## 3 Methodology  
### Overview  
In general, indoor space can be classified in two different applications: management of building components and indoor facilities; and use of indoor spaces [35]. Therefore, indoor space can be defined as a set of structural units with different functions composed of building components. As shown in Figure 1, according to the usage function and indoor navigation requirements, we divide the indoor space into navigable elements such as rooms, corridors and doors. Rooms and corridors are units separated by walls or partitions and enclosed by walls, ceilings and floors. Doors are the units responsible for connecting the various navigation elements in indoor navigation, and can be divided into \"thin doors\" and \"thick doors\" according to their characteristics [10; 35]. The \"thin door\" is a two-dimensional plane embedded in an opening in the indoor wall surface. The \"thick door\" is a three-dimensional space enclosed by a connecting transition space and two \"thin doors\", as shown in Figure 2. The connecting transition spaces are located inside the walls between rooms or corridors that have a connecting relationship.  
According to the hierarchical relationship between building components and navigation elements, this paper gives the flowchart of information extraction and reconstruction of indoor navigation elements, as shown in Figure 3. Firstly, we extract the building components from the point cloud. Then, the information of indoor navigation elements is produced based on the building components. Finally, the indoor navigation elements and navigation network are reconstructed and represented using the building components. There are four main steps:  
1. **Building components extraction**. Extracting the possible planar data from the point cloud as alternative building components \(\mathbf{P}\) using the random sample consensus (RANSAC) algorithm [36]. Then the alternative building components are classified and integrated according to their space characteristics to obtain the walls, floors and ceilings;
2. **Wall segment restoration**. Project the point cloud of the wall surface onto the XOY plane to form the wall segment raster. Then the connectivity of disjoint wall segments is judged according to the relationship between building components. Finally, the energy minimization function is constructed to determine the best connectivity;  
Figure 1: Hierarchy of indoor space navigation elements and building components.  
3. **Navigation element information extraction**. Diving building components into navigation elements such as rooms, corridors and connecting transition space based on their geometric features and topological relationships. Then the openings on the wall surface that satisfy the threshold value are extracted as doors. Finally, the navigation elements are optimized according to the relationship between doors and connecting transition space;
4. **Navigation element reconstruction and navigation network generation**. First, reconstruct the navigation element 3D model using the building components and the extracted navigation element information. Then, the indoor navigation network is generated and represented based on the connectivity and local geometric features between the navigation elements.