# Indoor Building Reconstruction from Occluded Point Clouds Using Graph-Cut and Ray-Tracing
## 4 Applications and Accuracy Evaluation
### Results  
Figure 11 shows the reconstruction results for the data sets used. It is worth noting that all rooms were successfully reconstructed and all doors and windows detected except one window that was almost completely occluded by curtains, which is in conflict with the assumption of this method. The list of parameters controlling the data processing are reported in Table 2. They may be categorized into four groups. The first one is mainly addresses point cloud smoothing and regularization. Indeed, even if the RANSAC extraction method is quite robust against noise and outliers the enhancement of the point cloud simplifies and speeds up the plan identification phase. In particular, the principal parameters in this step (and also of the element classification and occlusion labelling step) is the choice of the voxel grid spacing (\(V_{R}\)). The optimal \(V_{R}\), as previously discussed, is a function of the mean sampling resolution of the point cloud and in particular, it should be slightly larger with respect to the average distance between points in the point cloud. Indeed, shorter spacing will produce computational overload and will determine the generation of a large set of disconnected components. On the other hand, larger spacing would result in a loss of the accuracy smoothing effect. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Technical Characteristics**} \\ \hline Maximum measurement range & 80 m \\ Data acquisition rate & 600.10\({}^{3}\) points/s \\ Resolution & 0.125\({}^{\circ}\) horizontal, 0.125\({}^{\circ}\) vertical \\ Angular Field of View (FoV) & 360\({}^{\circ}\)\(\times\) 360\({}^{\circ}\) \\ Relative accuracy & 30 mm (0.1 to 10 m) \\ Absolute position accuracy & 2 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical characteristics of the Viametris IMS3D laser scanning device according to the manufacturer’s datasheet. Figure 10: The data set provided by the ISPRS Scientific Initiative on Indoor modelling used as case study. In particular, for the data set adopted in the experiments, \(V_{R}\) was set 1.5 times the mean point spacing. A similar consideration can be formulated for parameters \(\beta_{1}\) and \(\beta_{2}\). \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Description** \\ \hline \multicolumn{3}{c}{Point cloud consolidation} \\ \(V_{R}\) & Voxel grid spacing \\ \(K\) & Neighbor size for estimation of normal \\ \(n_{c}\) & Number of points in each voxel \\ \hline \multicolumn{3}{c}{Point cloud segmentation} \\ \(\varepsilon\) & Bandwidth for the RANSAC based plan extraction (i.e., maximum distance between inliers \\ \(\varepsilon\) & points and the estimated plan in the RANSAC algorithm) \\ \(\alpha\) & Maximum distance between local point normal and plan normal in the estimated plan \\ \(\beta_{1}\) & Cell size to generate binary image \\ \(\tau_{R}\) & Dominant line threshold \\ \(n_{R}\) & Minimum number of inlier points in RANSAC primitive \\ \hline \multicolumn{3}{c}{Indoor component reconstruction} \\ \(\lambda\) & Weight balancing the data term and the smoothness term \\ \hline \multicolumn{3}{c}{Element classification and occlusion labelling} \\ \(\beta_{2}\) & Cell size to generate the occupancy map \\ \(V_{R}\) & Voxel grid spacing \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters adopted during data processing. Figure 11: Experimental results: (**a**) the input point cloud and the analyzed area (green boundaries); (**b**) a detail of the analyzed area without the ceiling; (**c**) the reconstructed model without ceiling; and (**d**) a wireframe view of the model. The second category of parameters is used to set point cloud processing and planar primitive extraction. Since the RANSAC plane detection is affected by noise and inaccuracy in normal estimation because of outliers and noise, parameters \(\varepsilon\) and \(\alpha\) are designed to compensate for these possible effects.