## 2 Materials and Methods
### Methods
#### 2.3.3. Pix2 Pix  
Pix2 Pix [23] was inspired from the idea of CGAN. The condition in CGAN influences the generator network and generates fake images based on the specific condition and input noise, thus performing image-to-image translation. In our image segmentation study, we used Pix2 Pix's original model structure, allowing the model to learn maximum features through the loss function in the training phase. However, we included threshold segmentation in the final layer during testing to maintain class consistency between the prediction results and labels. The structure of Pix2 Pix is shown in Figure 4.  
Our model employed the U-Net architecture for generator network (\(G\)) to encode and decode the input image \(x\) into a post-classification image. The role of PatchGAN, a type of conditional discriminator, in the discriminator network (\(D\)) was to assess the authenticity of \(G\)(\(x\)) and the actual post-classification image with the condition of the image \(x\). If the generated image does not match the real image, the PatchGAN will judge it as fake. Both the generator and discriminator used the model structure of Convolution + BatchNorm + ReLU. The loss function of the CGAN is shown in Equation (4), and Pix2 Pix used \(\mathcal{L}1\) regularization to make the generated images sharper, as shown in Equation (5), \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Features** & **Spectral** & & **Topographical** & & **Vegetation Index** & **Texture** \\ \hline \multirow{4}{*}{Indicators} & Band 1 & Slope & Plan Convexity & Maximum Curvature & NDVI & Mean & Dissimilarity \\  & Band 2 & Aspect & Longitudinal Convexity & RMS & DVI & Variance & Entropy \\  & Band 3 & Shaded Relief & Cross-Sectional & Slope Percent & RVI & Homogeneity & Second Moment \\  & Band 4 & Profile & Minimum Curvature & - & Contrast & Correlation \\ \hline Total & 4 bands & & 11 bands & & 3 bands & 32 bands \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Feature information. Note: topographical feature was calculated by DEM, and others were calculated by GF/Landsat imagery. Figure 4: F-Pix2 Pix network structure. Note: we propose a threshold self-adaptive segmentation algorithm, which uses Pix2 Pix model to transform semantic segmentation tasks into image translation tasks, namely F-Pix2 Pix. i.e., the \(\mathcal{L}1\) distance (Manhattan distance) between the generated fake images and the real images, which ensured the similarity between the input and output images [27]. The final goal was the minimax two-player game of the generator and discriminator in the case of regular constraints. The loss function is shown in Equation (6). \[\mathcal{L}_{\text{cGAN}}(G,D)=\mathbb{E}_{x,y}[\log D(x,y)]+\mathbb{E}_{x,z}[ \log(1-D(x,G(x,z)))] \tag{4}\]  
\[\mathcal{L}_{L1}(G)=\mathbb{E}_{x,y,z}[\|y-G(x,z)\|_{1}] \tag{5}\]  
\[G^{*}=\text{arg min}_{\text{G}}\text{max}_{D}\mathcal{L}_{cGAN}(G,D)+\lambda \mathcal{L}_{L1}(G)+\mathcal{L}_{Focal}(G) \tag{6}\]  
During the training process, the output image was classified by assigning each pixel to the class with the highest probability value among the 3 channels. During the prediction process, the output image was a probability map indicating the likelihood of each pixel belonging to a specific class. Each image was then arranged in a mosaic pattern. The survey statistics included area data, which were used to calculate a self-adaptive threshold. To compute the threshold, the number of pixels for each category was calculated using Equation (7). Here, _class_ represents the forest classification, _Pixels_ represents the number of pixels, _Area_ represents the corresponding area from the statistical data, and _Rimage_ represents the spatial resolution of the satellite images, measured in meters. Next, the output images of the entire area were mosaicked, and the probability values for each classification were arranged in descending order. The _Pixels_ were chosen from this arrangement, and the minimum value among these pixels was used as the threshold.