Local Symmetry Analysis for Corner Point Detection of Building Roofs and Its Application in Contour Regularization and 3D Reconstruction

The determination of roof corner points in UAV building point clouds is crucial for the regularization of building point cloud contours and 3D reconstruction. This paper proposes a corner point determination method based on local symmetry characteristics in view of the isosceles symmetry characteristics of the corner area. First, the two farthest points are identified based on the minimum vector angle characteristic, and the third point is subsequently determined by maximizing the vector angle. Second, the vector angle formed by the third point and the two farthest points is utilized as an indicator to recognize the corner region. Finally, a cutoff distance is applied to constrain adjacent corner points and the definitive corner points are determined in conjunction with the expected number of corners. Experiments on a UAV dataset with 49 buildings show that the method accurately detects corner points for rectangular, L-shaped, T-shaped, U-shaped, trapezoidal, and triangular roofs, producing closed regularized contours robust to point cloud holes and outperforming the RMBR, ICBF, and MCG methods. Furthermore, the determined corner points were successfully applied to 3D building reconstruction by extending roof corners to the ground and to roof contour length measurement, where over 70% of the measured contour lengths exhibited errors below 0.1 m. Robustness analysis shows that the method remains effective under low noise levels. The method provides a reliable geometric basis for UAV-based building reconstruction, although its performance depends on boundary point quality.