# SCCDNet: A Pixel-Level Crack Segmentation Network
## 2 Methods
### SSE Module  
We designed an embedded SSE module [37] based on the skip-connection and Attention strategy, which is an important part of the SCCDNet. [PERSON] et al. [35] proved that the AG model is more efficient than the concatenating operation used in U-Net. Inspired by their work, we designed the SSE module to connect the feature map with the same resolution in the Encoder and Decoder. Instead of considering the global feature obtained by the output of early layers directly, the SSE module could emphasize useful channels and suppress useless channels of the feature map, which could alleviate the problem that the correlation of feature maps decreases due to the increase of network depth. This kind of skip-connection strategy is useful for increasing model performance in Encoder-Decoder structures. The SSE module is used to recalibrate the feature map output by the Encoder module, then used as the input of the Decoder module.  
The structure of the SSE module is shown in Figure 2. The input of Squeeze operation is the feature map \(\mathbf{FM}_{i}\), and its spatial dimensions will be aggregated in each channel, that is, use global average pooling, compress the size of size \(H_{i}\times W_{i}\) in each channel to \(1\times 1\), and get the channel-wise feature descriptor \(\mathbf{d}\in\mathbb{R}^{C_{i}}\), the formula is as follows:  
\[d_{c}=\mathbf{F}_{sq}(\mathbf{FM}_{ci})=\frac{1}{H_{i}\times W_{i}}\sum_{m=1}^ {H_{i}}\sum_{m=1}^{W_{i}}\mathbf{FM}_{ic}(m,n), \tag{1}\]  
where \(d_{c}\) is the value of c-th channel in the channel descriptor \(\mathbf{d}\) and \(\mathbf{FM}_{ic}\) refers to the c-th channel of the feature map \(\mathbf{FM}_{i}\).  
In order to alleviate the gradient irrelevance, we select the deeper feature map \(\mathbf{FM}_{j}\) to interact with the channel information descriptor \(\mathbf{d}\) obtained from the output of early layers. However, the number of channels of them are usually different. In order to multiply the two, we have to process \(\mathbf{d}\) further. The Squeeze is the attention to the spatial dimension and it can obtain the global eigenvalues of each channel; however, it does not consider the relationship between the channels, so the Excitation part uses the gating strategy [38] to focus on establishing the correlation between the channels:  
\[\mathbf{d}^{{}^{\prime}}=\mathbf{F}_{ex}(\mathbf{d},\mathbf{W}_{1},\mathbf{W}_ {2})=\delta(\mathbf{W}_{2}\delta(\mathbf{W}_{1}\mathbf{d})), \tag{2}\]  
where \(\mathbf{d}^{{}^{\prime}}=\begin{bmatrix}d_{1}^{\prime},d_{2}^{\prime},\dots, d_{c}^{\prime},\dots,d_{j}^{\prime}\end{bmatrix}\), \(\delta\) refers to the ReLU activation function, \(\mathbf{W}_{1}\in\mathbb{R}^{\frac{C_{i}}{\tau}\times C_{i}}\), \(\mathbf{W}_{2}\in\mathbb{R}^{C_{j}\times\frac{C_{i}}{\tau}}\), r is reduction ratio. To build up the correlation between channels, we take the channel descriptor \(\mathbf{d}\) as the input of two fully-connected layers. The first fully-connected layer changes the number of channels from \(C_{i}\) to \(C_{i}/r\), and the second changes the number of channels from \(C_{i}/r\) to \(C_{j}\), which is the same as the channels number of the feature map \(\mathbf{FM}_{j}\). The final output of the SSE module is obtained by the following formula:  
\[\mathbf{SSE}_{c}=\mathbf{F}_{sc}(\mathbf{FM}_{jc},d_{c}^{\prime})=d_{c}^{ \prime}\mathbf{FM}_{jc}, \tag{3}\]  
where \(\mathbf{SSE}=\begin{bmatrix}\mathbf{SSE}_{1},\mathbf{SSE}_{2},\dots, \mathbf{SSE}_{c},\dots,\mathbf{SSE}_{j}\end{bmatrix}\), \(\mathbf{F}_{sc}(\mathbf{FM}_{jc},d_{c}^{\prime})\) refers to channel-wise multiplication between the channel weights \(d_{c}^{\prime}\) and the feature map \(\mathbf{FM}_{jc}\).