## 3 Methods
### Mixed Loss Function  
This section introduces the loss function utilized during the training of the network. The article discusses the use of a hybrid loss function combining Binary Cross-Entropy (BCE) and Sorensen-Dice (DICE) to compute the total loss. These loss functions are commonly employed in deep learning for tasks such as image segmentation, particularly in binary segmentation tasks. In the task of remote sensing image change detection, the BCE loss function is a commonly used and effective choice [29]. Change detection in remote sensing is often approached as a binary classification problem, where the goal is to determine if each pixel has changed. The BCE loss function is well suited for modeling and optimizing this type of binary classification task. Remote sensing images typically have a small proportion of changed areas, leading to a significant imbalance between positive and negative samples. The BCE loss function is robust in handling this imbalance and effectively addresses sample imbalance issues. By utilizing the BCE loss function in conjunction with the Sigmoid activation function, the probability of change for each pixel can be directly predicted. This probability output serves as a crucial foundation for subsequent tasks such as change area extraction and selection of change detection thresholds. Moreover, the BCE loss function demonstrates good numerical stability and mitigates the risk of gradient vanishing or exploding, thus promoting model convergence. \[L_{BCE}=-(y\cdot\log(\hat{y})+(1-y)\cdot\log(1-\hat{y})) \tag{1}\]  
Figure 8: Second stage decoder block De-3. Figure 9: Second stage decoder block De-4. where \(y\) is the true label of the sample, \(\hat{y}\) is the probability predicted by the model. In the context of binary classification, the BCE loss function penalizes the model based on the difference between the predicted probability \(\hat{y}\) and the true label \(y\). When the true label is 1, the loss is \(-\log(\hat{y})\), pushing the model to predict probabilities close to 1. Conversely, when the true label is 0, the loss is \(-\log(1-\hat{y})\), encouraging the model to predict probabilities close to 0. The goal of minimizing the BCE loss is to reduce the discrepancy between the predicted probability and the actual label, with small values indicating correct predictions and large values indicating errors. Therefore, the BCE loss function is commonly utilized in remote sensing image change detection for its simplicity, efficiency, robustness to sample imbalance, and compatibility with change probability output. This function plays a crucial role in the development of a reliable and effective change detection model. The Sorensen-Dice (DICE) [30] coefficient is frequently utilized to assess the similarity between predicted segmentation results and actual labels. It can also serve as a loss function for training segmentation models. The DICE loss function is defined as follows:  
\[L_{Dice}=\frac{2(|y\cap\hat{y}|)}{|y|+|\hat{y}|} \tag{2}\]  
In the formula above, \(|y|\) represents the actual change label, \(|\hat{y}|\) represents the predicted change probability map by the model, and \(|y\cap\hat{y}|\) represents the intersection area between the actual change area and the predicted change area. A higher value indicates a greater overlap between the two. The Dice loss function ranges between 0 and 1, where 0 signifies no overlap and 1 signifies complete overlap. The Dice loss function formula effectively assesses the similarity between predicted results and actual labels, making it a popular choice for segmentation tasks like remote sensing change detection. By minimizing this loss function, the model's predictions can closely align with the actual change areas. The advantages of the two loss functions can be combined to make the model consider both pixel-level classification accuracy and region-level overlap in the training process.