## 5 Experiments
### Ablation Studies
Analysis of Results: Our experiments have demonstrated that the 3D labels and the \(Loss_{dis}\) we developed, building on PE3D, have notably enhanced the testing accuracy of the SCN, ESR-9, and EmoFAN models. Despite these enhancements appearing marginal, they are significant given that the baseline models selected are among the state-of-the-art across several public FER datasets. Moreover, our approach distinguishes itself by concentrating on the textures and colors of art paintings rather than on real human faces. We employed class probability vectors to present our final results visually, accurately depicting the models' prediction outcomes (see Figure 14). We also selected three faces from the FER+ testing set to demonstrate the effectiveness of our methods (see Figure 17). The diagram shows the final emotion distribution (probability) of different methods. The three samples we showed are one fear and two neutral faces, where the other methods (SCN, EmoFAN, and ESR-9) made wrong predictions (baseline model results). However, by combining the final output with 3D distance labels, the wrong prediction can be corrected, which explains the improvement in the final accuracy. After applying the PST module, the probability of the right emotion can be further improved. However, as a tradeoff, the PST weakens the capability of the model to describe the complexity of the emotion. The results show that the PE3D labels could not only correctly predict the categorical emotion but also describe the complexity of the emotion. There are several limitations to this approach. One is the computing time for training. Table 13 shows that when using an NVIDIA RTX 3090 GPU for training, the synthesized model is slower than the original model, more than 100% slower on average. This is mainly because the parameters added by the Swin Transformer significantly increased the model's size and the amount of calculation during training. This will be a challenge for real-time scenario applications. Another limitation is that the model's generalization ability is weak for classes with fewer samples, such as for imbalanced datasets. For example, labels with fewer training and testing samples, such as the accuracies of \"contempt\" and \"disgust\", are relatively poor. This problem can be addressed by balancing the dataset or performing data augmentation methods. Based on the above limitations, in the future, we want to improve the model training efficiency and the versatility of small datasets by simplifying the model parameters to optimize the model structure and adding data augmentation strategies during training. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Modification** & **Loss Function** & **Accuracy** \\ \hline \multirow{3}{*}{Res18 [84]} & - & \(Loss_{ce}\) & 80.6 \\  & +PE3D & \(Loss_{ce}\) & 81.3 \\  & +PE3D + PST & \(Loss_{ce}+Loss_{dis}\) & **81.8** \\ \hline \multirow{3}{*}{SCN [49]} & - & \(Loss_{ce}\) & 81.0 \\  & +PE3D & \(Loss_{ce}\) & 81.2 \\  & +PE3D + PST & \(Loss_{ce}+Loss_{dis}\) & **81.8** \\ \hline \multirow{3}{*}{EmoFAN [24]} & - & \(Loss_{ce}\) & 79.6 \\  & +PE3D & \(Loss_{ce}\) & 80.3 \\  & +PE3D + PST & \(Loss_{ce}+Loss_{dis}\) & **80.8** \\ \hline \multirow{3}{*}{ESR-9 [25]} & - & \(Loss_{ce}\) & 87.2 \\  & +PE3D & \(Loss_{ce}\) & 87.8 \\ \cline{1-1}  & +PE3D + PST & \(Loss_{ce}+Loss_{dis}\) & **88.3** \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Effectiveness Of proposed module and loss function. Figure 17: Emotion distribution for FER+ testing samples. One fear and two neutral faces are selected from the FER+ testing set. All of them are wrongly predicted by the baseline model (they are predicted as surprise, surprise, and happy). After applying PE3D labels and PST, the prediction result can be corrected.