# FD-YOLO: A YOLO Network Optimized for Fall Detection
## 3 Materials and Methods
### Evaluation Metrics  
The primary objective of this study was to detect falls accurately using images. Because undetected falls can prevent timely intervention, we placed particular emphasis on analyzing the false negative (FN) rate because missed detections can have serious consequences. Given that the YOLO network is designed for real-time image processing and can detect falls in video-based scenarios, we assumed that falls would be detected within the standard 60 frames of video footage. Thus, our goal was to develop a network capable of maintaining an FN count at or below 60, ensuring reliable fall detection across various scenarios. The evaluation of object detection networks commonly involves performance metrics derived from a confusion matrix, including recall, precision, accuracy, and mean average precision (mAP). The confusion matrix is used to assess the predictive performance of a network and consists of four key values: true positive (TP), true negative (TN), false positive (FP), and FN. These values were used in different combinations to calculate the performance metrics used in this study. Figure 5: FD module. Figure 6: FD-YOLO structure. The performance metrics evaluated in this study are described below:  
Recall, as defined in Equation (8), is the proportion of actual positive cases (falls) correctly identified by the model. It is a crucial metric in fall detection as it directly relates to minimizing missed detections (false negatives):  
\[\text{Recall}(\text{R})=\frac{\text{TP}}{TP+FN} \tag{8}\]  
Precision, as shown in Equation (9), represents the proportion of correctly identified positive cases among all predicted positives. This metric emphasizes the model's ability to reduce false positives:  
\[\text{Precision}(\text{P})=\frac{\text{TP}}{TP+FP} \tag{9}\]  
Accuracy, expressed in Equation (10), measures the overall proportion of correctly classified instances (both positive and negative) among all predictions made by the model:  
\[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{TP+FN+FP+TN} \tag{10}\]  
The mean average precision (mAP), defined in Equation (11), evaluates the model's performance by averaging the precision scores over all object classes. It is derived by integrating the precision-recall curve for each class and computing the mean across all classes:  
\[\text{Average Precision}\;(\text{AP})=\int_{0}^{1}PdR,\text{mAP}=\frac{1}{N} \sum_{i=1}^{N}AP_{i} \tag{11}\]  
In object detection, Intersection over Union (IoU), as defined in Equation (12), is another critical metric for performance evaluation:  
\[\text{Intersection over Union (IoU)}=\frac{Area\;of\;Overlap}{Area\;of\;Union} \tag{12}\]  
IoU measures the accuracy of the predicted object's location by quantifying the degree of overlap between the predicted bounding box and the ground truth bounding box. Specifically, IoU is defined as the ratio of the overlapping area between the predicted and actual bounding boxes to the total area of their union. This metric provides a precise and quantitative assessment of how well the predicted bounding box aligns with the actual object. IoU is widely utilized in object detection tasks to refine model predictions and evaluate detection accuracy. The overlapping area refers to the portion where the predicted and actual bounding boxes intersect, whereas the union area represents the total combined area of both the predicted and actual bounding boxes. The IoU value ranges from 0 to 1, where an IoU of 1 indicates perfect alignment between the predicted and actual bounding boxes, and an IoU of 0 indicates no overlap. The IoU is commonly used in conjunction with mAP to assess the performance of object detection models. Typically, the mAP is evaluated at different IoU thresholds. For instance, [EMAIL_ADDRESS] refers to the mAP when the IoU threshold is set to 0.5, which means that a prediction is considered valid only if the IoU between the predicted and actual bounding boxes is 0.5 or higher.