## 2 Dataset and Methodology
### Methodology
#### 2.2.4 Implementation Pipeline  
1. Data Preprocessing and Augmentation The pipeline initiates with domain-specific data standardization. Mining VHR images \(X\) undergo radiometric calibration using dark current subtraction: \[I_{\text{calibrated}}\ =\ \frac{I_{\text{raw}}-\mu_{\text{dark}}}{\sigma_{\text{ dark}}^{2}+\epsilon},\] (11) where \(\mu_{\text{dark}}\) and \(\sigma_{\text{dark}}^{2}\) denote the mean and variance of dark channel measurements, and \(\epsilon=10^{-6}\) prevents division instability. Road masks \(Y\) are converted to topological graphs \(\text{g}=(V,E)\), with vertices \(V\) representing road junctions and edges \(E\) encoding connectivity. Spatial augmentations apply stochastic transformations to input pairs \((x,y)\): \[x^{\prime}=\mathcal{T}_{\theta}(x),\ \ \ y^{\prime}=\mathcal{T}_{\theta}(y).\] (12) Here, \(\mathcal{T}_{\theta}\) denotes a random affine transformation parameterized by \(\theta\), including rotation (\(\theta_{rot}\in[-15^{\circ},15^{\circ}]\)), scaling (\(\theta_{scale}\in[0.9,1.1]\)), and shear (\(\theta_{shear}\in[-0.1,0.1]\)). Pixel-wise Gaussian noise \(\eta\sim\mathcal{N}\big{(}0,0.05^{2}\big{)}\) is injected into \(x^{\prime}\) to simulate sensor variability.
2. Adversarial Training Protocol The training alternates between generator and discriminator updates in a four-step cycle: 1. Generator Forward Pass: For a batch \(\mathcal{B}_{X}\subset X\), compute \(G(\mathcal{B}_{X})\) and reconstruct \(F(G(\mathcal{B}_{X}))\). 2. Discriminator Update: Evaluate \(D_{Y}(G(\mathcal{B}_{X}))\) and \(D_{Y}(\mathcal{B}_{Y})\) (for \(\mathcal{B}_{Y}\subset Y\)), then optimize \(D_{Y}\) via gradient ascent on \(\mathcal{L}_{\text{adv}}\). 3. Generator Backward Pass: Calculate cyclic gradients through \(\mathcal{L}_{\text{cyc}}\) and \(\mathcal{L}_{id}\), propagating errors to update \(G\) and \(F\). 4. Domain Alignment: Apply gradient reversal layers (GRL) after every third epoch to enforce feature space alignment between \(X\) and \(Y\). The learning rate \(\alpha\) for generators follows a cosine annealing schedule: \[\alpha(t)=\alpha_{0}\cdot\left(\cos\left(\frac{\pi t}{T}\right)+1\right)/2,\] (13) where \(\alpha_{0}=2\times 10^{-4}\) is the initial rate, \(t\) is the current epoch, and \(T=20\) is the total epochs.
3. Dynamic Pseudo-Label Refinement A sliding confidence threshold \(\tau^{(t)}\) governs pseudo-label selection during self-training: \[\tau^{(t)}=\tau_{\text{min}}+(\tau_{\text{max}}-\tau_{\text{min}})\cdot sigmoid (10(t/T-0.5)),\] (14) with \(\tau_{\text{min}}=0.7\) and \(\tau_{\text{max}}=0.95\). Predicted masks \(\widetilde{y}\) are retained if \(\text{max}(\text{softmax}(\widetilde{y}))\geq\tau^{(t)}\).  
Retained labels undergo geometric validation using morphological operations \(\mathcal{M}\):  
\[\hat{y}_{\text{clean}}=\mathcal{M}_{\text{open}}(\mathcal{M}_{\text{close}}( \hat{y})), \tag{15}\]  
where \(\mathcal{M}_{\text{open}}\) and \(\mathcal{M}_{close}\) denote opening and closing operations with a \(5\times 5\) rectangular kernel.  
Hardware Configuration  
Training leverages mixed-precision computation with PyTorch's (version 2.7.0) automatic mixed precision (AMP). Loss gradients are scaled by a factor s = 1024 to prevent underflow in FP16 tensors. Batch sizes are dynamically adjusted per GPU memory availability.