# An Efficient Bidirectional Point Pyramid Attention Network for 3D Point Cloud Completion
## 4 Experimental
### Completion Results on ShapeNet  
We applied the mean Chamfer Distance as the evaluation metric, which contained two items in our experiments: \(\mathrm{Pred}\rightarrow\mathrm{GT}\) and \(\mathrm{GT}\rightarrow\mathrm{Pred}\). The Chamfer Distance from a predicted point cloud to the ground truth (\(\mathrm{Pred}\rightarrow\mathrm{GT}\)) measures the difference between the predicted and real point clouds, which is calculated with:  
\[\mathrm{d_{CD}(F_{Pred},F_{GT})}=\frac{1}{\mathrm{F_{Pred}}}\sum_{\alpha\in \mathrm{F_{Pred}}}\min_{y\in\mathrm{F_{GT}}}\|x-y\|_{2}^{2} \tag{8}\]  
The Chamfer Distance from the ground truth to a predicted point cloud (\(\mathrm{GT}\rightarrow\mathrm{Pred}\)) manifests the extent to which the shape of the prediction covers the real point cloud, which is calculated with:  
\[\mathrm{d_{CD}(F_{GT},F_{Pred})}=\frac{1}{\mathrm{F_{GT}}}\sum_{\alpha\in \mathrm{F_{GT}}}\min_{y\in\mathrm{F_{Pred}}}\|x-y\|_{2}^{2} \tag{9}\]  
Results on ShapeNet-13: We compared the results of our model with those of L-GAN [29], PCN [15], 3D-point Capsule Networks [30] and PF-Net [14] on standard metrics. In Table 1, the results of the above four methods are cited from [14]. Our method surpassed the other ones on 13 categories in terms of \(\mathrm{Pred}\rightarrow\mathrm{GT}\) and \(\mathrm{GT}\rightarrow\mathrm{Pred}\) errors, and achieved the best average Chamfer Distance in the missing region. This suggests that our network was able to reconstruct the missing point cloud with higher precision. Results on ShapeNet-16: We experimented with our method and the most advanced PF-Net method on ShapeNet-16. Since PF-Net was only trained on the ShapeNet-13 dataset, we trained and tested it again using the same dataset according to their open-source code for fair comparison and quantitative analysis. Table 2 shows that our method resulted in a lower average Chamfer Distance error when increasing the dataset from 13 to 16 categories. The three new categories, namely, Earphone, Knife, Rocket, on both \(\mathrm{Pred}\rightarrow\mathrm{GT}\) andGT \(\rightarrow\) Pred  errors were all smaller than those of PF-Net. These results justify that the proposed network could handle a larger dataset and effectively reconstruct the full shape. Figure 6 shows the qualitative results of our method and PF-Net on ShapeNet-16. Our method preserved the original input geometry while better computing and refining the missing parts of the completion for the shown examples. Furthermore, we compared the number of trainable parameters in PF-Net and our method. As shown in Table 2, our method performed significantly better with fewer parameters than those of PF-Net. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Category** & **LGAN-AE** & **PCN** & **3D Capsule** & **PF-Net** & **BiPPAN** \\ \hline Airplane & 3.357/1.130 & 5.060/1.243 & 2.676/1.401 & 1.091/1.070 & 0.964/0.875 \\ Bag & 5.707/5.303 & 3.251/4.314 & 5.228/4.202 & 3.929/3.768 & 2.864/2.823 \\ Cap & 8.968/4.608 & 7.015/4.240 & 11.04/4.739 & 5.290/4.800 & 4.371/3.489 \\ Car & 4.531/2.518 & 2.741/2.123 & 5.944/3.508 & 2.489/1.839 & 2.28/1.681 \\ Chair & 7.359/2.339 & 3.952/2.301 & 3.049/2.207 & 2.074/1.824 & 1.758/1.442 \\ Guitar & 0.838/0.536 & 1.419/0.689 & 0.625/0.662 & 0.456/0.429 & 0.377/0.376 \\ Lamp & 8.464/3.627 & 11.61/1.739 & 9.912/5.847 & 5.122/3.460 & 3.731/2.513 \\ Laptop & 7.649/1.413 & 3.070/1.422 & 2.129/1.733 & 1.247/0.997 & 1.118/0.864 \\ Motorbike & 4.914/2.036 & 4.962/1.922 & 8.617/2.708 & 2.206/1.775 & 1.931/1.562 \\ Mug & 6.139/4.735 & 3.590/3.591 & 5.155/5.168 & 3.138/3.238 & 3.036/2.914 \\ Pistol & 3.944/1.424 & 4.484/1.414 & 5.980/1.782 & 1.122/1.055 & 0.929/0.831 \\ Skateboard & 5.613/1.683 & 3.025/1.740 & 11.49/2.044 & 1.136/1.337 & 1.007/1.029 \\ Table & 2.658/2.484 & 2.503/2.452 & 3.929/3.098 & 2.235/1.934 & 1.744/1.626 \\ Mean & 5.395/2.603 & 4.360/2.661 & 5.829/3.008 & 2.426/2.117 & 2.008/1.694 \\ \hline \end{tabular}
\end{table} 
Table 1: Results of a comparison between our method and most advanced methods on the ShapeNet-13 dataset.