## 3 Methodology
### Spaces Division and Extraction
#### 3.3.2 Generation of Wall Candidates
The door category achieves the most accurate results because \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case ID** & **Components** & **Recognized Number (RgN)** & **Recall Number (RcN)** & **Total Number (TN)** & **Accuracy (\%)** \\ \hline \multirow{3}{*}{1} & Walls & 6 & 0 & 6 & 100 \\  & Door & 1 & 0 & 1 & 100 \\  & Ceiling & 1 & 0 & 1 & 100 \\  & Floor & 1 & 0 & 1 & 100 \\ \hline \multirow{3}{*}{2} & Wall & 14 & 1 & 14 & 100 \\  & Door & 2 & 0 & 2 & 100 \\  & Ceiling & 1 & 0 & 1 & 100 \\  & Floor & 1 & 0 & 1 & 100 \\ \hline \multirow{3}{*}{3} & Wall & 26 & 1 & 29 & 89 \\  & Door & 23 & 0 & 25 & 92 \\ \cline{1-1}  & Window & 8 & 0 & 9 & 88 \\ \cline{1-1}  & Ceiling & 6 & 0 & 6 & 100 \\ \cline{1-1}  & Floor & 6 & 0 & 6 & 100 \\ \hline \multirow{3}{*}{4} & Wall & 22 & 1 & 23 & 95 \\ \cline{1-1}  & Door & 6 & 0 & 6 & 100 \\ \cline{1-1}  & Ceiling & 5 & 0 & 5 & 100 \\ \cline{1-1}  & Floor & 5 & 0 & 5 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation of the extracted components. Figure 12: Reconstruction results for case study (1). of the use of specific frames. As expected, the walls, ceilings, and floors generate similar results and achieve lower accuracy due to the deficiencies of the raw point cloud data. To further validate the robustness of the proposed methodology, two more case studies are conducted. Figure 13. shows the reconstruction process for case study (2), which is a single room with more complex layout comparing with case study (1). Two frames are labeled with the tag \"door\". Due to the limitation of the view angle, only the bottom of the room is scanned. Similar to case study (1), the reconstruction results for wall and door components are illustrated in Figure 13c, and the corresponding CityGML modeling is shown in Figure 13d. In case study (2), 13 walls and two doors are recognized directly from the raw data set. Due to the occlusion problem during data collection, a wall component is missing when wall candidates are generated, as shown in Figure 13c (bottom). As expected, the missing wall is recalled based on the rules of wall determination noted in Section 3.3.3. The algorithm constructs a new line when the normal angle of two adjacent lines is less than the angle threshold \(\theta_{th}=50\) and a new wall is reconstructed in Figure 13c (top). The evaluation of the extracted components of case study (2) is shown in Table 1. It achieves 100% accuracy in component reconstruction in this situation. As shown in Table 2, case study (2) generated similar results. The absolute errors of recognized dimension were all within 2%, and the door component achieved the best result. In case study (3), the tested building has a more complicated structure containing 1278 RGB-D frames, six functional spaces, dozens of door components, and several window components Figure 14a (1) shows the raw data set with camera trajectory and sample frames containing doors and windows. Six functional spaces are segmented and reconstructed successfully according to the tags of RGB-D frame, shown in Figure 14a (2). Figure 14a (3) and (4) show the skeleton of the whole model and the CityGML model of the scenes. Based on the evaluation results shown in Table 1, two of 28 walls, two of 25 doors and one of nine windows are not successfully recognized from the point cloud data, and the proposed reconstruction method achieves recognized accuracy of 89%, 92%, and 88% respectively. One wall is recalled based on the rules of wall determination. Figure 14b lists the reconstruction results of each functional space. In the reconstruction results of Spaces 3 and 4 in Figure 14b, two recognized door components marked with red borders contain more than one door entity, which results in a lower number of recognized door components. Similarly, Figure 15 shows the reconstruction results of case study (4), which contains 857 RGB-D frames, five functional space and several openings. Raw data associated with camera trajectory and the reconstruction results are presented in (a).