Geometry and Topology Preservable Line Structure Construction for Indoor Point Cloud Based on the Encoding and Extracting Framework

The line structure is an efficient form of representation and modeling for LiDAR point clouds, while the Line Structure Construction (LSC) method aims to extract complete and coherent line structures from complex 3D point clouds, thereby providing a foundation for geometric modeling, scene understanding, and downstream applications. However, traditional LSC methods often fall short in preserving both the geometric integrity and topological connectivity of line structures derived from such datasets. To address this issue, we propose the Geometry and Topology Preservable Line Structure Construction (GTP-LSC) method, based on the Encoding and Extracting Framework (EEF). First, in the encoding phase, point cloud features related to line structures are mapped into a high-dimensional feature space. A 3D U-Net is then employed to compute Subsets with Structure feature of Line (SSL) from the dense, unstructured, and noisy indoor LiDAR point cloud data. Next, in the extraction phase, the SSL is transformed into a 3D field enriched with line features. Initially extracted line structures are then constructed based on Morse theory, effectively preserving the topological relationships. In the final step, these line structures are optimized using RANdom SAmple Consensus (RANSAC) and Constructive Solid Geometry (CSG) to ensure geometric completeness. This step also facilitates the generation of complex entities, enabling an accurate and comprehensive representation of both geometric and topological aspects of the line structures. Experiments were conducted using the Indoor Laser Scanning Dataset, focusing on the parking garage (D1), the corridor (D2), and the multi-room structure (D3). The results demonstrated that the proposed GTP-LSC method outperformed existing approaches in terms of both geometric integrity and topological connectivity. To evaluate the performance of different LSC methods, the IoU Buffer Ratio (IBR) was used to measure the overlap between the actual and constructed line structures. The proposed method achieved IBR scores of 92.5% (D1), 94.2% (D2), and 90.8% (D3) for these scenes. Additionally, Precision, Recall, and F-Score were calculated to further assess the LSC results. The F-Score of the proposed method was 0.89 (D1), 0.92 (D2), and 0.89 (D3), demonstrating superior performance in both visual analysis and quantitative results compared to other methods.