## 3 DCNA-YOLO Method Construction
### Multi-Branch Coordinate Attention
The optimization weight matrix is then split along the spatial dimension into independent weights \(g_{1}^{h}\) and \(g_{1}^{w}\) for the vertical and horizontal directions, respectively. Finally, the two independent weights \(g_{1}^{h}\) and \(g_{1}^{w}\) are applied to the corresponding tensors, and after passing through a sigmoid function, the outputs \(g^{h}\) and \(g^{w}\) are expanded and used as attention weights. \[ \begin{cases}f=\delta\Big{(}F_{3\times 1}\Big{(}\Big{[}Z^{h},Z^{w}\Big{]} \Big{)}\Big{)}\\ g_{1}=\sigma(\delta(F_{1}(f)))\\ g_{1}^{h}=F_{h}(g_{1})\\ g_{1}^{w}=F_{w}(g_{1})\\ g^{h}=\sigma\Big{(}F_{h}\Big{(}f^{h}\Big{)}\times g_{1}^{h}\Big{)}\\ g^{w}=\sigma\Big{(}F_{w}(f^{w})\times g_{1}^{w}\Big{)}\end{cases}  \tag{3}\]  
where \([,\cdot]\) represents the concatenation operation along the spatial dimension. \(F_{3\times 1}(\cdot)\) denotes the 3 \(\times\) 1 convolution transformation function, \(\delta(\cdot)\) represents the non-linear activation function hard_swish. \(f\) represents the intermediate feature map with horizontal and vertical spatial information, where \(fe\)\(R^{C/r\times(W+H)}\). \(r\) is the reduction ratio, taken as 16. \(F_{h}\) and \(F_{w}\) represent 1 \(\times\) 1 convolution operations in the vertical and horizontal directions, respectively. \(f^{h}\) and \(f^{w}\) represent intermediate feature maps in the vertical and horizontal directions, where \(f^{h}eR^{C/r\times 1\times H}\) and \(f^{w}eR^{C/r\times 1\times W}\). \(\sigma\) denotes the sigmoid activation function. \(g_{1}\) represents the feature map optimization weight matrix. \(g_{1}^{h}\) and \(g_{1}^{w}\) represent optimization weights in the vertical and horizontal directions, respectively. \(g^{h}\) and \(g^{w}\) represent attention weights in the vertical and horizontal directions, respectively. For global attention generation, the global information feature map generated from Equation (2) is multiplied element-wise by the average-weighted optimization weight matrix \(g_{1}\). Subsequently, the result passes through a sigmoid function to obtain the global attention weights \(g^{G}\). \[ \begin{cases}f_{c}=\delta(F_{1}(Z_{c}))\\ g^{G}=\sigma(mean(g_{1})\cdot f_{c})\end{cases}  \tag{4}\]where \(F_{1}(\cdot)\) represents the \(1\times 1\) convolution transformation function. \(mean(\cdot)\) represents the mean function. \(f_{c}\) represents the intermediate feature map with global information, where \(f_{c}\epsilon R^{C\times 1\times 1}\). \(g_{1}\) represents the feature map optimization weight matrix. \(g^{G}\) represents the global attention weights. The attention weights \(g\) are calculated by multiplying the vertical and horizontal direction attention weights by the global attention weights. \[g_{c}=g_{c}^{h}(i)\times g_{c}^{w}(j)\times g_{c}^{G}(i,j) \tag{5}\]  
where \(g_{c}\) represents the attention weight at channel \(c\). \(g_{c}^{h}\) represents the vertical direction attention weight at channel \(c\). \(g_{c}^{w}\) represents the horizontal direction attention weight at channel \(c\). \(g_{c}^{G}\) represents the global attention weight at channel \(c\). It computes the average of all elements within each feature map of the input, resulting in a feature map with a size of \(1\times 1\). When direct multiplication or addition operations are needed for the original input, reverse average pooling (UNAP) can be used to expand the feature map to the desired size. The specific pooling operations are illustrated in Figure 4.  
The multi-branch coordinate attention (MBCA) mechanism is established by the two steps above, introducing global-level information and optimizing the perception of specific target positions at the local level. Figure 3: The principle of the multi-branch coordinate attention (MBCA) algorithm.