cs.CVApr 2, 2026
SaveDelaunay Canopy: Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph
Organizations: Emory University, Atlanta GA, USA · Yonsei University, Seoul, Republic of Korea
Abstract
Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed to achieve accurate wireframe reconstruction in regions afflicted by significant noise, sparsity, or internal corners. This failure stems from the inability to establish an adaptive search space to effectively leverage the rich 3D geometry of large, sparse building point clouds. In this work, we address this challenge with Delaunay Canopy, which utilizes the Delaunay graph as a geometric prior to define a geometrically adaptive search space. Central to our approach is Delaunay Graph Scoring, which not only reconstructs the underlying geometric manifold but also yields region-wise curvature signatures to robustly guide the reconstruction. Built on this foundation, our corner and wire selection modules leverage the Delaunay-induced prior to focus on highly probable elements, thereby shaping the search space and enabling accurate prediction even in previously intractable regions. Extensive experiments on the Building3D Tallinn city and entry-level datasets demonstrate state-of-the-art wireframe reconstruction, delivering accurate predictions across diverse and complex building geometries.
Figures & tables
Figure 2: Comparison of geometric context between 2D heightmap and Delaunay scoring. While the 2D heightmap collapses 3D structural details and obscures internal corners (red box), our Delaunay scoring effectively preserves the underlying geometric context.
Figure 3: Visualization of the edge-wise dihedral angle and vertex-wise corner score , derived through Delaunay graph scoring across input point clouds, projected onto the Bird’s-Eye View (BEV). The results demonstrate a robust capability to accurately capture the underlying surface and the curvature of the corresponding region. Notably, the scoring adeptly represents even the most minute degrees of surface curvature (fourth column) and maintains efficacy even when the point cloud is highly sparse (fifth column).
Figure 4: Overall pipeline of Delaunay Canopy. The pipeline begins by utilizing Delaunay triangulation to construct the point cloud into a Delaunay graph. The method then sequentially computes metrics that represent the local curvature around each element, proceeding in the order of face, edge, and vertex. This process encapsulates rich 3D information and introduces a judicious search space into the pipeline.
Figure 5: Comparison between Corner Score Sampling (ours) and Farthest Point Sampling (FPS). Resultant point sets after sequentially sampling 500 points ( = 500) and then 150 points ( = 150) with each method are shown. For enhanced clarity, the ground truth wireframe is visualized. While FPS performs a uniform sampling, our corner score sampling method retains points located in areas of pronounced curvature ( e.g . , roof corners and edges), making them highly probable corner candidates.
| Method | Tallinn City | Entry-Level | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Distance | Corner | Wire | Distance | Corner | Wire | |||||||||||
| WED | ACO | CP | CR | CF1 | EP | ER | EF1 | WED | ACO | CP | CR | CF1 | EP | ER | EF1 | |
| Building3D (PointNet) [ 27 ] | 0.264 | 0.241 | 88.2 | 77.6 | 82.6 | 80.4 | 71.9 | 75.9 | 0.262 | 0.239 | 89.1 | 77.8 | 83.1 | 80.7 | 72.7 | 76.5 |
| PC2WF [ 17 ] | 0.554 | 0.508 | 21.4 | 50.5 | 30.1 | 2.8 | 16.7 | 4.8 | 0.490 | 0.422 | 28.5 | 16.3 | 20.7 | 3.1 | 19.1 | 5.3 |
| Point2Roof [ 14 ] | 0.260 | 0.236 | 89.3 | 78.5 | 83.6 | 81.2 | 72.2 | 76.4 | 0.257 | 0.238 | 89.5 | 78.1 | 83.4 | 81.4 | 73.4 | 77.2 |
| PointTransformer ∗ [ 44 ] | 0.257 | 0.238 | 89.7 | 79.1 | 84.1 | 81.3 | 72.4 | 76.6 | 0.259 | 0.233 | 89.7 | 79.4 | 84.2 | 81.5 | 73.8 | 77.5 |
Table 1: Quantitative comparisons on the Building3D Tallinn city and entry-level datasets. The notation signifies a model acting as the feature extractor within the Point2Roof [ 14 ] pipeline. Best , second best , and third best are highlighted.
Figure 6: Qualitative comparison with other methods. The notation signifies a model acting as the feature extractor within the Point2Roof [ 14 ] pipeline. The blue boxes illustrate the robustness of our framework, demonstrating its capability to reconstruct the wireframe even in regions that are severely sparse (first row), highly noisy (second row), or exhibit minute degrees of curvature (third row).
Figure 7: Qualitative comparison with the strongest baseline BWFormer [ 19 ] on challenging cases with complicated roof structures. The orange boxes show our method’s ability to fully leverage 3D geometric context, a capability often absent when only 2D information is employed, thus facilitating superior detection of interior corners in addition to those on the periphery.
| Exp. | Wire Selection | Prior-based | Distance | Corner | Wire | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| # | Module | Query Scaling | WED | ACO | CP | CR | F1 | EP | ER | F1 |
| 1 | Point2Roof | - | 0.248 | 0.225 | 92.4 | 80.5 | 86.0 | 85.8 | 72.8 | 78.8 |
| 2 | Ours | - | 0.239 | 0.210 | 93.1 | 81.1 | 86.7 | 85.6 | 73.7 | 79.2 |
| 3 | Ours | ✓ | 0.232 | 0.194 | 94.5 | 82.8 | 88.3 | 87.1 | 74.0 | 80.0 |
Table 5: Analysis of geometric prior vs. architecture.
