## 2 Method
### New Backbone: Lightweight Channel Attention Network (LCANet)  
In order to reduce the model volume while maintaining high detection accuracy, we designed a new lightweight backbone: LCANet. The structure of LCANet is shown in Figure 3, which consists of 1 Conv module and 10 DWConv blocks. The Conv module include a 2D convolution, batch norm and RELU activation function. The DWConv block consists of a depthwise separable convolution, residual structure, efficient channel attention(ECA) module and RELU activation function. The specific structure of the DWConv block is shown in Figure 4.  
Standard convolution uses filters in the format of K \(\times\) K \(\times\) C. A single filter can perform feature extraction for each channel and feature fusion between multiple channels. Depthwise separable convolution consists of a depthwise convolution, which applies a one-dimensional convolution to each channel of the input tensor for feature extraction in a single channel, and a point convolution, which applies a 1 \(\times\) 1 multi-dimensional convolution to combine the feature maps extracted by the depthwise convolution. The using of depthwise separable convolution drastically reduced the computation and model size of the network. Figures 5 and 6 illustrate the implementation of standard convolution and depthwise separable convolution, respectively. Figure 4: The structure of DWConv block. Figure 3: The structure of LCA-YOLOv8n-seg. A standard convolutional layer takes as input a \(H_{A}\times W_{A}\times M\) feature map \(A\) and produces a \(H_{B}\times W_{B}\times N\) feature map \(B\), where \(H_{A},W_{A}\) is the spatial height and width of an input feature map, \(M\) is the number of input channels, \(H_{B},W_{B}\) is the spatial height and width of an output feature map and \(N\) is the number of output channels. The standard convolutional layer is parameterized by filter K of the format \(H_{K}\times W_{K}\times M\times N\), where \(H_{K},W_{K}\) is the size of the convolving kernel, \(M\) is the number of input feature map channels and \(N\) is the number of filters and output feature map channels. The output feature map of standard convolution is usually calculated as:  
\[O_{k,l,n}=\sum_{i,j,m}K_{i,j,m,n}\cdot A_{k+i-1,l+j-1,m} \tag{1}\]  
The computational cost of a standard convolution is:  
\[D_{K}\cdot D_{K}\cdot M\cdot N\cdot H_{A}\cdot W_{A} \tag{2}\]  
where the computational cost depends multiplicatively on the number of input channels \(M\), output channels \(N\), the kernel size \(H_{K}\times W_{K}\) and the feature map size \(H_{A}\times W_{A}\). Depthwise convolution with one filter per input channel (input depth) can be written as:  
\[\hat{O}=\sum_{i,j}\hat{K}_{i,j,m}\cdot A_{k+i-1,l+j-1,m} \tag{3}\]  
where \(\hat{K}\) is the depthwise convolutional kernel of size \(H_{K}\times W_{K}\times M\), where the \(m_{th}\) filter in \(\hat{K}\) is applied to the \(m_{th}\) channel in \(A\). Depthwise convolution has a computational cost of:  
\[H_{K}\cdot W_{K}\cdot M\cdot H_{A}\cdot W_{A} \tag{4}\]  
Figure 5: The implementation of standard convolution. Figure 6: The implementation of depthwise separable convolution. The \(1\times 1\) (pointwise) convolution has a computational cost of:  
\[1\cdot 1\cdot M\cdot N\cdot H_{A}\cdot W_{A} \tag{5}\]  
The combination of depthwise convolution and \(1\times 1\) (pointwise) convolution is called depthwise separable convolution, and the depthwise separable has a computational cost of:  
Figure 4:0  
which is the sum of the depthwise and \(1\times 1\) pointwise convolutions. By expressing convolution as a two-step process of filtering and combining we get a reduction in computation of:  
\[ \begin{array}{l}\frac{H_{K}\cdot W_{K}\cdot M\cdot H_{A}\cdot W_{A}+M\cdot N \cdot N\cdot H_{A}\cdot W_{A}}{H_{K}\cdot W_{K}\cdot W_{A}\cdot W_{A}\cdot W_{A }}\\ =\frac{1}{N}+\frac{1}{H_{K}\cdot W_{K}}\end{array}  \tag{7}\]  
In DWConv blocks, we use depthwise separable convolutions with kernel size 3 and 5, which results in 8-9 times less computation than standard convolutions.