# Multilevel Regularization Method for Building Outlines
## 4 Results and Analysis
### Experimental Analysis
#### 4.1.2 Quantitative Evaluation  
Because the results extracted from the images with 0.075 m resolution exhibit high accuracy and visually resemble the actual building outlines, the manually labeled ground truth was taken as the reference for evaluation. This evaluation reflects the performance of different algorithms in repairing jagged outline data. The statistical evaluation metrics for various methods are summarized in Table 3.  
As shown in Table 3, Method A has a relatively low P value, indicating that more building areas are classified as nonbuilding areas. This is because during the removal of noise points, redundant nodes, and small line segments, some nodes belonging to building outlines may be mistakenly removed, resulting in the loss of some outline details, which also explains the slightly lower IOU and F1 score values of this method. Method B achieves balanced scores in all evaluation metrics because it employs an iterative approach from overall to local, limiting outline deformation within a certain range. Method C has a relatively low R value, indicating that more nonbuilding areas are classified as building areas. This is because the iterative use of the MBR for splitting and fitting building outlines is likely to classify some nonbuilding areas as buildings, which also leads to the relatively low IOU and F1 score of Method C. The proposed method achieves the highest P and R values of 95.97% and 98.41%, respectively, among the considered methods. This indicates that the proposed method can better complement missed building outline parts during regularization and remove erroneously extracted portions than the other methods. Moreover, the proposed method has the highest IOU (94.50%), signifying that the regularization results of this method have a higher overlap ratio with the manually labeled ground truth than those of any other contrasted method. Furthermore, the proposed method achieves the highest F1 score (97.17%), further demonstrating its superiority and general applicability. The main reasons that the regularization results of the proposed method are higher than those of the other methods in each index are as follows. First, in the overall regularization phase, the proposed method uses an improved MBR, which is more accurate than the traditionally used MABR. Moreover, in the local regularization phase, the proposed method splits individual building outlines into various types and processes them separately, enhancing the regularization accuracy for non-orthogonal building outlines. Next, in the detailed regularization phase, the proposed method incorporates building orientation and reinforces parallel, perpendicular, and orthogonal characteristics to address acute convex nodes, inaccurate corners, and non-straight segments, mimicking the process of manual sketching while ensuring that our regularization results approximate the manually labeled ground truth. Besides the accuracy of regularization results, the high efficiency of the regularization method is also valuable in practical applications. The proposed outline optimization method is primarily divided into three stages. The first stage, overall regularization, consists of three steps: (1) MBR calculation with a time complexity of O(\(n^{2}\)), (2) regularization based on the Hausdorff distance method with a time complexity of O(\(n\)), and (3) removal of redundant points with a time complexity of O(\(n\)). Therefore, the time complexity of the first stage is O(\(n^{2}\)). The second stage, local regularization, also includes three steps: (1) outline splitting, and classification based on convex hull with a time complexity of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **P (\%)** & **R (\%)** & **IOU (\%)** & **F1 (\%)** \\ \hline A & 91.62 & 96.74 & 88.88 & 94.11 \\ \hline B & 94.96 & 96.45 & 91.75 & 95.70 \\ \hline C & 93.42 & 88.85 & 83.62 & 91.08 \\ \hline Proposed method & 95.97 & 98.41 & 94.50 & 97.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of regularization results from different methods.