# FD-YOLO: A YOLO Network Optimized for Fall Detection
## 3 Materials and Methods
### Swin Transformer Module  
To further optimize the performance and enhance the accuracy of fall detection, we integrated transformer-based modules into an existing CNN-based model. As previously noted, the ability to capture global information is particularly crucial in scenarios in which parts of the body may be occluded by objects, potentially hindering detection accuracy. To capitalize on the strength of transformers in learning and extracting global information, we incorporated a modified Swin Transformer module into the YOLO network [39]. By integrating the Swin Transformer, which is designed to efficiently process global dependencies in visual data, the capability of the model to capture contextual relationships across the entire image is improved. This modification aims to address the limitations posed by partial occlusions and improve the ability of the model to detect falls in diverse and complex environments. The hierarchical design of the Swin Transformer, combined with its ability to capture both local and global information, allows for enhanced feature representation, further contributing to overall performance improvements in fall detection.  
The Swin Transformer operates by applying self-attention across sliding windows, which allows it to process the input data by dividing them into patches, which are then arranged linearly for transformer processing. Initially, self-attention is performed through the window multihead self-attention (W-MSA) mechanism, which computes the relationships within patches confined to a specific window. Subsequently, the shift window multihead self-attention (SW-MSA) mechanism shifts the window boundaries to analyze the relationships between patches located in different windows. These two complementary processes enable the model to capture the correlations between patches across different regions of the input image. The calculation formula for self-attention is the same as Equation (5):  
\[\text{Attention}(Q,K,V)=\text{SoftMax}\left(\frac{QK^{T}}{\sqrt{d}}+B\right)V \tag{5}\]  
Here, \(Q\), \(K\), and \(V\) represent the matrix for Query, Key, and Value, respectively, while B denotes the matrix for relative positional bias. The matrix V corresponds to the value matrix with attention weights applied, and the similarity between Query and Key is computed using the formula \((\frac{QK^{T}}{\sqrt{d}})\). The Shifted Window mechanism facilitates interaction between adjacent windows by alternating window positions across consecutive blocks. This process is represented mathematically as in Equation (6) where \(\hat{z^{l}}\) is the output of block \(l\), W-MSA denotes Window-based Multi-head Self-Attention, and LN refers to Layer Normalization.  
\[\hat{z^{l}}=W-\text{MSA}\left(\text{LN}\left(z^{l-1}\right)\right)+z^{l-1} \tag{6}\]  
The Self-Attention in the Shifted Window is calculated as shown in Equation (7), where SW-MSA indicates Shifted Window-based Multi-head Self-Attention.  
\[z^{l}=\text{SW}-\text{MSA}\left(\text{LN}\left(\hat{z^{l}}\right)\right)+\hat {z^{l}} \tag{7}\]  
By leveraging this approach for fall detection, the model emphasizes spatial location information during hierarchical feature extraction. This helps enhance the detection of falls by considering both local and global dependencies between image patches, even when parts of the body are occluded or positioned in challenging ways. We anticipate that this method will yield more effective and accurate fall detection results. The basic structure of this process is illustrated in Figure 4.