# VB-Net: Voxel-Based Broad Learning Network for 3D Object Classification
## 4 Experiments and Analysis
### Noise Resistance Test  
To examine noise resistance in our model, we added Gaussian noise to original point clouds, and then generated the voxel. Figure 5 gives examples under Gaussian noise with \(20\times 20\times 20\) and \(32\times 32\times 32\) voxel resolution with original voxels in the ModelNet40 and ModelNet10 datasets. We employed our method, VoxNet [26], and model D mentioned in Section 4.2 in the experiments. Experimental results are shown in Table 6. The VoxNet [26], feature extractors in model D, and VB-Net were trained 120 times on the training set (accuracies of VoxNet [26] on the ModelNet40 and ModelNet10 datasets under \(32\times 32\times 32\) voxel resolution were cited from [26] directly).  
VoxNet [26] was the most affected by Gaussian noise, and its accuracy dropped by half on ModelNet10, with even worse performance on ModelNet40. The accuracies of methods with BLS decreased much more slightly compared to VoxNet [26], while some even increased a little. When comparing the original BLS and the BLS employing VoxNet [26] as the feature extractor, our method also had better performance. We carried out more experiments with different scales of Gaussian noise to test the robustness of our system, as shown in Figure 6.  
Figure 5: Samples with Gaussian noise and their original shape.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Conv3D** & **Conv3D** & **Max** & **Accuracy** & **Training Time** & **Test Time** \\  & **(32,5,2)** & **(32,3,1)** & **Pooling** & **Accuracy** & **(s)** & **(s)** \\ \hline F & \(\surd\) & & \(\surd\) & 89.86\% & 2.91 & 0.1149 \\ G & & \(\surd\) & \(\surd\) & 89.42\% & 44.78 & 0.4047 \\ H & \(\surd\) & \(\surd\) & & 87.77\% & 13.72 & 0.1928 \\ I & \(\surd\) & \(\surd\) & \(\surd\) & 89.64\% & 1.91 & 0.0829 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Ablation experiment of feature extractor.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**ModelNet10**} & \multicolumn{4}{c}{**ModelNet0**} \\ \cline{2-9}
**Method** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** \\  & **(32\(\times\) 32\(\times\) 32\(\times\) 32\(\times\) 32)** & **(32\(\times\) 20\(\times\) 20)** & **(20\(\times\) 20\(\times\) 20)** & **(20\(\times\) 32\(\times\) 32)** & **(20\(\times\) 32\(\times\) 32)** & **(32\(\times\) 32)** & **(20\(\times\) 20)** \\  & **(No Noise)** & **(20\(\times\) 20\(\times\) 20)** & **(No Noise)** & **(No Noise)** & **(No Noise)** & **(No Noise)** & **(No Noise)** \\ \hline BLS & 83.92\% & 86.01\% & 87.55\% & 86.56\% & 72.33\% & 76.86\% & 77.99\% & 79.13\% \\ Our method & 90.63\% & 90.08\% & 90.08\% & 89.64\% & 82.78\% & 83.99\% & 81.24\% & 82.41\% \\ Model D & 89.53\% & 89.75\% & 89.31\% & 88.76\% & 82.08\% & 81.07\% & 81.56\% & 80.87\% \\ VoNet [20] & 42.73\% & 92\% & 47.79\% & 87.88\% & 17.26\% & 83\% & 20.98\% & 76.29\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Classification accuracies of original data and Gaussian noise data.  
Obviously, the accuracy of VoxNet [26] decreased as the scale of noise increased, while the accuracies of methods with BLS were stable at about 90%. We also noticed that, in some experiments, the accuracy of data with noise was higher than that without noise. This situation happened in all methods with BLS. We think this phenomenon was mainly due to the settings in BLS. According to Section 4.1, the performance of BLS was influenced by the number of nodes in the feature layer and enhancement layer. The reason for the improvement in accuracy was that we did not find the best combination of enhancement nodes and feature nodes in the experiments. Considering that there is no theory regarding the relationship among accuracy, nodes in BLS, and voxel resolutions, and considering that the number of possible combinations is large, we think that meeting this phenomenon is acceptable.