# Application of Split Coordinate Channel Attention Embedding U2 Net in Salient Object Detection
## 3 Proposed Method  
### Split Channel Coordinate Attention  
The split channel coordinate attention (SCCA) module in this paper is used to process the feature maps extracted by U2 Net. The attention module can guide the network to process information selectively, focusing on the more meaningful spatial parts.  
Given an intermediate feature map \(F\in R^{2C\times H\times W}\), SCCA divides the feature map into halves \(F_{1},F_{2}\in R^{C\times H\times W}\) along the channels, which is performed in different ways--line 1 and line 2, respectively. For line 1, \(F_{1}\) is operated by convolution, normalization, and activation to obtain the high-level semantic information. For line 2, \(F_{2}\) is operated by two transformations along the height and width direction to obtain the location of salient objects. The overall attention mechanism can be summarized as  
\[F_{1}^{\prime}=M_{1}(F_{1})\odot F_{1} \tag{1}\]  
\[F_{2}^{\prime}=M_{2}(F_{2})\odot F_{2} \tag{2}\]  
where \(\odot\) denotes the element-wise multiplication, \(F_{1}^{\prime}\), \(F_{2}^{\prime}\) is the output of \(F_{1}\), \(F_{2}\), and \(M_{1},\ M_{2}\) denotes line 1, line 2, respectively. Figure 2 depicts the whole computation process of SCCA.  
\(F_{2}\) is processed on each channel by an average pooling transformation along the height and width, where \(H,W\) denotes the height and width of \(F_{2}\), \(x_{c}(h,i),\ x_{c}(j,w)\) is the pixel value at the location \((h,i),\ (j,w)\) in the channel equal to \(c\), and \(z_{c}^{h}(h),\ z_{c}^{w}(w)\) is the output along two directions, respectively.  
\[z_{c}^{h}(h)=\frac{1}{W}\sum_{0\leq i<W}x_{c}(h,i) \tag{3}\]  
\[z_{c}^{w}(w)=\frac{1}{H}\sum_{0\leq j<H}x_{c}(j,w) \tag{4}\]  
The above two transformations aggregate feature maps along the channels, respectively, to obtain a pair of direction-aware feature matrices \(z^{h},\ z^{w}\). Then, \(z^{h}\) is transposed and concatenated by \(z^{w}\), and \(\left[\left(z^{h}\right)^{T},\ z^{w}\right]\) is operated by convolution, normalization, and a non-linear activation function. Where [ ] is the concatenate operation along the channels, \(\phi\) denotes a series convolution, batch normalization, \(\sigma\) denotes the activation function, and \(f\in R^{C\times H\times W}\) denotes the output.  
\[f=\sigma\bigg{(}\phi\bigg{[}\left(z^{h}\right)^{T},\ z^{w}\bigg{]}\bigg{)} \tag{5}\]  
Then, SCCA repeats the transformation along the height and width to obtain \(f^{h},\ f^{w}\) and performs convolution and regularization in two dimensions to obtain \(g^{h}\), \(g^{w}\), respectively. To avoid the problem of gradient explosion and gradient disappearance, \(f\) is element-wise multiplied by the matrices \(g^{h},\ g^{w}\). \(x_{c}(i,j)\) denotes the pixel value of \(f\), and \(y_{c}(i,j)\) denotes the pixel value of the final output on every channel of line 2. Then, SCCA concatenates both outputs to aggregate the semantic information and location information. \(y_{1},y_{2}\) denotes the output from the different line 1 and line 2s, and \(Y\) is the final output of SCCA.  
\[g^{h}=\sigma\bigg{(}\phi_{h}\Big{(}f^{h}\Big{)}\bigg{)} \tag{6}\]  
\[g^{w}=\sigma(\phi_{w}(f^{w})) \tag{7}\]  
\[y_{c}(i,j)=x_{c}(i,j)\times g_{c}^{h}(i)\times g_{c}^{w}(j) \tag{8}\]  
\[Y=[y_{1},y_{2}] \tag{9}\]