## 3 Experimental Results and Evaluations
### Segments Extracted and Evaluations  
An automated segmentation process based on the proposed methodology was, first, carried out using four different datasets. The flatness of the surfaces, the roughness of the materials, and the instrumental accuracies were considered when the accuracies of the laser datasets in the depth direction were determined. The values from the Vaihingen, Toronto, and Seoul datasets, respectively, were 0.15 m, 0.15 m, and 0.10 m. Descriptions, values, and justifications for the thresholds used in the segmentation process for four buildings are provided in Table 3.  
To see the impact of the neighborhood definition on the segmentation results, the adaptive cylindrical and spherical approaches were carried out and compared with each other. More specifically, two different attribute files are generated separately based on the adaptive cylindrical and spherical neighborhood definitions. Afterwards, the exactly same remaining segmentation procedures were applied to those attributes. The final segmentation results based on the adaptive cylindrical and \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Threshold** & **Description** & **Value (Building \#1/2/\#3/\#4)** & **Justification** \\ \hline \multirow{2}{*}{Searching radius} & Radius of the spherical neighborhood centered at a point & 2.00 m/2.00 m/2.00 m/0.30 m & Including sufficient number of points to define reliable attributes \\ \hline \multirow{2}{*}{Buffer threshold} & Buffer defined above and below the final fitted plane & \multirow{2}{*}{0.30 m/0.30 m/0.30 m/0.20 m} & Two times the accuracy of the laser data in the depth direction \\ \hline \multirow{2}{*}{Co-planarity test threshold} & Threshold for testing the co-planarity of points at the peak of the accumulator array & \multirow{2}{*}{0.30 m/0.30 m/0.30 m/0.20 m} & Two times the accuracy of the laser data in the depth direction \\ \hline \multirow{2}{*}{Proximity threshold} & Maximum distance for determining the proximity among points in the object space & \multirow{2}{*}{0.50 m/0.50 m/0.50 m/0.15 m} & Approximately equal to the average point spacing of the laser data \\ \hline \multirow{2}{*}{Minimum size of detectable peak} & Minimum size of the detected points at the highest peak & 4.00 m\({}^{2}\)/4.00 m\({}^{2}\)/4.00 m\({}^{2}\)/0.50 m\({}^{2}\) & Prior knowledge about building planar patch size within the area of interest \\ \hline \multirow{2}{*}{Accumulator Cell resolution} & \multirow{2}{*}{Cell size of the accumulator array} & Two times the accuracy of the laser data in the depth direction \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptions, values, and justifications for the thresholds used in the segmentation process. Figure 15: A large dataset over University of Calgary, Canada. spherical neighborhood definitions are provided in Figures 16 and 17 respectively. Each color indicates a planar patch of different slope and aspect. Figures 16 and 17 also show a number of extracted planar patches, a number of missing patches, and the missing object types. When the segmentation results were visually checked for Figure 16, most of the planar patches had been correctly extracted, excepting a very small object and three windows. The missing objects could be accounted for by the facts that the small patch belonging to building #2 had just very few points and that the windows belonging to building #4 have very noisy and few laser points. On the other hand, the segmentation results based on the spherical neighborhood have many missing objects as seen in Figure 17. Several small patches, windows, and doors are not detected in the segmentation results except for building #1. For more detailed quantitative evaluations of the experimental results, the automatically extracted patches (_i.e._, from adaptive cylindrical and spherical approaches) were compared with those manually derived by experienced operators. The manually derived patches functioned in this research as references.