# Advanced Methods for Point Cloud Processing and Simplification
## 8 Results
### Evaluation of Processing Algorithms  
Following Figure 21 shows the planar surfaces visualization by using the level images from Figure 13c,d. The level images were achieved by the LCCL algorithm. For a better illustration, the segmented points are also included. From both visualizations, it is obvious the good covering of all points. From this follows that the results of the developed algorithms strongly depend on the quality of an input point cloud. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Idx** & **A\({}_{\text{CH}}\) (m\({}^{2}\))** & **A\({}_{\text{phys}}\) (m\({}^{2}\))** & **\(\Delta\) A (\%)** & **P\({}_{\text{CH}}\) (m)** & **P\({}_{\text{phys}}\) (m)** & **\(\Delta\) P (\%)** \\ \hline
1 & 69.044 & 54.32 & 21.33 & 32.062 & 44.28 & 38.11 \\
4 & 0.938 & 0.79 & 15.78 & 5.07 & 4.86 & 4.23 \\
6 & 0.789 & 0.712 & 9.76 & 4.60 & 4.33 & 5.80 \\
8 & 4.033 & 1.765 & 56.24 & 8.40 & 9.45 & 12.52 \\
12 & 0.948 & 0.81 & 14.56 & 4.92 & 5.15 & 4.61 \\
21 & 71.703 & 56.392 & 21.35 & 32.786 & 38.507 & 17.45 \\ \hline \end{tabular}
\end{table} 
Table 10: Physical area and perimeter, difference in percent from convex hull (Z-axis). Figure 20: Planar surface area with a hole: **(a)** Level image; **(b)** Convex hull. The results of the planar surface segmentation can be improved by the fine segmentation, as we introduced in reference [32]. Figure 22 gives an example of the usage for the level detection in Figure 10. For the processing of the final point cloud composing the flat, we did not use this fine ranging. Figure 22d shows the problematic case. The noisy curve is the histogram of the points representing a level in the scanning dimension \(\text{dim}_{\text{s}}\). The green line is the moving average of the histogram with the selected window size 1 cm. From the filtered curve, it is possible to surely estimate positions of both elbows, where the derivation is smaller than the desired threshold. For example, due to measurement errors and the worse result of the registration process, points from two scans covering one wall can be slightly shifted and two local maxima of points concentration can be close to each other. When this situation occurs, the algorithm ends with a similar result as in Figure 22d. This can lead to the detection of double walls. For this reason, it is better to not use this approach on data with measurement errors. Prior information about the point cloud data quality or the demands on the planar surface detection is desirable. We are focusing on the two main parameters, the expected standard point deviation from a detected planar surface and the minimal distance between two planar surfaces in the direction of analyzing individual levels. This reflects the selection of the parameters _lvls_ and _lvlRS_. The _lvls_ value also expresses the expected standard point deviation from a planar surface. If this parameter is set too high, the two close planar surfaces can be detected as one. The higher _lvlRS_ value selection is always recommended, as this ensures the sufficient data range selection in the scanning dimension and the histogram of points concentration will find the best probability of a level position for a planar surface presence. To ensure the probability that a point belongs to the best planar surface, we can follow the statistical parameters of all planar surfaces. Next, Figure 23 shows the possibility of using the level image for the point cloud segmentation. For a level image, its physical origin in space, orientation angle, and quantization parameter are known. From this, we can easily extract desired points as shown in this example. Figure 21: Planar surface visualization: (**a**) Point cloud with a hole; (**b**) Normal surface. Figure 22: Fine planar surface range estimation: (**a**) Points histogram in the scanning dimension with marked thinner range; (**b**) Thinner range selection in the comparison with Figure 10a,b; (**c**) Selected points by this range; (**d**) Illustration of the problematic case.