# 3D Point Cloud Completion Method Based on Building Contour Constraint Diffusion Probability Model
## 4 Experimental Section
### Comparative Analysis of Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Building 1**} & \multicolumn{4}{c}{**Building 2**} \\ \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{\(d_{\text{CD (\downarrow)}}\)} & \multicolumn{2}{c}{\(d_{\text{EMD (\downarrow)}}\)} & \multicolumn{2}{c}{\(d_{\text{CD (\downarrow)}}\)} & \multicolumn{2}{c}{\(d_{\text{EMD (\downarrow)}}\)} \\ \cline{2-9}  & **G\(\rightarrow\)R** & **R\(\rightarrow\)G** & **G\(\rightarrow\)R** & **R\(\rightarrow\)G** & **G\(\rightarrow\)R** & **R\(\rightarrow\)G** & **G\(\rightarrow\)R** & **R\(\rightarrow\)G** \\ \hline PCN & 5.674 & 5.763 & 9.156 & 9.043 & 7.263 & 7.038 & 11.847 & 11.647 \\ PF-Net & 4.835 & 4.785 & 7.248 & 6.97 & 6.098 & 5.945 & 8.566 & 8.891 \\ VRC-Net & 4.248 & 4.196 & 6.863 & 6.725 & 5.059 & 4.903 & 7.695 & 7.633 \\ Ours & 3.831 & 3.781 & 6.324 & 6.428 & 4.817 & 4.512 & 7.314 & 7.062 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Below are the comparison results of \(d_{\text{CD}}\) and \(d_{\text{EMD}}\) for point cloud completion in missing areas of buildings between our method and PCN, PF-Net, and VRC-Net on the BuildingNet dataset. For each model, the paired numerical values represent \(d_{\text{CD}}\) and \(d_{\text{EMD}}\) for G\(\rightarrow\)R and R\(\rightarrow\)G. Lower values indicate better performance. As can be seen from the comparison of experimental results in Figure 11, our method has better point cloud completion effect. In Figure 11, PCN focuses on global features and generates point clouds from coarse to fine during decoding. However, due to insufficient extraction of local features, it fails to completely recover these structures and exhibits uneven distribution of generated point clouds in space, as shown in 'complete' for Building 1 and 'View 1.' Additionally, PCN is trained based on the assumption of smooth features, which leads to the smoothing of the roof parts connecting different sections, as seen in 'View 2' for Building 1 and 'View 1' for Building 2. Despite PF-Net's utilization of multiple fully connected layers to improve the smoothness of prediction outcomes and simplify the point cloud generation process, during the encoding stage, it exclusively downsamples the input point cloud for feature extraction and does not effectively capture all the local point cloud features. As a result, when it attempts to recover missing areas, the point clouds generated at the boundaries deviate from the original geometric space of the building, as shown in 'View 1' for Building 1 and in Building 2. VRC-Net consistently provides a smooth global shape, and the generated point clouds exhibit good spatial uniformity. It effectively retains the intricate details present in the input point cloud. However, the edges of the buildings are sharp, and excessive smoothing results in some non-realistic points at the edges, as shown in 'View 2' for Building 1. Similarly, for approximately curved multi-planar surfaces, they are smoothed into curves, as seen in 'View 1' for Building 2. Our  
Figure 11: Comparison of building point cloud completion results using different methods: This figure encompasses the initial incomplete point cloud, the completed point clouds generated by PCN, PF-Net, VRC-Net, and our method, alongside their respective real point clouds for reference. model addresses this by using contour-constrained shape codes to constrain the diffusion probability model; the generated point clouds do not deviate from the original geometric space of the buildings. As shown in Building 1, compared to other methods, its edges closely match the geometric edges of the real building. In the case of Building 2, View 2, our method accurately completes the building point cloud in the corner area between two parts, while other methods connect these two parts together.