Constrained planar primitive segmentation for building component extraction from airborne LiDAR point clouds

Accurately segmenting planar primitives from airborne LiDAR point clouds is crucial for urban planning applications and three-dimensional (3D) building reconstruction. However, existing approaches often exhibit limited extensibility and diminished robustness when segmenting buildings with diverse architectural styles. To address this issue, this paper proposes an enhanced constrained k-Plane Clustering (kPC) method that segments building point clouds into distinct planar primitives. The kPC algorithm formulates the segmentation task as a mixed-integer non-convex optimization problem incorporating three geometric constraints: point-to-plane distance minimization, cluster-center proximity enforcement, and directional regularization. This problem is solved via an alternating minimization strategy, which iteratively updates cluster assignments and plane parameters using Singular Value Decomposition (SVD) until convergence is reached. The proposed constrained kPC method provides two key advantages. First, it effectively mitigates the infinite extensibility of fitted planes. This issue is common in conventional kPC methods, and its mitigation directly addresses a major source of suboptimal segmentation performance. Second, the framework demonstrates robustness to variations in the optimization objective’s coefficients while maintaining consistent performance. Extensive experiments on both synthetic and real-world multi-style building datasets demonstrate that the proposed method achieves superior segmentation accuracy and outperforms state-of-the-art approaches in both qualitative and quantitative evaluations. Furthermore, the performance of the proposed method is robust to variations in its parameters, maintaining effectiveness across a wide range of values. • Proposes novel constrained kPC strategy to mitigate segmentation artifacts. • The proposed kPC framework incorporates a non-convex optimization formulation integrating three geometric constraints. • Extensive experimental results demonstrate that the proposed method achieves superior performance.