## 3 Proposed Method
### Spatial Attention Gate (sAG)  
Naive skip connections [11] just concatenate the encoder and decoder features, so it is a waste computational resources and redundant information is produced, since the model cannot recognize where an object is located. Because the encoder feature has rich location information, it is better to focus on salient region that are beneficial to find the location of the object and determine the target structure of the object. The proposed sAG aims to provide insight into 'where' is an important region to predict and segment an object. The spatial attention map is constructed based on the interrelation between the spatial information that focuses on the salient regions.  
As illustrated in Figure 2, the spatial attention map is a combination of spatial information from both encoder and decoder features. To compute the spatial attention map in each encoder and decoder feature, we first apply average pooling, max pooling, and \(1\times 1\) convolution through the channel dimension and then concatenate them to construct a capable feature representation. Applying the average pooling and max pooling through the channel dimension, inspired by [25], and applying a \(1\times 1\) convolution, inspired by [26; 27], are effective to represent the important information. We then apply a convolution layer on the concatenated features to produce a spatial attention map \(M_{s}(F)\in\mathbb{R}^{1\times H\times W}\) that highlights the salient region. The above process is applied for each encoder and decoder feature separately. Finally, we summarize the spatial attention map from the encoder feature and decoder feature to compute the final spatial attention map. The detailed operations are shown below.  
We aggregate information along the channel dimension of each encoder and decoder feature by utilizing pooling and a \(1\times 1\) convolution operation. \(F_{avg}^{s}\in\mathbb{R}^{1\times H\times W}\), \(F_{max}^{s}\in\mathbb{R}^{1\times H\times W}\), and \(F_{1\times 1}^{s}\in\mathbb{R}^{1\times H\times W}\) denote the map generated from average pooling, max pooling and \(1\times 1\) convolution, respectively. Those generated maps are concatenated, and then a convolution is applied with a large kernel size \(7\times 7\) (a large kernel size is effective to capture long-range contextual information [25]) to generate the spatial attention map. \(M_{s}^{e}(F_{e})\) and \(M_{s}^{d}(F_{d})\) denote the generated spatial attention maps of the encoder and decoder features, respectively. The final spatial attention map \(M_{s}(F_{e},F_{d})\) is calculated by applying a sigmoid function on the summation of \(M_{s}^{e}(F_{e})\) and \(M_{s}^{d}(F_{d})\).  
\[\begin{split} M_{s}^{e}(F_{e})&=F_{1}^{7\times 7}([ AvgPool(F_{e}),MaxPool(F_{e}),F_{1}^{1\times 1}(F_{e})])\\ &=F_{1}^{7\times 7}([(F_{e})_{avg}^{s},(F_{e})_{max}^{s},(F_{e})_{1 \times 1}^{s}])\end{split} \tag{2}\]  
\[\begin{split} M_{s}^{d}(F_{d})&=F_{1}^{7\times 7}([ AvgPool(F_{d}),MaxPool(F_{d}),F_{1}^{1\times 1}(F_{d})])\\ &=F_{1}^{7\times 7}([(F_{d})_{avg}^{s},(F_{d})_{max}^{s},(F_{d})_{1 \times 1}^{s}])\end{split} \tag{3}\]  
Figure 4: Process of refining the input feature.  
\[M_{s}(F_{e},F_{d})=\sigma(M_{s}^{e}(F_{e})+M_{s}^{d}(F_{d})) \tag{4}\]  
where \(f_{b}^{a\times a}\) denotes the \(b\) filters of the \(a\times a\) convolution, and \(\sigma\) indicates the sigmoid function.