## 3 Experimental Results and Evaluations
### Segments Extracted and Evaluations
Since this research focused on planar segmentation, the laser points belonging to non-planar surfaces were not considered when the manually derived patches were prepared. The correctness, completeness, plane fitting precision, plane fitting precision difference, centroid difference, and angle difference were considered as quantitative measures. The correctness and completeness measures were, first, computed point-by-point, automatic-to-manual comparison of the clustered point IDs. In computing these measures, the total number of laser points with matching IDs, between the automatic and manual clusters, was calculated. The correctness measure in Equation (9) evaluates the percentage of the matched laser points among the established ones (_i.e._, the automatically detected  
Figure 16: Segmentation results based on the adaptive cylindrical neighborhood definition. ones). On the other hand, the completeness measure in Equation (10) provides an indication of the percentage of the matched points among the actual ones (_i.e._, the manually detected ones). Tables 4 and 5 list the correctness and completeness values computed from the adaptive cylindrical and spherical approaches for the four buildings, respectively. \[Correctness=\frac{Total\ number\ of\ laser\ points\ matched}{Total\ number\ of\ laser\ points\ detected\ automatically} \tag{9}\]  
\[Completeness=\frac{Total\ number\ of\ laser\ points\ matched}{Total\ number\ of\ laser\ points\ detected\ manually} \tag{10}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **No. of Points** & **No. of Points Detected** & **No. of Points** & **Correctness** & **Completeness** \\  & **Detected Manually** & **Automatically** & **Matched** & **(\%)** & **(\%)** \\ \hline Building \#1 & 1490 & 1475 & 1367 & 92.68 & 91.74 \\ Building \#2 & 2988 & 3007 & 2946 & 97.97 & 98.59 \\ Building \#3 & 11,394 & 10,509 & 10,378 & 98.75 & 91.08 \\ Building \#4 & 33,778 & 34,117 & 32,892 & 96.41 & 97.38 \\ Minimum & - & - & - & 92.68 & 91.08 \\ Maximum & - & - & - & 98.75 & 98.59 \\ Overall & 49,650 & 49,108 & 47,583 & 96.89 & 95.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correctness and completeness values of four buildings (Adaptive cylindrical approach). Figure 17: Segmentation results based on the spherical neighborhood definition. In case of adaptive cylindrical approach (as seen in Table 3), the minimum and maximum values of the correctness measure were 92.68%, and 98.75%, respectively. The minimum and maximum values of the completeness measure were 91.08%, and 98.59%, respectively. In terms of the overall correctness and completeness measures, the adaptive cylindrical segmentation algorithm provided 96.89% and 95.84% values, respectively. On the other hand, the spherical approach (as seen in Table 4) showed worse segmentation results compared to the adaptive cylindrical one. In this case, the minimum and maximum values of the correctness measure were 87.20%, and 99.70%, respectively. The minimum and maximum values of the completeness measure were 87.82%, and 92.06%, respectively. In terms of the overall correctness and completeness measures, the spherical segmentation algorithm provided 90.43% and 91.08% values, respectively. Those values mostly affected by the results from buildings #2 and #4. As seen in Table 4, building #2 has much less number of points detected automatically than the points detected manually. This caused the maximum value of the correctness (_i.e._, 99.70%) and the minimum value of the completeness (_i.e._, 87.82%). However, it is the other way around in case of building #4. There are much more automatically detected points than the manually detected ones. This caused the minimum value of the correctness (_i.e._, 87.20%) and the maximum value of the completeness (_i.e._, 92.06%). After the segmentation process completed, plane fitting was carried out for all of the automatically and manually derived planar patches. In this process, the plane fitting precisions are determined by calculating the RMS errors of the planes.