# 3D Point Cloud Completion Method Based on Building Contour Constraint Diffusion Probability Model
## 4 Experimental Section
### Comparative Analysis of Experimental Results  
To demonstrate the superiority of our model, we conducted comparative experiments between PCN [16], PF-Net [37], VRC-Net [39], and our model on the BuildingNet dataset. We used the metrics described in Section 4.3 to evaluate the point clouds generated by the above-mentioned models and summarized the results in Tables 1 and 2. In Figure 11, we present the results of a visual comparison between the three-point cloud completion technique and our approach. Tables 1 and 2 show the quantified comparison results of the models. G\(\rightarrow\)R refers to the error from the generated point cloud to the real point cloud, which measures the difference between the generated and real scenarios. R\(\rightarrow\)G refers to the error from the real point cloud to the generated point cloud, which reflects the degree to which the ground truth surface is covered by the predicted point cloud. The \(d_{\text{CD}}\) score is multiplied by \(10^{3}\), and the \(d_{\text{EMD}}\) score is multiplied by \(10^{2}\). In Table 1, the overall point cloud completion error consists of two components: prediction error in the missing regions and shape variation in the original parts. Table 1 unmistakably demonstrates that our approach surpasses other currently available methods in the comprehensive completion of building point clouds. In Table 2, the missing area error is calculated to ensure the fairness of the model evaluation. Table 2 continues to affirm that our approach is better suited for completing building point clouds, specifically in terms of filling in the gaps, when compared to other methods. The findings presented in Tables 1 and 2 illustrate that our approach excels in producing point clouds with increased precision and reduced distortion, addressing both overall point cloud completion and the specific task of filling in missing areas. \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 & 2.896 & 3.112 & 6.121 & 6.099 & 3.405 & 2.887 & 7.335 & 7.686 \\ PF-Net & 2.06 & 1.838 & 4.001 & 3.773 & 2.417 & 2.165 & 4.808 & 4.431 \\ VRC-Net & 1.419 & 1.307 & 3.853 & 3.531 & 1.774 & 1.579 & 4.434 & 4.182 \\ Ours & 1.057 & 0.828 & 3.568 & 3.196 & 1.646 & 1.522 & 4.253 & 4.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: We present the comparative results of \(d_{\text{CD}}\) and \(d_{\text{EMD}}\) between our approach and PCN, PF-Net, and VRC-Net on the BuildingNet dataset for complete building point cloud completion. The paired numerical values indicate \(d_{\text{CD}}\) and \(d_{\text{EMD}}\) for G\(\rightarrow\)R and R\(\rightarrow\)G, where lower values are preferable.