## 3 Method
### Low-Light Image Enhancement Sub-Network
The deep curve fitting network uses an ordinary CNN with six alternately connected convolutional layers, each consisting of \(32\times 3\) convolutional kernels with a step size of \(1\). A ReLu function is added at the end of the network. where \(V\) denotes the number of non-overlapping regions with a size of \(16\times 16\), and \(\hat{I}\) represents the average luminance value of localized region \(V\) in the augmented image \(\hat{X}_{T_{n}}\), \(e\) was set to 0.5 in the experiment. The color constancy loss employed in this paper was based on the Gray-World [36] color constancy assumption, which posits that each color channel is averaged as gray over the whole image. This loss rectifies potential color deviations in the enhanced image, recovers color information affected by changes in illumination, improves the quality and visual perception of the image, and determines the relationship among the three color channels, as shown in Equation (4). \[L_{cc}=\sum_{\forall(a,b)\in\tau}{(\bar{E}^{(a)}-\bar{E}^{(b)})^{2}}, \tag{4}\]  
where \(\bar{E}^{(a)}\) and \(\bar{E}^{(b)}\) denote the average intensity values of the \(a\)-channel and the \(b\)-channel, respectively, in the enhanced image \(\hat{X}_{T_{n}}\), and \((a,b)\) denotes a pair of channels, \(\tau=\{(R,G),(R,B),(G,B)\}\). The smaller value of \(L_{cc}\) indicates that the color of the brightened image is more balanced, and the larger \(L_{cc}\) indicates that the brightened image may have the problem of color bias. In this paper, an illumination smoothness loss [37] was built into each curve parameter mapping \(\mathcal{A}\) to maintain a monotonic relationship between adjacent pixels. The loss assists the model in learning that the illumination changes in the neighboring regions exhibit both consistency and smooth transition and improving image processing performance and image quality. It is shown in Equation (5). \[L_{is}=\frac{1}{M}\sum_{m=1}^{M}\sum_{s=1}^{L_{\forall N}+C}\Bigl{(}\bigl{|} \
abla_{x}\mathcal{A}_{m}^{(s)}\bigr{|}+\bigl{|}\
abla_{y}\mathcal{A}_{m}^{( s)}\bigr{|}\Bigr{)}^{2}, \tag{5}\]  
where \(M\) stands for the number of iterations. Specifically, \(C\) denotes the RGB color channels, and \(C=3\). \(\
abla_{x}\) and \(\
abla_{y}\) denote the horizontal and vertical gradient operations, respectively. The smaller the value of \(L_{is}\), the smoother the light of the brightened image, and vice versa, which indicates that there are mutations or artifacts in the light of the brightened image. The total enhancement loss is shown in Equation (6). \[L_{en}=L_{cc}+\lambda_{1}L_{cc}+\lambda_{2}L_{is}, \tag{6}\]  
where \(\lambda_{1}\) and \(\lambda_{2}\) are hyperparameters used to balance the size of the loss and were set to 0.5 and 20 in the experiments, respectively. Contributing to the realm of LIE-SubNet, this paper explores the combination of a set of higher-order curves that can be iterated with a deep learning network for different numbers of iterations to verify the optimal performance and enhance nighttime pixel contrast. The method reduces the domain gap among the daytime and nighttime domains without resorting to an intermediate domain or the training of multiple distinct models and feeds the segmentation network with smaller differences in illumination images.