# RE-PU: A Self-Supervised Arbitrary-Scale Point Cloud Upsampling Method Based on Reconstruction
## 5 Conclusions  
In this paper, we propose RE-PU, a novel point cloud upsampling method, which is based on point cloud reconstruction, achieving self-supervised upsampling at arbitrary rates. This feature can expand the scope of application of the method.  
The proposed method consists of two main stages: the first stage involves training the autoencoder or decoder using the original point cloud data and a prior distribution. The  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Model 1** & **Model 2** & **Model 3** & **Ours** \\ \hline
**CD\(\downarrow\)** & 0.874 & 0.697 & 0.512 & **0.421** \\ \hline \hline \end{tabular} Note: The downward arrows (\(\downarrow\)) indicate that lower values are better for the corresponding metrics.  
\end{table}
Table 4: Quantitative results of different models.  
Figure 13: Qualitative results of different models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**KNN** & **10** & **15** & **20** & **25** & **30** \\ \hline
**CD \(\downarrow\)** & 0.598 & 0.523 & **0.421** & 0.498 & 0.592 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Effect of neighborhood size on dynamic graph.  
encoder identifies input point clouds, and the decoder takes the encoder's output along with a prior distribution as input to reconstruct the prior distribution into the input point cloud. And the second stage is to upsample the point cloud data by increasing the number of sampled points on the prior distribution with the trained model. The experimental results demonstrate that the proposed method can achieve comparable outcomes to other state-of-the-art methods in terms of both visual quality and quantitative metrics. We achieved the best results in two indicators and second-best results in the remaining two on the PU-GAN dataset. Our results show a 4% enhancement in both the CD and EMD metrics over the current state-of-the-art methods. We also achieved the best results in three indicators and second-best results in the remaining two on the PU1K dataset. We improved the existing best results by about 13% on the HD metric, 16% on the EMD metric, and 4% on the P2F (std) metric.  
Additionally, we explored the effectiveness of our network architecture and the impact of different prior distributions. It turns out that the dynamic graph and offset attention modules play a crucial role in the network, which can significantly improve the performance of the network compared to the baseline model. The results also show that the choice of prior distribution can have a significant impact on the performance of the network, and the introduction of noise to the sampled points can enhance the performance of the network.  
We also demonstrate the results of our method on point clouds of different scenes. The results show that our method can effectively handle noisy point clouds and point clouds of different sizes, and it can upsample point clouds at arbitrary rates.  
In the future, we will delve deeper into exploring the relationship between point cloud reconstruction and point cloud upsampling. Additionally, we plan to investigate the application of the proposed method in other tasks, such as point cloud completion and point cloud generation.  
Conceptualization, Y.H.; methodology, M.Y.; validation, F.Z.; formal analysis, F.Y.; writing--original draft preparation, Y.H.; writing--review and editing, M.Y.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.