# Multilevel Regularization Method for Building Outlines
## 4 Results and Analysis  
### Experimental Analysis  
#### 4.1.1 Qualitative Evaluation  
Figure 16 presents examples of the regularization results of the four methods for extracting building outlines from the images with 0.075 m resolution, along with the manually labeled ground truths. The top two rows display regularization results for relatively regular building outlines, whereas the bottom three rows show results for more complex building outlines. Comparing the building outlines before and after simplification, all methods clearly achieve satisfactory results in the regularization of relatively regular building outlines, as shown in Figure 16a,b. However, for more complex building outlines, Methods A, B, and C exhibit certain shortcomings, as illustrated in Figure 16c-e. These shortcomings can be categorized into two types: some parts of the complex outline are eliminated through regularization, and some parts that do not align with the main direction of the building outline are excessively regularized. Figure 16: Comparison of manually labeled ground truth, regularization results of different methods, and extracted building outlines, the inside of the green dotted line shows the contrast of the outline details. (**a**–**e**) The first column is the remotely sensed images of buildings in five randomly selected areas, the second column is the superposition of manually labeled ground truth with the extracted building outlines, and the last four columns are the superposition of Methods A, B, and C and the proposed method with the extracted building outlines, respectively. To visualize and assess the regularization performance of each method better, the regularization results from different methods were overlaid with the manually labeled ground truth, as shown in Figure 17.  
Method A divides the building outline regularization process into two steps. The first step is to remove noise points, redundant nodes, and small outline segments. When dealing with densely populated complex outlines, this step may lead to the loss of some outline details. The second step employs the long edge weighting method to determine the main direction and adjusts the line segments composing the outline accordingly. Because only one main direction is used for control, there may be instances where outlines inconsistent with the main direction of the building are over-regularized as shown in Figure 17a. Method B initially rotates the building outline to align the edges of its MBR with the coordinate axes. Then, it divides the building outline into four parts using the four nodes closest to the four vertices of the MBR on the building outline. Each part is iteratively split using the regression line method, and the resulting regression lines satisfying certain conditions are intersected and recombined to obtain the regularization results. This method utilizes the MABR. When a deviation exists between the long edge of the MBR and the main direction, the overall orientation of the regularized outline may deviate from the true outline, as shown by the yellow dashed line inside the building outline in Figure 17b. Moreover, Method B uses a vertical regression processing strategy that maximizes the orthogonality of the building outline. However, it may produce locally inaccurate results for non-rectangular building outlines, as indicated by the blue dashed line inside the building outline in Figure 17b. Method C iteratively employs the MBR to segment and hierarchically organize the building outline, mapping the outlines of each hierarchy to their corresponding MBR to eliminate jagged nodes and regularize the shape of the building. This method performs well for building outlines with clear rectangular features but produces locally inaccurate results for complex building outlines and non-rectangular combinations of building outlines, as shown in Figure 17c. The proposed method is based on the concept of manual sketching when regularizing building outlines.