## 3 Proposed Method
### Cross-Attention Fusion Module (CAFM)  
Attention mechanisms have been used to correlate local and global features in low-light image enhancement [26; 27; 28; 29]. Inspired by this, and to better fuse underexposed images of the same scene and their corresponding exposure-corrected images, we use the Cross-Attention Fusion Module (CAFM). Figure 4 shows the overall architecture of our used CAFM, which consists of both cross-attention fusion (XAF) and Channel Attention Fusion (CAF). The principle of CAFM is to compensate the content of underexposed images with the exposure correction information of one image. CAFM uses the strip pool [30] to locate well-exposed regions in the global image horizontally and vertically from the secondary input (\(l^{a}\)) and uses them to complement the primary input (\(l^{b}\)), as shown in the XAF in Figure 4. The strip pool [30] averages row pixels using horizontal single-pixel-long kernels and column pixels using vertical single-pixel-long kernels, and then merges them to discover dependencies between features across regions. CAFM further extends the strip pool to cross-fuse two inputs in different domains. We iteratively use CAFM four times. First, the exposure-corrected image and the low-light image are converted from RGB color space to YCbCr color space, and then both images are input to the first CAFM to obtain the first intermediate enhancement result. The intermediate enhancement result is still in the YCbCr color space. The inputs of the remaining three CAFM are the output of the previous CAFM and the exposure-corrected image corresponding to the original input low-light image. In image fusion, the RGB channel is highly correlated and the input image is usually converted from RGB color space to YCbCr color space in order to maintain the image color and detail information [26; 31]. To illustrate CAFM in detail, we explain the first CAFM in the network, and the remaining three CAFM are based on the same principle as the first one. **Cross-attention fusion (VAF):** We assume that the exposure-corrected image in YCbCr color space is \(l^{a}\in R^{C\times H\times W}\), and the low-illumination image is \(l^{b}\in R^{C\times H\times W}\). \(l^{b}\) is the primary input and \(l^{a}\) is the secondary input. Horizontal and vertical bar pooling is performed on the secondary input \(l^{a}\) to find the well-exposed regions in each channel space. The horizontal bar result \(I^{V}_{i,c}\in R^{H\times 1\times C}\) and the vertical bar result \(I^{L}_{j,c}\in R^{1\times H\times W}\) are obtained from the secondary input. Where C is the number of feature channels, and H and W are the tensor height and width. Here,  
\[I^{V}_{i,c}=\frac{1}{W}\sum_{j=0}^{W-1}I^{a}_{i,j,c},1\leq i\leq H \tag{6}\]  
\[I^{L}_{j,c}=\frac{1}{H}\sum_{i=0}^{H-1}I^{a}_{i,j,c},1\leq j\leq W \tag{7}\]  
Figure 4: CAFM is Cross-Attention Fusion Module, XAF is cross-attention fusion, and CAF is Channel Attention Fusion. GAP denotes global average pooling: FC layer is fully connected layer. Then, upsample \(I_{i,c}^{V}\) and \(I_{i,c}^{L}\), respectively, and fuse the feature tensor after upsampling to obtain \(I_{i,j,c}^{M}\). Converting \(I_{i,j,c}^{M}\) to an attention mask \(M_{I}\) whose larger value reflects the information part in the suboutput, \(M_{I}\) can be expressed as:  
\[M_{I}\text{=}\sigma(c_{1\times 1}(I^{M})) \tag{8}\]  
\(c_{1\times 1}\) is a \(1\times 1\) convolutional layer and \(\sigma\) is the sigmoid activation function. The primary and secondary inputs are summed to obtain feature \(I^{5}\). The output of cross-fusion attention (XAF) is equal to \(I^{5}\) plus \(I^{5}\) multiplied by the feature that passes the attention mask \(M_{I}\). \[I^{O}=I^{5}+c_{3\times 3}(M_{I}\otimes(I^{5})) \tag{9}\]  
Here, \(\otimes\) stands for element multiplication, \(I^{5}\) for (\(I^{a}+I^{b}\)), and \(c_{3\times 3}\) for the \(3\times 3\) convolutional layer.