# 3D Mesh Model Classification with a Capsule Network
## 4 Experimental Evaluation
### Influencing Factor Experiment  
In MeshCaps, there are two modules. In order to verify the effectiveness of feature fusion in the feature extraction module and the effectiveness of the capsule network in the classification module, the capsule network was replaced with a three-layer convolutional neural network and LeNet for experiments. To compare the classification accuracy, Table 4 shows the classification accuracy of different structures.  
In the case of using the same feature method, MeshCaps achieved an accuracy of 93.8% compared with different classification network models, which illustrates the superiority of MeshCaps in the classification task of the SHREC15 data set. For complex data and capsule network comparison, the multilayer CNN structure has certain advantages. Compared with MeshCaps, which directly classifies polynomial parameter features through a three-layer convolutional neural network, the average accuracy reached 89.9%, which is higher  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Network Structure** & **Acc** \\ \hline Feature+3-Layer CNN & 89.9\% \\ Feature+LeNet & 90.8\% \\ MeshCaps & 93.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Network structure comparison.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Window Size K** & **Acc** \\ \hline
140 & 89.3\% \\
142 & 91.8\% \\
144 & 91.6\% \\
146 & 92.2\% \\
148 & 92.9\% \\
150 & 93.0\% \\
151 & 93.3\% \\
**152** & **93.8\%** \\
153 & 93.5\% \\
154 & 92.8\% \\
156 & 93.0\% \\
158 & 92.2\% \\
160 & 91.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Convolution window size.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Network** & **Capacity (MB)** & **FLOPs/Sample (M)** \\ \hline MeshCNN [(9)] & 1.323 & 498 \\ MeshNet [(10)] & 4.251 & 509 \\ SPH [(28)] & 2.442 & 435 \\ Ours-MeshCaps & 3.342 & 605 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter comparison test.  
than the accuracy of SPH method 88.2%, and also proves the effectiveness of the feature extraction method.  
Since the method in this paper is different from the MeshCNN and MeshNet network structures, there was no pooling operation in the network, and the vertices were directly selected according to the breadth-first search method to obtain the local surface as an input unit. Therefore, the method of random sampling of the vertices was simplified during training, and the sampling points were the quantities shown in Table 5.  
Because a patch unit is composed of multiple points around a vertex, a too high sampling percentage will inevitably cause the phenomenon of overlap of the patches, which affects the entire network training, and a model with a too low sampling ratio is prone to underfitting. The total number of vertices in the random sampling model was selected to be 85 % of vertices as input.  
In the network design, the center point coordinates, normal vectors and polynomial parameters were feature fused, and the capsule composition layer was added for feature mapping. Comparative experiments were done on the influence of the capsule composition layer and feature fusion. The results are shown in Table 6.  
The average accuracy of MeshCaps classification without feature fusion and no capsule composition layer still reached 91.2%, which is higher than the results obtained by the convolutional neural network method, and proves the certain advantages of the capsule network for complex data models. After fusing the features, classification of the increase in accuracy illustrates the effectiveness of feature fusion, but it was lower than the accuracy of the capsule composition layer and the unfused features, which verifies the importance of the capsule composition layer in the entire network structure.