# Occlusion-Robust Facial Expression Recognition Based on Multi-Angle Feature Extraction
## 3 Method
### Con-Feature Recognition Module  
In the initial two modules, the fusion feature \(F_{H}\) and image feature \(F_{X}\) of input image \(X\) are obtained. In order for the network to learn more precise and consistent features, the feature selection process of the model is optimized using con-feature loss. Subsequently, the image feature \(F_{X}\) is passed to the MLP to return the predicted label \(Y\). As illustrated in Figure 6, Figure 5(a) represents \(F_{X}\), extracted by PTIR-50, and \(F_{H}\), whereas Figure 5(b) depicts \(F_{X}\) using con-feature loss. In Figure 5(b), these two features inform one another in order to obtain more discriminative expression features, thereby improving the robustness and accuracy of the model. We now provide a comprehensive description of the loss function that is employed for training purposes. In the field of recognition tasks, the acquisition of more discriminative and precise image features is of paramount importance. This improves both the classification accuracy and the model's robustness regarding different categories and details. Optimizing feature extraction reduces misclassification and improves real-world performance. Con-feature loss is a loss function that is used to combine the features extracted from two networks,  
Figure 6: Demonstration of the con-feature loss effect. The images in (**a**) illustrate the attentions of \(F_{X}\) and \(F_{H}\); (**b**) depicts attention utilizing con-feature loss. with the objective of optimizing the model's performance. This makes the extracted features more precise and discriminative. The concept of con-feature loss is based on the idea that 'two networks do not make the same mistake'. The proposed idea is that features identified by both networks in the expression recognition task will be more discriminative, improving model performance. Con-feature loss helps the model to capture more detailed and precise expression information through the mutual guidance of fused and global features. This approach enhances feature representation, increases sensitivity to subtle expression differences, and avoids feature redundancy from simple fusion. This significantly boosts expression recognition accuracy. The experiments and results supporting this hypothesis are shown in Section 4. Con-feature loss is designed as follows:  
\[L_{con-f}=\frac{1}{N}\frac{1}{L}\sum_{i=1}^{N}\sum_{l=1}^{L}\left\|F_{H}(i,l)- F_{X}(i,l)\right\|_{2} \tag{8}\]  
where \(N\) denotes the number of samples and \(L\) denotes the length of the feature sequence. RB-loss is designed as follows:  
\[L_{RB}=\max\{0,\omega-(\mu_{\max}-\mu_{0})\} \tag{9}\]  
where \(\omega\) is the hyperparameter, \(\mu_{0}\) is the attentional weight of the original face image, and \(\mu_{\max}\) denotes the maximum weight of all region blocks. Furthermore, the prevalence of ambiguous images in the FER dataset engenders uncertainty in the model with regard to specific samples, which, in turn, affects the model's assessment of that classification. To mitigate this effect, a label-smoothing strategy \(Loss_{sm}\) is employed, whereby label smoothing affords these images a certain degree of error tolerance probability, thereby preventing the model from placing undue credence in the sample labels. \(Loss_{sm}\) is designed as follows:  
\[ \begin{split} L_{\text{sm}}&=\frac{1}{N}\sum_{i=1}^ {N}\left[(1-\tau)\left(-\log\left(\frac{\exp(x_{i,y_{i}})}{\sum_{k}\exp(x_{i,k} )}\right)\right)\right.\\ &\quad+\tau\left(-\frac{1}{C}\sum_{j}\log\left(\frac{\exp(x_{i,j} )}{\sum_{k}\exp(x_{i,k})}\right)\right)\right]\end{split}  \tag{10}\]  
where \(N\) denotes the number of samples, \(C\) denotes the number of categories, \(i\) denotes the index of the sample, \(j\) and \(k\) denote the index of the category, \(x\) denotes the output of the model, \(x_{i,j}\) denotes the output value of the \(i\) sample on the \(j\) category, \(y_{i}\) denotes the value of the sample label of the \(i\) sample, and \(\tau\) denotes the smoothing factor.