## 3 Proposed Method
### Decoder for Precise Segmentation  
Decoding is a process of expanding and restoring the feature map output from the encoder to the size of the input image. In EAR-Net, the basic decoder structure consists of a transposed convolution, \(3\times 3\) convolution, and a concatenation (Figure 1). The transposed convolution upsamples the size of the feature map, and the \(3\times 3\) convolution reconstructs the feature map. The concatenation uses the intermediate feature maps extracted from the  
Figure 6: Atrous spatial pyramid pooling diagram. Symbols \(C,H,W,r\) indicate the number of channels, height, width, and rate, respectively. ADSC, GAP, and Concat denote depthwise separable convolution with atrous convolution, global average pooling, and concatenation, respectively.  
encoder to reconstruct detailed parts, such as contour lines. This decoder operation process significantly improves the segmentation accuracy. In this case, the transposed convolution and \(3\times 3\) convolution involve a large amount of computation. Therefore, the EAR-Net replaces the transposed convolution with a bilinear interpolation and the \(3\times 3\) convolution with a \(3\times 3\) DSConv.  
First, the transposed convolution achieves excellent performance because the model can learn the upsampling process. However, the number of parameters and the computation costs are significantly increased. Bilinear interpolation is a method of filling values between adjacent pixels by interpolation and achieves slightly lower performance than transposed convolution. However, it does not use parameters and requires less computation. After considering the trade-off between the performance and computation costs, we adopt interpolation in our model. Second, we replace the \(3\times 3\) convolution with a \(3\times 3\) depthwise separable convolution to minimize the computation costs and parameters.  
The decoder of EAR-Net consists of three decoding blocks. Each decoding block doubles the input feature map by bilinear interpolation and reduces the number of channels by \(1\times 1\) convolution of the intermediate feature map of the encoder with the same resolution as the extended feature map. Then, the two feature maps are concatenated. Figure 7a shows a diagram of concatenation, and Equation (4) represents concatenation.  
\[Concat(2c,h,w)=[T(x)_{c,h,w};E(y)_{c,h,w}] \tag{4}\]  
\[DecodingBlock=f_{dsconv}^{3\times 3}(f_{dsconv}^{3\times 3}([T(x)_{c,h,w};E(x)_{ c,h,w}])) \tag{5}\]  
In Equations (4) and (5), \(T(x)\) is a feature map extended by transposed convolution, and \(E(y)\) is an intermediate feature map taken from the encoding block; \(c,h,w\) represent the number of channels, height, and width, respectively.  
Finally, \(3\times 3\) depthwise separable convolution, batch normalization, and ReLU are repeated twice on the combined feature map to reconstruct the feature map. Figure 7b shows the structure of the decoding block, and Equation (5) represents the decoding block. The number of channels of the combined feature map is doubled, according to Equation (4), and the number of channels of the reconstructed feature map is reduced two times again to maintain the number of channels before combining (Figure 7b).