## 3 Experimental Results and Evaluations
### Real Data Description  
Two types of laser scanned data, acquired by airborne and terrestrial laser scanning systems, were utilized for the purposes of the experiments. Three airborne laser scanning datasets were captured over Vaihingen (Germany), Toronto (Canada), and University of Calgary (Canada). One terrestrial laser dataset, additionally, was acquired at Yonsei University (Seoul, Korea). Descriptions of these datasets are summarized in Table 2. The two airborne laser scanning datasets taken over Vaihingen and Toronto have similar point densities. One airborne laser data over University of Calgary has lower point density. On the other hand, the terrestrial dataset has a higher point density than the three airborne datasets.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Radius (m)**} & \multicolumn{2}{c}{**Spherical Approach (Degrees)**} & \multicolumn{2}{c}{**Adaptive Cylindrical Approach (Degrees)**} \\ \cline{2-5}  & **Mean** & **STD** & **Mean** & **STD** \\ \hline
2.0 & 6.738 & 8.240 & 4.058 & 4.991 \\
2.5 & 7.399 & 7.872 & 4.484 & 7.605 \\
3.0 & 7.116 & 5.894 & 3.257 & 5.582 \\
3.5 & 7.018 & 4.252 & 1.738 & 3.067 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical evaluations of the angles between the surface normal vector calculated and the true one.  
Figure 13: Angles between the surface normal vector calculated and the true one: (**a,c,e,g**) Spherical and (**b,d,f,h**) Adaptive cylindrical approaches applying different radii of 2.0 m (**a,b**); 2.5 m (**c,d**); 3.0 m (**e,f**); and 3.5 m (**g,h**).  
As seen in Figure 14, four buildings from different areas were selected from Vaihingen, Toronto, and Seoul for the experiments. The three buildings in Vaihingen and Toronto included a historic building having a rather complex shape, a high-rise residential building, and a business tower in a modern city, respectively. The forth building, located at Yonsei University, also a modern building, was used as a camera calibration test field. These buildings consisted of planar patches having different slopes, aspects, sizes, heights, and materials. Such buildings are utilized to carry out the detailed quantitative measures (_i.e._, correctness, completeness, plane fitting precision, plane fitting precision difference, centroid difference, and angle difference values) of the experimental results. Figure 15 illustrates a large dataset taken over University of Calgary, Canada with 320,325 laser points. Also, additional evaluation is carried out using the large dataset over the university.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Location** & **Scanner Type** & **Airborne/Terrestrial** &
\begin{tabular}{c} **Point Spacing (m)/Point** \\ **Density (Points/m\({}^{2}\))** \\ \end{tabular} \\ \hline Vaihingen & Leica ALS50 & Airborne & 0.38/6.7 \\ Toronto & Optech ALTM-ORION M & Airborne & 0.41/6.0 \\ Calgary & Optech ALTM 3100 EA & Airborne & 1.15/0.76 \\ Seoul & Leica Scanstation 2 & Terrestrial & 0.15/44.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Descriptions of Vaihingen, Toronto, and Seoul datasets.  
Figure 14: Optical images and displayed laser data of four buildings.