# CA-CGNet: Component-Aware Capsule Graph Neural Network for Non-Rigid Shape Correspondence
## 4 Experiments and Evaluation
### Correspondence Results  
In this section, we evaluate the experimental results of the proposed algorithm and other classical algorithms on four non-rigid datasets. We test our model on the original FAUST dataset, and Figure 8 shows the correspondence results, where intra-pair represents different poses of the same subject and inter-pair represents different subjects. The average error (AE) of our method compared with other state-of-the-art methods on the original FAUST dataset is shown in Table 3, including the average error of intra-pair and the average error of inter-pair. On the intra-pairs, our method achieves 1.85 cm, which outperforms ResNet-LDDMM significantly by 4.15%. On the inter-pairs, our method achieves 2.37 cm, which even outperforms the state-of-the-art method by 9.20%. Our method has the smallest average error in inter-pair and also performs well in intra-pair. Furthermore, SP [18] uses distributed inference to predict the model in the model initialization phase and combines local-based human pose inference with graph form human body shape models, the average error is smaller in the intra-pair. However, our method is more concerned with the generalization of shape matching, the combined average error is smaller than SP. Figure 8: Correspondence results on the original FAUST dataset. The four columns on the left are intra-pairs, and the four columns on the right are inter-pairs. In all matched pairs, the left side is the reference shape and the right side is the matching result of our method. Figure 7: Component matching results of different models. (**a**) is the component matching result of the same subject with different poses, and (**b**) is the component matching result of different subjects. In order to verify the robustness of the proposed method, we resample the original FAUST dataset to 4096 vertices for testing. Figure 9 visualizes the matching results of some methods on the remeshed FAUST dataset. It shows that our method achieves the best matching results in deformable shape correspondence. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Intra AE** & **Inter AE** & **Average** \\ \hline FMNet [12] & 2.44 & 4.83 & 3.635 \\ Cyclic-FM [21] & 2.12 & 4.07 & 3.095 \\ SP [18] & 1.57 & 3.13 & 2.350 \\
3D-CODED [8] & 1.98 & 2.88 & 2.430 \\ FARM [22] & 2.81 & 4.12 & 3.465 \\ SURFMNet [13] & 1.73 & 3.63 & 2.680 \\ MGCN [23] & 2.51 & 3.65 & 3.080 \\ ResNet-LDDMM [24] & 1.93 & 2.61 & 2.270 \\ Ours & 1.85 & 2.37 & 2.110 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average errors of different methods on the original FAUST dataset. The error is expressed as the distance between the mapping point and the ground truth (cm). Figure 9: Correspondence results on the remeshed FAUST dataset. The first column shows the reference shape, the second column shows ground truth, and columns three through six show the corresponding results of different networks. Furthermore, the correspondence performance of several methods is compared on the FAUST dataset and the remeshed FAUST dataset by using the Princeton benchmark protocol [39], as shown in Figure 10. With the increase of the geodesic error threshold, the matching accuracy is improved gradually. On the original FAUST dataset, our method is slightly improved compared with FMNet, SURFANet, and MGCN, while the corresponding accuracy of our method is significantly improved compared with other methods on the remeshed FAUST dataset. Our approach achieves good matching for meshes of different resolutions, which indicates that it has strong robustness. We further test on SCAPE, TOSCA, and KIDS datasets to verify the generalization of our approach. For a more intuitive comparison of experimental results, Figure 11 illustrates the geodesic errors of these methods on remeshed SCAPE, TOSCA, and KIDS datasets.