# Advanced Methods for Point Cloud Processing and Simplification
## 8 Results
### Processing Results
By using the level image, it is possible to easily express the statistical parameters of the represented planar surface, process plane visualization, and decrease the number of points necessary for the planar surface description. The presented algorithms were tested on the CPU i5-2410M 2,3 GHz. The input point cloud consists of 219,216 points and the detection time of all planar surfaces is not higher than three seconds. The mentioned algorithms in Section 1 can be used for the detection of planar surfaces. Then, the segmented raw point cloud of a planar surface can be processed by our proposed approach utilizing a level image with the connection of image processing methods. This concept allows us to easily get the important physical space properties, decrease the descriptive point amount, or visualize the planar surface. The following tables (Tables 5-7) give the percentage difference between the real physical area and perimeter in each coordinate axis. Columns marked by _phys_ determine the physical values. The estimated values directly reflect the level image content which depends mainly on the objects covering by measurement points. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Idx** & **dL (m)** & **Pos (m)** & **A\({}_{\text{E}}\) (m\({}^{2}\))** & **P\({}_{\text{E}}\) (m)** & \(\sigma\) (m)** & **PC p.** & **I\({}_{\text{L}}\) px.** & **V** & **P. decr.\%** \\ \hline
1 & 0.023 & 0.262, 0.018, 0.023 & 55.835 & 45.643 & 0.006 & 14,223 & 34,897 & 270 & 98.1 \\
4 & 0.987 & 0.091, 3.936, 0.987 & 0.76 & 4.61 & 0.010 & 2673 & 475 & 36 & 98.65 \\
6 & 0.942 & 4.415, 7.593, 0.942 & 0.739 & 4.537 & 0.014 & 1710 & 462 & 21 & 98.77 \\
8 & 0.926 & 8.013, 5.763, 0.926 & 1.845 & 9.8 & 0.012 & 6629 & 1153 & 58 & 99.13 \\
12 & 1.353 & 10.129, 5.853, 1.353 & 0.773 & 4.96 & 0.009 & 2555 & 483 & 22 & 99.14 \\
21 & 2.956 & 0.102, 0.012, 2.672 & 59.246 & 39.319 & 0.019 & 16,173 & 37,029 & 162 & 99 \\ \hline \end{tabular}
\end{table} 
Table 4: Detected planes with the physical description in the Z-axis. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Idx** & **dL (m)** & **Pos (m)** & **A\({}_{\text{E}}\) (m\({}^{2}\))** & **P\({}_{\text{E}}\) (m)** & \(\sigma\) (m)** & **PC p.** & **I\({}_{\text{L}}\) px.** & **V** & **P. decr.\%** \\ \hline
1 & 0.081 & 3.926, 0.081, 2.88 & 13.334 & 15.226 & 0.0013 & 22,161 & 8270 & 82 & 99.63 \\
7 & 2.647 & 3.653, 2.647, 2.92 & 9.7856 & 12.4 & 0.0008 & 13,456 & 6054 & 49 & 99.64 \\
10 & 3.949 & 0.135, 3.949, 2.96 & 10.026 & 12.69 & 0.0007 & 14,802 & 6192 & 39 & 99.74 \\
14 & 4.497 & 7.115, 4.497, 2.80 & 7.7008 & 16.89 & 0.0009 & 9847 & 4748 & 85 & 99.14 \\
29 & 7.819 & 0.271, 7.819, 3.12 & 21.661 & 35.236 & 0.0018 & 26,529 & 13840 & 162 & 99.39 \\ \hline \end{tabular}
\end{table} 
Table 3: Detected planes with the physical description in the Y-axis. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Idx** & **A\({}_{\text{E}}\) (m\({}^{2}\))** & **A\({}_{\text{phys}}\) (m\({}^{2}\))** & **\(\Delta\) A (\%)** & **P\({}_{\text{E}}\) (m)** & **P\({}_{\text{phys}}\) (m)** & **\(\Delta\) P (\%)** \\ \hline
2 & 7.174 & 6.97 & 2.84 & 19.33 & 18.95 & 1.97 \\
4 & 9.862 & 8.976 & 8.98 & 18.177 & 16.856 & 7.27 \\
5 & 11.645 & 11.728 & 0.71 & 21.41 & 21.68 & 1.26 \\
14 & 13.278 & 13.489 & 1.59 & 20.833 & 21.34 & 2.43 \\
16 & 8.754 & 8.28 & 5.41 & 11.96 & 11.22 & 6.19 \\
22 & 7.15 & 6.95 & 2.80 & 15.443 & 15.133 & 2.01 \\ \hline \end{tabular}
\end{table} 
Table 5: Physical area and perimeter, difference in percent (X-axis). The comparison of both tables (Tables 5-7) with (Tables 8-10) shows that in several cases the percentage difference is in units of percent. Even in four cases, the convex hull method overcomes our method in the determination of at least one compared value. However, in many cases, the difference is even more than 15%.