## 4 Results
### Evaluation Metrics  
For instance, for segmentation tasks such as building contour extraction, it is important to evaluate not only pixel-level segmentation performance but also instance-level building extraction effectiveness. To quantify the performance of different models, we utilize the following metrics: Overall Accuracy (OA), IoU, Precision for IoU threshold \(>\) 0.5 called \(P_{50}^{IoU}\), Precision for Boundary IoU [55] threshold \(>\) 0.5 called \(P_{50}^{Boundary}\), Recall for IoU threshold \(>\) 0.5 called \(R_{50}^{IoU}\) and Recall for Boundary IoU threshold \(>\) 0.5 called \(R_{50}^{Boundary}\). Among the metrics used for evaluation, OA and IoU are employed to assess the pixel-level effectiveness of building extraction. \(P_{50}^{IoU}\) is used to evaluate the precision of extracting building polygon instances, while \(P_{50}^{Boundary}\) is utilized to evaluate the precision of the boundaries of the extracted building polygon instances. \(R_{50}^{IoU}\) is used to evaluate the recall of extracting building polygon instances, while \(R_{50}^{Boundary}\) is utilized to evaluate the recall of the boundaries of the extracted building polygon instances. The evaluation metrics are designed such that larger values indicate better performance of the models. The specific calculation methods for these evaluation metrics are as follows:  
\[OA=\frac{TP+TN}{TP+TN+FP+FN} \tag{11}\]  
where \(TP\) indicates the number of pixels predicted to be true positives, \(TN\) indicates the number of pixels predicted to be true negatives, \(FP\) indicates the number of pixels predicted to be false positives, and \(FN\) indicates the number of pixels predicted to be false negatives. \[IoU(X,Y)=\frac{X\cap Y}{X\cup Y} \tag{12}\]where \(X\) represents the predicted results, and \(Y\) represents the ground truth labels. IoU measures the intersection-to-union ratio between the predicted building polygon and the ground truth building polygon. A higher IoU value indicates a better match between the predicted building polygon and the ground truth, signifying more accurate building prediction results. The Boundary IoU metric provides a reasonable measure to assess the accuracy of polygon boundaries. It helps to reveal the precision of the boundaries of the detected polygon instances in a meaningful way. For two polygon instances \(X\) and \(Y\), Boundary IoU calculates the IoU only for pixels that are within a distance d of the boundaries of the two polygon instances. It focuses on evaluating the IoU specifically for the pixels that lie within a specified distance d from the boundaries of the polygon instances \(X\) and \(Y\). Define the boundaries of \(X\) and \(Y\) as \(X_{d}\) and \(Y_{d}\). Similar to IoU, a larger value of Boundary IoU indicates better extraction performance. The calculation formula for Boundary IoU can be represented as follows:  
\[Boundary\ IoU(X,Y)=\frac{|(X_{d}\cap X)\cap(Y_{d}\cap Y)|}{|(X_{d}\cup X)\cup( Y_{d}\cup Y)|} \tag{13}\]  
The value of parameter d in the formula is set based on reference [55], where \(d=0.2\). \[P_{50}^{IoU}=\frac{TP_{50}^{IoU}}{TP_{50}^{IoU}+FP_{50}^{IoU}} \tag{14}\]  
where \(TP_{50}^{IoU}\) represents the number of true positive pixels within instances where the IoU is greater than 0.5. \(FP_{50}^{IoU}\) represents the number of false positive pixels within instances where the IoU is greater than 0.5. \[P_{50}^{Boundary}=\frac{TP_{50}^{Boundary}}{TP_{50}^{Boundary}+FP_{50}^{ Boundary}} \tag{15}\]  
where \(TP_{50}^{IoU}\) represents the number of true positive pixels within instances where the Boundary IoU is greater than 0.5. \(FP_{50}^{Boundary}\) represents the number of false positive pixels within instances where the Boundary IoU is greater than 0.5. \[R_{50}^{IoU}=\frac{TP_{50}^{IoU}}{TP_{50}^{IoU}+FN_{50}^{IoU}} \tag{16}\]  
where \(TP_{50}^{IoU}\) represents the number of true positive pixels within instances where the IoU is greater than 0.5. \(FN_{50}^{IoU}\) represents the number of false negative pixels within instances where the IoU is greater than 0.5.