# A Comprehensive Survey of Masked Faces: Recognition, Detection, and Unmasking
## 4 Evaluation Metrics  
This section will explain standard evaluation metrics, focusing specifically on those applied in MFR, FMR, and face unmasking (face mask removal). Evaluating model performance in these domains is essential for gauging their effectiveness in real-world applications. To this end, various evaluation metrics and benchmarking strategies are utilized to assess accuracy, robustness, and efficiency. In the following discussion, we explore the primary evaluation metrics and benchmarking approaches employed in these tasks. 1. **Accuracy** is a fundamental evaluation metric utilized across various domains, including facial recognition tasks. It represents the proportion of correct predictionsrelative to the total number of samples and can be formally defined as illustrated in Equation (1). \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\] (1)
2. **ERR (Error Rate)** is a crucial metric utilized in diverse classification tasks, offering valuable insights into model accuracy by measuring misclassifications relative to dataset size. Unlike accuracy, ERR accounts for both false positives and false negatives, providing a comprehensive assessment of model performance. Its sensitivity to imbalanced data underscores its importance, making it an essential tool for evaluating classification accuracy. Mathematically, ERR is calculated by dividing the sum of false positive and false negative predictions by the total number of instances, as shown in Equation (2). \[ERR=\frac{FP+FN}{TP+TN+FP+FN}=1-Accuracy\] (2)
3. **Precision** quantifies the proportion of accurate positive identifications among all the positive matches detected, and it can be formally expressed as depicted in Equation (3). \[Precision=\frac{TP}{TP+FP}\] (3)
4. **Recall** also known as **sensitivity** or **true positive rate** measures the proportion of true positive instances correctly identified by the system out of all actual positive instances. It is formally defined as shown in Equation (4). \[Recall=\frac{TP}{TP+FN}\] (4)
5. **F1-Score** is a pivotal evaluation metric, that represents the harmonic mean of precision and recall. This metric offers a balanced measure of the facial recognition model's performance, accounting for both false positives and false negatives. Particularly valuable for imbalanced datasets, the F1-Score provides a comprehensive assessment of the model performance. Unlike accuracy, which may overlook certain types of errors, the F1-Score considers both false positives and false negatives, rendering it a more reliable indicator of a model's effectiveness. Its calculation is demonstrated in Equation (5). \[F1-Score=2\times\frac{Precision\times Recall}{Precision+Recall}\] (5)
6. **ROC (Receiver Operating Characteristic) Curve** ROC curves [52] graphically represent the trade-off between sensitivity (true positive rate) and specificity (true negative rate) across various threshold values. This visualization aids in selecting an optimal threshold that strikes a balance between true positive and false positive recognition rates. By examining the ROC curve, decision makers can effectively assess the performance of a classification model and make informed decisions about threshold selection. 7. **AUC (Area Under the Curve)** is a pivotal evaluation metric in classification tasks, offering a comprehensive assessment of a model's performance. It quantifies the discriminative power of the model across varying threshold values, providing insights into its ability to correctly classify positive and negative instances. A higher AUC value signifies stronger discrimination, indicating a superior model performance. Conversely, an AUC value of 0.5 suggests that the model's predictive ability is no better than random chance. AUC is instrumental in gauging the effectiveness of classification models and is widely utilized in performance evaluation across diverse domains. 8. **Confusion Matrix** provides a detailed breakdown of the model's predictions, including true positives, true negatives, false positives, and false negatives.