## 3 Methodology
### Spaces Division and Extraction
#### 3.3.2 Generation of Wall Candidates
As shown in Figure 10, \(wP_{1}\) and \(wP_{2}\) share the same plane \(gP_{1}\), and \(gP_{2}\)

Figure 10: Strategy of global optimization for planes. Figure 9: Point filling and changing detection methods. is the global plane of \(wP_{3}\). Similarly, the connected wall planes of each opening can be detected and the plane parameters of corresponding opening are corrected, as shown in Figure 5:0

Figure 5:1

Figure 5:2

## 4 Experimental Results and Discussion

We tested our proposed methodology on synthetic multi-level data sets, four measurement data sets collected in a single room and one data set acquired from a space with complex layout. All of the datasets were collected using the RGB-D mapping system shown in Figure 11a and samples of the RGB image and depth image are plotted in Figure 11b,c. In our RGB-D system, Kinect sensors are mounted on NVIDIA Jetson TX2 and carried by a trolley. A RGB-D SLAM method presented by our previous work [8] is used for camera tracking and pose optimization, which enable to obtained accurate camera pose for each frame and the corresponding point cloud. To facilitate the identification of the start-end position of functional space interactively, the RGB-D sequences are endowed with specific tags through responding to the key board message. Therefore, each data set contains the colorized point cloud and the RGB-D sequences associated with timestamp, camera position and labeling tags. For each data set, sparse outlier removal and down-sampling algorithm are used to reduce the density and remove the noise of the raw colorized point cloud. To quantify the reconstruction results, two kinds of error metrics are used. The first is the accuracy of the quantity of the extracted components. The second is the accuracy of the area dimension. In the first case study, the data set contains 115 RGB-D frames. As shown in Figure 12a, because the windows are sheltered by a curtain, only the frames containing door components are labeled. From the

Figure 5:3 RGB-D system of data collection. view of the point cloud, most parts of the room are scanned and modeled. The room contains six walls and one door components. As shown in Figure 12b, the raw colorized point cloud was first segmented into a set of plane clusters. The planes are classified into vertical planes and horizontal planes based on the normal of the planes, and the wall candidates were distinguished by following the classification rules of the plane normal. In this experiment, we set the normal threshold \(n_{th}=5^{\circ}\) and a length threshold \(\mathrm{l_{m}}=1\) m. Subsequently, the interior elements filtering algorithm is used to separate the wall planes from the vertical planes and six wall planes can be extracted, as shown in Figure 12b. To obtain the wall planes connected to the door planes, we set the distance threshold between two planes \(\mathrm{d_{diff}}=5\) cm and the angle threshold of plane normal \(\theta_{diff}=2^{\circ}\). In Figure 12b, the door plane is projected to the connected wall plane and the point cloud of door component coloring in green is correctly extracted using the opening extraction method outlined in Section 3.4. Figure 12c shows the skeleton of the reconstructed components. Six walls, one door, one floor component, and one ceiling component are recognized from the data set. The relationship between the components is also correctly recovered. Based on the parameterization results, the components are saved according to the CityGML3.0 standard, as shown in Figure 12d. Recognized accuracy is measured to evaluate the performance of the component reconstruction (Table 1). In this case study, all recognized components are correctly categorized and reconstructed. The area dimension of the recognized components are also compared with the manually measured area dimensions from the point cloud. The absolute difference is calculated for each categorized component. Table 2 shows the comparison of results between the recognized dimension and measured dimension of each type of component.