## 3 Results
### Ablation Experiments of BMP_Net  
#### 3.4.1 Ablation Experiments on the Modules of BMP_Net  
To investigate the impact of key structures and modules in BMP_Net on overall performance, a series of ablation experiments was conducted. These experiments involved replacing or removing key modules, and the tests were carried out under identical conditions to validate the importance of each designed module. The results of the ablation study are shown in Table 3. Three design components or modules were ablated, including the PFMixer module, the Point Cloud Transition Downsampling module, and the N2P Attention (Neighbor Point Attention) module. We tested five different scenarios: 1. The model with only the main structure, where the PFMixer module was removed (replaced by the MixerBlock from the PointMixer network), the Point Cloud Transition Downsampling module was substituted by a regular downsampling layer, and the N2P Attention module was excluded. 2. The model with the PFMixer module removed only. 3. The model with  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Metrics** & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**MAPE**} \\ \hline Model\textbackslash{}loss & Focal\_L1 & \(\Lambda_{\text{sum}}^{\text{PSCDR}}\) & Focal\_L1 & \(\Lambda_{\text{sum}}^{\text{PSCDR}}\) & Focal\_L1 & \(\Lambda_{\text{sum}}^{\text{PSCDR}}\) \\ PointNet & 192.14 & 178.30 & 165.06 & 137.52 & 0.312 & 0.276 \\ PointNet++ & 187.32 & 175.42 & 152.89 & 130.53 & 0.284 & 0.268 \\ DGCNN & 157.19 & 154.41 & 131.68 & 127.18 & 0.235 & 0.242 \\ PointMixer & 113.41 & 102.11 & 93.26 & 77.93 & 0.194 & 0.167 \\ PointTransformer & 155.49 & 148.91 & 128.74 & 122.87 & 0.230 & 0.214 \\ PointNeXt & 146.96 & 134.69 & 116.76 & 103.49 & 0.215 & 0.198 \\ BMP\_Net & **84.48** & **75.92** & **67.31** & **63.19** & **0.131** & **0.115** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of the PSCDR method on different common point cloud models.  
the Point Cloud Transition Downsampling module removed only. 4. The model with the N2P Attention module removed only. 5. The full BMP_Net model proposed in this study.  
From the table, it can be observed that in Case 1, where all three key modules were removed, the model performance was the worst, which aligns with our expectations. After removing these three critical modules, the model's ability to extract and process the point cloud structure and features significantly declined. Without the PFMixer module, which performs deep feature extraction and data compression, and given the abundance of redundant information in the data, the model's performance dropped sharply.  
In Case 4, the evaluation metrics outperformed those of Case 2 and Case 3, indicating that the PFMixer module and Point Cloud Transition Downsampling module make significant contributions to the network's performance. The improvement in performance due to these two modules is not simply a linear addition, suggesting that careful consideration was given to the synergy between the two modules during network design, achieving a result where \"one plus one is greater than two.\" In both Case 2 and Case 3, where only the PFMixer module or the Point Cloud Transition Downsampling module was removed, the performance dropped significantly compared to Case 5 (the full BMP_Net model). Additionally, Case 4 demonstrated that the N2P Attention module effectively captured the surrounding information of each point, aiding in learning local features and enhancing the overall performance of point cloud data processing. This highlights the importance of N2P Attention in improving the model's ability to focus on relevant neighborhood information, which contributes to better performance in handling complex point cloud data.