# Multi-Scale Indoor Scene Geometry Modeling Algorithm Based on Segmentation Results
## 4 Experiments
### Analysis of Experimental Results in Synthetic Dataset  
To validate the feasibility of the algorithm proposed in this paper, C++ programming was used to simulate noise-free desktop scene point cloud data generated by a depth camera. Since the accurate dimensions and geometric parameters of different geometric objects cannot be obtained in real-world scenarios, three desktop scenes were synthesized with randomly placed objects of different shapes. The desktop was represented by a plane abstraction, and the desktop objects were represented by a cuboid, cylinder, cone, and sphere. The size of each object in the synthesized scene is known and used to estimate the error between the extracted parameters and the true values. Scene 1 consists of planar objects composed of cuboids with different poses and dimensions. Scene 2 consists of curved objects composed of spheres, cylinders, and cones. Scene 3 is a mixed scene composed of cuboids, spheres, cylinders, and cones. Figure 5: Reconstructed result diagram of curved objects. Figure 6 shows the experimental results of Scene 1, where the input point cloud data contain 372,344 points with an average density of 0.469 mm. From the figure, it can be observed that the plane and four cuboids with different poses and sizes were successfully segmented and labeled with different colors. The segmented objects were further evaluated for their corresponding types and geometric parameters. Based on the extracted parameters, the point cloud data with a specified density were generated as shown in Figure 6c, revealing the recovery of missing data and consistent orientations and positional relationships with the scene point cloud data [21]. Figure 7 shows the experimental results of Scene 2. The input point cloud data contain 361,218 points, with an average point cloud density of 0.485 mm. From the figure, it can be observed that the various regular objects on the table are segmented accurately and displayed with different colors. Based on the segmentation results, the types of objects are determined and their parameters are extracted. The reconstruction results, based on the extracted parameters and estimated sizes, are shown in Figure 7c. It can be seen from the figure that our algorithm can effectively recognize and model objects of different sizes, such as spheres, and different orientations, such as cylinders. This algorithm can also complete missing data [21]. The experimental results of Scene 3 are shown in Figure 8. The input point cloud data consist of 371,724 points, with an average point cloud density of 0.497 mm. From the graph, it can be observed that both planar and curved objects are completely segmented, and the object reconstruction results are consistent with the positions and orientations of the objects in the original scene point cloud. The experimental results demonstrate that, as the complexity of the scene increases, the algorithm still maintains a high accuracy in object segmentation and geometric parameter extraction. To verify the accuracy of the algorithm proposed in this paper for geometric reconstruction, a more complex scenario, referred to as Scenario 3, is taken as an example. The geometric parameters and size values of each object in the scenario are shown in Figure 9. In the figure, the parameter \(c\) represents the center point, \(\vec{n}\) represents the  
Figure 8: Experimental results of mixed object scene. Figure 6: Experimental results of plane object scene. Figure 7: Experimental results of curved object scene. normal vector, \(\vec{l}\) represents the axial direction, and \(p\) represents a point on the axis. These parameters are used to determine the position or orientation of the geometric object in three-dimensional space. The dimensions \(L,W,\) and \(H\) represent length, width, and height, respectively, while \(r\) represents the radius, which is used to determine the size of the geometric object in three-dimensional space.