Figure 9: The resulting mesh, reconstructed from the wireframe output generated by the Delaunay Canopy. The wireframe demonstrably encapsulates sufficient geometric information, allowing the resultant mesh to exhibit a highly faithful form.
| Method | Distance | Corner | Wire | |||||
|---|---|---|---|---|---|---|---|---|
| WED | ACO | CP | CR | CF1 | EP | ER | EF1 | |
| PointMAE † [ 26 ] | - | 0.330 | 75.0 | 47.0 | 58.0 | 52.0 | 12.0 | 20.0 |
| PointM2AE † [ 43 ] | - | 0.320 | 79.0 | 58.0 | 67.0 | 50.0 | 7.0 | 12.0 |
| Point2Roof [ 14 ] | - | 0.390 | 65.0 | 30.0 | 41.0 | 66.0 | 8.0 | 14.0 |
| Linear self-supervised [ 34 ] | - | 0.350 | 70.0 | 60.0 | 65.0 | 67.0 | 16.0 | 25.0 |
| Supervised [ 34 ] | - | 0.290 | 90.0 | 53.0 | 66.0 | 88.0 | 23.0 | 36.0 |
Table 6: Performance evaluation based on the official Building3D [ 34 ] Tallinn city dataset leaderboard. Baseline metrics are sourced from the public leaderboard. The notation designates models acting exclusively as the feature extraction backbone within the standard Building3D [ 34 ] architecture. Best , second best , and third best are highlighted.
| Method | Distance | Corner | Edge | |||||
|---|---|---|---|---|---|---|---|---|
| WED | ACO | CP | CR | CF1 | EP | ER | EF1 | |
| Building3D (PointNet) [ 27 ] | 0.271 | 0.245 | 87.8 | 77.9 | 82.5 | 80.8 | 71.5 | 75.9 |
| PC2WF [ 17 ] | 0.548 | 0.512 | 21.9 | 50.1 | 30.4 | 3.1 | 16.5 | 5.3 |
| Point2Roof [ 14 ] | 0.265 | 0.239 | 89.0 | 78.2 | 83.3 | 81.5 | 71.8 | 76.3 |
| PointTransformer ∗ [ 44 ] | 0.260 | 0.242 | 89.4 | 78.8 | 83.8 | 81.7 | 72.0 | 76.5 |
| PointMLP ∗ [ 21 ] | 0.258 | 0.236 | 90.3 | 79.3 | 84.4 | 82.1 | 72.5 | 77.0 |
Table 7: Robustness validation via 5-Fold Cross-Validation. The notation signifies a model acting as the feature extractor within the Point2Roof [ 14 ] pipeline. Best and second best are highlighted.
| Method | Distance | Corner | Edge | |||||
|---|---|---|---|---|---|---|---|---|
| WED | ACO | CP | CR | CF1 | EP | ER | EF1 | |
| Building3D (PointNet) [ 27 ] | 0.407 | 0.354 | 78.1 | 68.9 | 73.2 | 72.6 | 64.2 | 68.2 |
| PC2WF [ 17 ] | 0.658 | 0.612 | 14.2 | 38.7 | 20.8 | 1.6 | 10.4 | 2.7 |
| Point2Roof [ 14 ] | 0.384 | 0.341 | 79.5 | 70.3 | 74.6 | 73.9 | 65.4 | 69.4 |
| PointTransformer ∗ [ 44 ] | 0.367 | 0.325 | 80.8 | 71.5 | 75.9 | 75.2 | 66.5 | 70.6 |
| PointMLP ∗ [ 21 ] | 0.359 | 0.318 | 81.3 | 72.0 | 76.4 | 75.6 | 67.1 | 71.1 |
Table 8: Robustness validation assessed against a perturbed dataset characterized by augmented sparsity and noise. The notation signifies a model acting as the feature extractor within the Point2Roof [ 14 ] pipeline.
Figure 10: Visualization of performance differences between challenging (perturbed point cloud) and original inputs. The number next to indicates the absolute performance difference, and the percentage (%) shows the relative decrease compared to the original performance. The notation signifies a model acting as the feature extractor within the Point2Roof [ 14 ] pipeline.
Figure 11: Visualization of failure cases. Precise wireframe reconstruction is demonstrably compromised under several key scenarios. (a) When critical regions containing valid corner and wire features are unscanned and consequently absent from the point cloud. (b & c) When the intrinsic surface topology of the point cloud exhibits excessive smoothness. (d) When processing objects characterized by a closed topology, such as non-building volumetric structures.
Figure 12: Qualitative comparison with the strongest baseline BWFormer [ 19 ] . The orange bounding boxes specifically denote the regions where our method achieves a demonstrably superior reconstruction result.
Figure 13: Wireframe reconstruction results of Delaunay Canopy on Building3D dataset.
Figure 14: Wireframe reconstruction results of Delaunay Canopy on Building3D dataset.
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