Energy-constrained hierarchical polygons for building contour regularization from airborne LiDAR point clouds

Abstract

Abstract. Building contours constitute essential geometric information in fields such as 3D urban model reconstruction and low-altitude navigation and positioning. However, due to factors such as diverse building boundary structures, uneven density, and the lack of topological relationships in airborne LiDAR point clouds, existing methods often struggle to generate geometrically consistent representations, resulting in contours with poor regularity and low fitting accuracy. To address these problems, this paper proposes a building contour regularization algorithm based on energy-constrained hierarchical polygons for airborne LiDAR building point clouds. First, a grid-guided dual-threshold alpha shapes algorithm is employed to extract discrete contour points from the building point cloud. Second, hierarchical polygons representing diverse local boundary structures are derived via a local convex hull algorithm. An energy minimization constraint is then integrated to achieve adaptive simplification and boundary regularization by optimizing the trade-off between fitting accuracy and geometric smoothness. Finally, gap merging is accomplished by projecting the vertices of polygons from adjacent levels, and polygon Boolean operations constrained by contour point fitting accuracy are applied to combine the hierarchical bounding polygons, resulting in geometrically consistent and closed building contours. Using 18 groups of challenging building point clouds with complex boundary structures, we conduct quantitative and qualitative comparative analyses between the proposed algorithm and the convex hull, concave hull, minimum-area bounding rectangle, and multidirectional bands algorithms. Experiments demonstrate that the proposed algorithm achieves an average intersection over union of 95.17% and an average root mean square error of 0.3 m, which demonstrates that it has the advantages of clear and regular contour structure, complete overall geometry, and high fitting accuracy with building point clouds.