## 6 Conclusions  
With its unique blend of artist and subject emotions, artistic portraititure presents distinct challenges for Emotional Expression Recognition (EER) and Facial Expression Recognition (FER). Our research introduces three pivotal advancements to address this: the PortraitEmotion3D (PE3D) dataset, a novel 3D emotion estimation method, and a cutting-edge self-attention module. The PE3D dataset is designed to classify emotions in artistic portraits, providing a crucial resource for researchers and practitioners. Our 3D emotion estimation method offers a more nuanced understanding of emotions than traditional 2D methods, while the self-attention module enhances facial feature representation, improving emotion recognition accuracy. Extensive testing on the PE3D dataset confirms our method's superiority over existing FER techniques. By integrating our module and loss function, the accuracy of recent FER systems can have an average improvement of over 1%. Combining our method with ESR-9 also achieved a comparable accuracy of 88.3% to SOTA methods on the FER+ dataset. The PE3D dataset and our modules can benefit the comprehensive understanding of artistic emotions of different movements and eras. They can enhance the analysis of artist-artwork interactions, providing insights into the artist's emotional state. This research could deepen our understanding of emotional expression in art and facilitate applications in various fields, including human-computer interaction, security, healthcare diagnostics, and entertainment.  
Conceptualization, S.L. and S.A.; methodology, S.L. and S.A.; software, S.L.; validation, S.L., S.A. and A.G.; formal analysis, S.L., S.A. and A.G.; investigation, S.L.; resources, S.L.; data curation, S.L.; writing--original draft preparation, S.L.; writing--review and editing, S.A. and A.G.; visualization, S.L.; supervision, S.A.; project administration, S.A.; funding acquisition, S.A. and S.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Research Fellowships award provided by the Art Science Connect, Graduate Center, CUNY.  
The PE3D dataset is available on Google Drive ([[https://drive.google.com/file/d/1](https://drive.google.com/file/d/1) qJqZUlbQpQiqzlrxa0 KtgRTpsHICEI-P/view?usp=sharing]([https://drive.google.com/file/d/1](https://drive.google.com/file/d/1) qJqZUlbQpQiqzlrxa0 KtgRTpsHICEI-P/view?usp=sharing) (accessed on 18 June 2024)). The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} FER & Facial Expression Recognition \\ PE3D & PortraitEmotion3D \\ DVA & Dominance-Valence-Arousal \\ IM & Impressionism \\ RO & Rococo \\ HR & High-Renaissance \\ UK & Ukiyo \\ NR & Northern-Renaissance \\ PI & Post-Impressionism \\ ND & Not Defined \\ PST & Portrait Swin Transformer \\ \end{tabular}  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Training Speed** & **Model Size** \\ \hline EmoFAN [24] & 0.13 s/100 images & 53 MB \\ EmoFAN + Ours & 0.45 s/100 images & 167 MB \\ \hline ESR-9 [25] & 0.19 s/100 images & 77 MB \\ ESR-9 + Ours & 0.52 s/100 images & 192 MB \\ \hline SCN [49] & 0.38 s/100 images & 131 MB \\ SCN + Ours & 0.71 s/100 images & 242 MB \\ \hline \hline \end{tabular}
\end{table}
Table 13: Training cost of our method on FER+ (Single Nvidia RTX 3090).