## 2 YOLO Algorithm and Its Improvements
### MPDlou Loss Function  
The Minimum Point Distance Intersection over Union (MPDIou) loss [31], proposed by [PERSON], [PERSON], et al., addresses the issues of CIou failure when the actual and predicted bounding box centers coincide and aspect ratios match, as well as the problem of extensive overlap among multiple predicted boxes. MPDlou encompasses all relevant factors considered in existing loss functions, such as overlap or non-overlap  
Figure 7: Schematic diagram of the EMA. The input feature map is divided into \(g\) groups, each processed separately. For each group, the features are passed through an average pooling layer and concatenated. This is followed by sigmoid and softmax activation functions applied to the pooled features. The outputs are then normalized using group normalization. The resultant features are multiplied and summed, producing the final output feature map, which retains the input dimensions \(h\times w\times c\) after passing through a sigmoid activation function.  
area, center point deviation, and deviations in width and height, while simplifying the computational process.  
This approach directly minimizes the distance between the top-left and bottom-right corners of the predicted bounding box and the ground truth box. During the training phase, the formula forces the bounding box \(B^{prd}=[x^{prd},y^{prd},w^{prd},h^{prd}]\) to approach its actual bounding box \(B_{gt}=[x_{gt},y_{gt},w_{gt},h_{gt}]\):  
\[L=\underset{\Theta}{MIN}\sum_{B_{gt}\in B_{gt}}L(B_{gt},B_{prd}|\Theta) \tag{7}\]  
In Equation (7), \(B_{gt}\) represents the set of actual annotated boxes, while \(\Theta\) denotes the parameters used for regression in deep learning. The loss function of MPDIou is defined as shown in Equation (8).  
\[\begin{split}& d_{1}^{2}=(x_{1}^{B}-x_{1}^{A})^{2}+(y_{1}^{B}-y_{1}^ {A})^{2},\\ & d_{2}^{2}=(x_{2}^{B}-x_{2}^{A})^{2}+(y_{2}^{B}-y_{2}^{A})^{2}, \\ & MPDIou=\frac{A\cap B}{A\cup B}-\frac{d_{1}^{2}}{w^{2}+h^{2}}- \frac{d_{2}^{2}}{w^{2}+h^{2}},\\ & L_{MPDIou}=1-MPDIou\end{split} \tag{8}\]  
Thus, all factors of the existing bounding box loss function are determined by four points, with the transformation formula presented in Equation (9).  
\[\begin{split}&|C|=(\max(x_{2}^{gt},x_{2}^{prd})-\min(x_{1}^{gt},x_{ 1}^{prd}))\times(\max(y_{2}^{gt},y_{2}^{prd})-\min(y_{1}^{gt},y_{1}^{prd})), \\ & x_{c}^{gt}=\frac{x_{1}^{gt}+x_{2}^{gt}}{2},y_{c}^{gt}=\frac{y_{ 1}^{gt}+y_{2}^{gt}}{2},\\ & y_{c}^{prd}=\frac{y_{1}^{prd}+y_{2}^{prd}}{2},x_{c}^{prd}=\frac{ x_{1}^{prd}+x_{2}^{prd}}{2},\\ & w_{gt}=x_{2}^{gt}-x_{1}^{gt},h_{gt}=y_{2}^{gt}-y_{1}^{gt},\\ & w_{prd}=x_{2}^{prd}-x_{1}^{prd},h_{prd}=y_{2}^{prd}-y_{1}^{prd} \end{split} \tag{9}\]  
In Equation (9), \(|C|\) represents the area of the minimum bounding rectangle that encloses \(B_{gt}\) and \(B_{prd}\). The coordinates \((x_{c}^{gt},y_{c}^{gt})\) and \((x_{c}^{prd},y_{c}^{prd})\) represent the central coordinates of the actual annotated bounding box and the predicted bounding box, respectively. The width and height of the actual bounding box are denoted as \(w_{gt}\) and \(h_{gt}\), while those of the predicted bounding box are denoted as \(w_{prd}\) and \(h_{prd}\).