## 3 Results
### Testing Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**a [m]**} & \multirow{2}{*}{**b [m]**} & **Points in** & **\%** & **RMSD** & **RMSD\({}_{\text{E}}\)** & **\%** \\  & & **the Cloud** & **Original 1** & **[m]** & **[m]** & **Uniform 2** \\ \hline original & - & 728,137 & 100 & - & - & - \\ \hline
0.01 & uniform & 352,660 & 48.4 & 0.0005 & 0.0007 & 100 \\
0.01 & 0.02 & 249,549 & 34.3 & 0.0006 & 0.0007 & 70.8 \\
0.01 & 0.03 & 187,024 & 25.7 & 0.0006 & 0.0007 & 53.0 \\
0.01 & 0.05 & 120,506 & 16.5 & 0.0007 & 0.0008 & 34.2 \\ \hline
0.02 & uniform & 121,333 & 16.7 & 0.0010 & 0.0011 & 100.0 \\
0.02 & 0.04 & 81,622 & 11.2 & 0.0011 & 0.0012 & 67.3 \\
0.02 & 0.06 & 59,777 & 8.2 & 0.0012 & 0.0013 & 49.3 \\
0.02 & 0.10 & 36,728 & 5.0 & 0.0016 & 0.0016 & 30.3 \\ \hline
0.03 & uniform & 65,148 & 8.9 & 0.0015 & 0.0016 & 100.0 \\
0.03 & 0.06 & 40,194 & 5.5 & 0.0017 & 0.0017 & 61.7 \\
0.03 & 0.09 & 29,088 & 4.0 & 0.0020 & 0.0020 & 44.6 \\ \hline
0.05 & uniform & 26,194 & 3.6 & 0.0029 & 0.0030 & 100.0 \\
0.05 & 0.10 & 15,752 & 2.2 & 0.0033 & 0.0033 & 60.1 \\
0.05 & 0.15 & 11,100 & 1.5 & 0.0042 & 0.0042 & 42.4 \\ \hline \hline \end{tabular}  
* \({}^{1}\) % original—the percentage of points relative to the original cloud. 2 % uniform—the percentage of points relative to the uniformly diluted cloud with respective a.  
\end{table} 
Table 2: Results of dilution of the Data 1 cloud—numbers of points and RMSDs (R = 0.05 m). Figure 5: Examples of dilution: a = 0.02 m in all cases; (**a**) uniform dilution (i.e., b = 0.02 m); (b) b = 0.04 m; (c) b = 0.06 m; (d) b = 0.10 m.  
Figure 6 shows a detail of the point clouds diluted using various settings and their differences from the original could. Note in particular the differences between Figure 6b,f\(-\)two point clouds containing approximately the same numbers of points after dilution (Table 2). Figure 6b compares the original cloud with the result of uniform dilution with a = 0.020 m while (f) with the result of progressive dilution using a = 0.010 m and b = 0.050 m. The progressive cloud has a better RMSD (Table 2), which corresponds to the visual comparison where greater differences on the edges from the original cloud can be observed for the uniform dilution with higher alpha (red and blue points on the edges). This illustrates the main advantage of the progressive dilution--by using higher density only locally, it preserves greater detail only where needed, thus reaching better results with the same final cloud size. Figure 6: Details of the Data 1 point cloud: (**a**) original cloud, (**b**) differences between the cloud acquired by uniform dilution with a = 0.02 m and the original point cloud, (**c**) point cloud after uniform dilution with a = 0.01 m, (**d**) differences between the cloud acquired by uniform dilution with a = 0.01 m and the original point cloud, (**e**) point cloud after a = 0.01 m b = 0.05 m progressive dilution (approximately the same number of points in the cloud as for uniform dilution 0.02 m), (**f**) differences between the cloud acquired by progressive dilution with a = 0.01 m b = 0.05 m and the original point cloud. Note the higher representation of deviations on the edges of (**b**) compared to (**f**). Comparing Figure 6d,f we can see the comparison of two clouds with the same maximum detail a (0.010 m). The progressively diluted cloud contains approx. a third of points compared to the uniform dilution, which represents a significant compression of the data. Although the number of points with a greater difference from the original cloud (red) is somewhat higher in the progressively diluted cloud, we can see that such erroneous points are dissipated, representing largely chunks and slight unevenness in the relatively flat areas of stone faces while the edges and details are preserved very well.