# A Layer-Wise Strategy for Indoor As-Built Modeling Using Point Clouds
## 4 Experiments
### Parameters  
In this section, we clarify the reason for parameter settings by tuning different parameters. Some explanations and analyses will be given to explore the suggested values of our methods. We classify the parameters according to the different modules into planar primitive detection, contour extraction, and building reconstruction (please refer to Table 3). Parameters of planar primitive detection: There are three parameters to be predefined in this category. \(\theta_{th}\) is the threshold for the normal inconsistency between the current seed and neighboring points during the region-growing. \(k\) is the radius of neighborhood, which is used in region-growing and smoothness term calculation. \(\varsigma\) is a parameter to adjust the weight of smoothness term denoting the average space of the point clouds. We can calculate it through stuying the density of point clouds. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Output (from 3D Primitive)** & **Apartment 1** & **Apartment 2** & **Office 1** \\ \hline \# of rooms & 6 & 4 & 10 \\ \# of vertices & 358 & 194 & 260 \\ \# of faces & 689 & 390 & 522 \\ \hline
**Parameters** & **Apartment 1** & **Apartment 2** & **Office 1** \\ \hline \(s_{r}\) & 0.9 & 0.5 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of the output models. Figure 20: Modeling outputs of the proposed method. From top to bottom: The original point clouds, the reconstructed models with ceilings, and the transparent view of models. The red circles denote the missing room in the reconstruction. Parameters of contour extraction: The parameters utilized in the contour extraction are primarily based on the distance. The values of these parameters are insensitive since the indoor structures of civil architecture are similar. Therefore, the parameters do not need to be tuned for different point clouds. \(d_{b}\) and \(b_{h}\) are two parameters leveraged in point cloud partition. \(d_{b}\) is the parameter to restrict the distance from point clouds to key points of convex hulls. A large value of \(d_{b}\) considers more points as boundary points which decrease the discrepancy of the histogram. We suggest that the value of \(d_{b}\) is less than or equal to the bin size \(b_{h}\) (1/2-1 times of \(b_{h}\)). \(b_{h}\) denotes the bin size of the histogram in the representative layer selection as well as the interval of slice along the vertical direction. Although approaching layers keep more indoor structures as shown in Figure 21a, the supporting points of each layer suffer from a corresponding decrease. This decrease causes the problem in linear primitive extraction due to insufficient supporting points. On the other hand, in spite of the greater interval that can consolidate the 2D projection layer (see \(b_{h}=0.15\) m in Figure 21d) and accelerate the processing speed, lots of structure information is thrown away simultaneously. Considering the trade-off between the processing speed, layer consolidation, and indoor structures, we set the interval threshold \(b_{h}\) as 0.05-0.1 m.  
\(s_{r}\) denotes the searching radius of parallel inner walls to divide the 2D point clouds into several subsets for simplifying the contour regularization. Although increasing the searching radius can improve the ability of locating parallel structures, a large value of \(s_{r}\) gives rise to the over-partition. As illustrated in Figure 22, the smaller value dismisses some large interval parallel walls. However, a large searching distance introduces errors as indicated in blue circle of Figure 22b. Typically, the thickness of inner walls is about 20 cm. Therefore, in order to improve the tolerant rate and deal with the exceptional case as in Figure 22, we set a reasonable range of \(s_{r}\) as 0.5-1.0 m.