# 3D Point Cloud Completion Method Based on Building Contour Constraint Diffusion Probability Model
## 4 Experimental Section
### Ablation Experiment  
To evaluate the influence of the shape latent code with incorporated contour constraints in our approach on point cloud completion, we performed ablation experiments using the BuildingNet dataset. The errors reported in the table are mainly divided into two parts: G\(\rightarrow\)R and R\(\rightarrow\)G, with \(d_{\text{CD}}\) scores multiplied by \(10^{3}\). Smaller \(d_{\text{CD}}\) scores indicate better performance. The quantitative results are shown in Table 4. When using the point cloud diffusion probability model alone to extract features, the highest error values were obtained, with \(d_{\text{CD}}\) values of 1.711/1.508. When adding the contour-constrained shape latent code \(C\), the results were better than the Baseline Model, with a \(d_{\text{CD}}\) value of 1.556/0.923. Similarly, when adding the contour-constrained shape latent code \(M\), the results were also better than the Baseline Model, with a \(d_{\text{CD}}\) value of 1.231/1.126. The contour-constrained shape latent code \(C\) introduces outward redundancy, which results in a larger difference between the generated \(d_{\text{CD}}\) and the ground truth, leading to relatively higher \(d_{\text{CD}}\) values for G\(\rightarrow\)R. However, this redundancy increases the coverage of the ground truth surface by the predicted point cloud, and hence the \(d_{\text{CD}}\) value for R\(\rightarrow\)G is relatively lower. On the other hand, the contour-constrained shape latent code \(M\) causes inward contraction, leading to a relatively smaller difference between the generated \(d_{\text{CD}}\) and the ground truth. However, this contraction reduces the coverage of the ground truth surface by the predicted point cloud, resulting in relatively lower \(d_{\text{CD}}\) values for G\(\rightarrow\)R and relatively higher \(d_{\text{CD}}\) values for R\(\rightarrow\)G. Our model combines contour-constrained shape latent codes \(C\) and \(M\), leveraging their advantages to minimize the difference between the generated point cloud and the real point cloud while achieving a higher coverage of the ground truth surface by the predicted point cloud. The \(d_{\text{CD}}\) values were 0.928/0.751, which was better than all the models mentioned above. This suggests that the inclusion of building contour constraints enhances the performance of point cloud completion. The visualization results, as shown in Figure 13, demonstrate that the point cloud diffusion probability model based on building contour constraints produces the best results. As shown in Figure 13, the Baseline Model can extract the complete shape of building point clouds. However, in comparison to the real building model, there is some redundancy at the edges of the completion area. This suggests that the point cloud diffusion probability can capture global building features. The model that only integrates the contour-constrained shape latent code \(C\) shows slight redundancy at the edges of the completion area. Compared to the Baseline Model, the completed point cloud deviates less, aligning better with the real building point cloud shape. The model that only integrates the contour-constrained shape \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Contour-Constrained Shape Latent Code** & \multicolumn{2}{c}{\(d_{\text{CD}}\) (\(\downarrow\))} \\ \hline
**Type** & \(C\) & \(M\) & G\(\rightarrow\)R & R\(\rightarrow\)G \\ \hline Baseline Model & \(\times\) & \(\times\) & 1.711 & 1.508 \\ Model 1 & \(\bigvee\) & \(\times\) & 1.556 & 0.923 \\ Model 2 & \(\times\) & \(\bigvee\) & 1.231 & 1.126 \\ Our & \(\bigvee\) & \(\bigvee\) & 0.928 & 0.751 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative results of our approach to ablation experiments \(d_{\text{CD}}\) on the BuildingNet dataset. For each model, the paired numerical values represent \(d_{\text{CD}}\) for G\(\rightarrow\)R and R\(\rightarrow\)G. Lower values indicate better performance.