## 3 Experiments and Evaluation
### Compare and Local Details  
In this section, the proposed methods are compared with classical RANSAC and the polygon boundaries outlined directly from the rooftop point clouds. The qualitative results are provided in Figure 6. For boundaries directly from the building roof, since housing structures such as eaves and doorways are prevalent in rural buildings, the precision of wall corners is very low; mostly larger than 0.2 m. Meanwhile, the recessed objects are no longer considered, resulting in low edge completeness and quality indexes. That is the reason that results from single top-view images are no longer used in recent applications. We also compare our methods with traditional RANSAC. It can be seen that our results are closer to the manual outputs, with much lower RMSE and higher corner and edge indexes. This is due to the fact that spurious or multiple edges are avoided and the edge locations are more precise. This verifies the effectiveness of our weighted RANSAC and non-maximum suppression.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Area**} & \multicolumn{4}{c}{**Corners**} & \multicolumn{4}{c}{**Edges**} & \multicolumn{4}{c}{**Polygons**} \\ \cline{2-11}  & **RMSE** & **Coor** & **Comp** & **Qua** & **Coor** & **Comp** & **Qua** & **Coor** & **Comp** & **Qua** \\ \hline a & 0.066 & 100.0 & 90.0 & 90.0 & 89.5 & 81.0 & 74.0 & 100 & 100 & 100 \\ b & 0.065 & 90.0 & 85.7 & 78  
The local details are compared in Figure 7, where the classical RANSAC and roof-based approaches are compared. It can be seen that our results are more consistent with the manual ground truth than the compared methods. Most building boundaries are closed, and the eaves and doorways are well distinguished and extracted. For locations A, B, and C, both compared methods have difficulties to obtain the complete and precise results. Our method can balance the advantages of both wall and roof information well, thus producing outputs close to the ground truth. For D and E in Figure 7, we notice a large roof eave, and it can be seen that roof-based methods will produce a large spurious region, leading to poor wall corner precision. As for G, H, and I, many spurious line segments will be extracted, leading to error line segment topology relationships. In conclusion, our methods generate better corner precision and edge completeness, and, meanwhile, can distinguish different boundary types well.  
Figure 6: Comparison of the proposed methods with traditional RANSAC and the polygon boundaries outlined directly from the roof top point clouds. (**a,b**) are the RMSE and quality index for wall corners defined in Equation (6), (**c,d**) are the quality indexes for edges and polygons.  
Figure 7: Comparison of local details. From left to right are input point clouds, ground truth, our results, and results of classical RANSAC and direct output from roof point clouds. For areas A, B, and C, incomplete results will be caused by porches for compared methods; for D and E, roof-based approaches are more likely to produce enlarged boundaries; for G, H, and I, spurious lines are extracted for traditional RANSAC-based methods.