Roof Boundary Points Extraction From LiDAR Point Cloud Data Using Adaptive Neighbourhood-Based α-Shape Algorithm

Accurate building roof boundary extraction from airborne LiDAR point clouds remains a challenge due to abrupt density variations and complex roof structures. Existing $\alpha $ -shape-based methods are capable of detecting building boundary points. However, their reliance on fixed neighbourhood selection strategies can lead to inaccurate boundary point extraction in regions with abrupt variations in point density. This paper presents a boundary point extraction technique that selects optimal $\alpha $ values adaptively for individual points by analyzing local geometric point density using an adaptive variable point neighbourhood selection technique. The proposed method first constructs a Delaunay triangulation network from input building roof point cloud data, then iteratively selects optimal neighbouring points from multiple scanlines to compute point-specific $\alpha $ values that adapt to local density variations. This approach effectively mitigates the misclassification of densely clustered points as boundary points by adaptively adjusting to local point distributions. The proposed method is tested on sample buildings of five different datasets with various point densities. Experimental results confirm that this approach outperforms conventional $\alpha $ -Shape-based algorithms, geometric rule-based approaches, and recent adaptive methods by successfully preserving the actual boundary points of a roof while filtering out false positives caused by the fluctuating abrupt point density. The proposed method significantly reduces the Relative Area Error (RAE) and RCC distances, aligning with the expected performance of roof boundary extraction. Furthermore, an ablation study validates the contribution of the proposed adaptive $\alpha $ value and the adaptive neighbourhood selection.