difference values for building #4 (Spherical approach). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Centroid Difference (m)** & **Angle Difference (Degree)** \\ \hline Overall mean & 0.250 & 0.941 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Overall mean values of centroid difference and angle difference measures (Adaptive cylindrical approach). The segmentation performance of the proposed approach is also compared with J-linkage, RHA, multiRANSAC, sequential RANSAC, and mean-shift. The comparisons are carried out by using the same dataset as [14] (_i.e._, a 3D point cloud data of Pozzoveggiani church, Italy; see Figure 20a,b). One should note that the 3D point data of the church is actually derived from a set of images. The 3D plane extraction results using the above-mentioned algorithms are taken from [14] and shown in Figure 20d-h. As seen in Figure 20c, the proposed approach derived 11 planar surface segments. J-linkage also has 10 planar surfaces as seen in Figure 20d. Except for the proposed approach and J-linkage, the other approaches extract the surfaces incorrectly or have missing ones as seen in the figures. The only difference between the proposed approach and J-linkage is on the areas enclosed by the red dashed circles in Figure 20c-d. To take a closer look at the area in Figure 20c, it is enlarged as seen in Figure 21. Two segments indicated by the red and blue arrows are separated and derived using the proposed approach; however, J-linkage does not have two separated planes. The result comparison shows that the proposed approach works well with the 3D point data derived even from a set of images. Moreover, the result from the proposed approach is a bit better than the J-linkage and superior to the other approaches (_i.e._, RHA, MultiRANSAC, Sequential RANSAC, and mean- shift). Figure 21: Enlarged area which is enclosed by the red dashed circles in Figure 20c. Figure 20: Result comparison using Pozzoveggiani dataset: (**a**) image of Pozzoveggiani church; (**b**) 3D points of Pozzoveggiani church; (**c**) top view of the result from the proposed approach; (**d**) result from J-linkage; (**e**) result from Residual Histogram Analysis (RHA); (**f**) result from MultiRANSAC; (**g**) result from sequential RANdom SAmple Consensus (RANSAC); and (**h**) result from mean-shift.