# Multilevel Regularization Method for Building Outlines
## 4 Results and Analysis
### Overall Discussion of the Algorithms and Future Work  
The proposed method integrates various techniques, including surface fitting based on an improved Hausdorff distance method and an improved MBR method, line fitting based on the least squares method, and point fitting based on centroid coordinate substitution. The excellent experimental results of the proposed method are because of the improvements of the algorithm. First, a multilevel regularization framework was established, involving three steps: overall regularization, local regularization, and detailed regularization. This framework ensures that building outlines are processed at different levels from the overall to local scales. Second, problems encountered by the commonly used MBR method, including direction deviation and poor fitting to building outlines, were mitigated by improving the MBR method. Consequently, the proposed method can better maintain the consistency of the main direction and overall shape of building outlines during regularization, fundamentally reducing the severity of directional deviations. Third, the Hausdorff distance regularization algorithm was optimized, significantly improving the efficiency and accuracy of regularization. Finally, the process of manual sketching was used as a reference to perform detailed regularization adjustments, making the regularization results closer to the real outlines.  
Our proposed method uses building outlines extracted through deep learning techniques as experimental data. The main reason is that the method of extracting building outlines from high-resolution remote sensing images using deep learning techniques is very mature through the research of many scientists, and the extraction results are more accurate and robust. and have better generalization ability compared to traditional extraction methods. Whereas feature extraction in traditional methods mainly relies on the work design of the extractor, which requires specialized knowledge and a complex process of parameter adjustment, the algorithms are application-specific, and the generalization ability and robustness are not as good as in deep learning methods. In the future, with the gradual improvement of the resolution of deep remote sensing images, the advantages of deep learning algorithms will become increasingly obvious, and the application prospects of our proposed method will become broader.  
Figure 19: Regularization results for complex building outlines from different methods, the inside of the green dotted line shows the contrast of the outline details.  
The proposed method is primarily applicable to the regularization of building outlines composed of straight segments. Its applicability in complex building outlines containing curved segments was also tested. Figure 20 shows the regularization results of the proposed method for building outlines with various shapes. As shown, for building outlines composed of straight segments, the proposed method can correct the missing parts of the extracted outlines (Figure 20a) and remove erroneously extracted parts (Figure 20b), making the regularization results closer to the actual building outlines. However, for building outlines that include curved segments, the proposed method outputs polygonal outlines (Figure 20c), indicating that further research is needed to improve regularization in such cases, which will be a focus of future work.