Delaunay Canopy

Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph

Donghyun Kim1,2 Chanyoung Kim1,2 Youngjoong Kwon2* Seong Jae Hwang1*
1Yonsei University    2Emory University
*Corresponding authors
ECCV 2026
Paper Supplementary arXiv Code
TL;DR

Delaunay Canopy scores a Delaunay graph with geometric priors to reconstruct building wireframes precisely, even in sparse, noisy, and internal-corner regions.

Delaunay Canopy teaser

Delaunay Graph Scoring

Delaunay triangulation quantifies local curvature, transforming the underlying surface geometry into essential curvature signatures.

Adaptive Search Space

Corner and wire selection leverages the geometric cue to adaptively adjust the search space, focusing the model on probable candidates.

State of the Art

State-of-the-art results on the Building3D Tallinn city and entry-level datasets, supported by a comprehensive experimental study.

Overview

From point cloud to wireframe

Overall pipeline of Delaunay Canopy
  1. 01 Delaunay Graph Scoring. Delaunay triangulation approximates the underlying surface of the point cloud, then region-wise curvature metrics are computed for each element in the order of face, edge, and vertex.
  2. 02 Corner Selection. Leveraging the vertex-wise prior, corner score sampling isolates a small, geometry-aware subset of points likely to represent true corners, and the corner selection module refines them into the final corners.
  3. 03 Wire Selection. Leveraging the edge-wise prior, each wire candidate takes a path score averaged along its shortest Delaunay path, and the wire selection module uses that score to determine valid wires.
Delaunay Graph Scoring

Curvature signatures from geometry

We apply Delaunay triangulation to the airborne LiDAR building point cloud to approximate its underlying surface. This process generates a Delaunay graph \(G = (V, E, F)\), and geometric priors for curvature characterization are assigned to its faces, edges, and vertices in turn.

Delaunay graph scoring, from the graph to edge-wise dihedral angles to vertex-wise corner scores

Face Normal Computation

For every face within the Delaunay graph, the normal vector is computed from its three constituent vertices.

Edge-Wise Dihedral Angle

For every edge, the dihedral angle is the angle between the normal vectors of its two adjacent faces. A large dihedral angle signifies a sharp fold or corner where the two adjacent faces meet.

Vertex-Wise Corner Score

For every vertex, the corner score is determined by aggregating the dihedral angles of all its incident edges into their mean. A high corner score suggests that the vertex is highly likely to be an actual corner of the building.

Corner Score Sampling

Sampling where corners live

As shown below, each panel samples the points with the highest corner scores, first 500 and then 150. While farthest point sampling performs a uniform sampling, corner score sampling retains points located in areas of pronounced curvature (roof corners and edges), making them highly probable corner candidates. The corner selection module then refines this focused subset into the final set of predicted corners.

Wire-Wise Path Score

Curvature along the shortest path

For each wire candidate connecting two predicted corners, we first find the shortest path between them on the Delaunay graph. The edges along that path share the same local region as the wire candidate, so averaging their dihedral angles gives a path score that represents the wire curvature.

Through prior-based query scaling, each wire query is then modulated by its path score, which acts as a scale factor that rescales the query. This damps low-score wires and emphasizes high-confidence ones, focusing the model's attention on geometrically plausible structures and leading to stable and accurate wire predictions.

Qualitative Results

From input to reconstruction

Drag the divider to wipe between the input point cloud and the reconstructed wireframe. Drag anywhere else to orbit, scroll to zoom. Each building turns on its own. Auto-rotation pauses the moment you grab a view.

Qualitative Results

Recovering Interior Corners

Against the strongest baseline BWFormer, on challenging cases with complicated roof structures. Fully leveraging 3D geometric context, a capability often absent when only 2D information is employed, facilitates superior detection of interior corners in addition to those on the periphery. Each row is one building, with the input on the left and the two reconstructions sharing the right cell. Drag the divider there to swap between them, drag anywhere else to orbit.

Qualitative Results

Complex Buildings

Our framework exhibits strong robustness across challenging real-world scenarios, successfully handling highly complex geometrical cases. Drag a divider to wipe between the input and the reconstruction, drag anywhere else to orbit.

Quantitative Results

State of the art on Building3D

Citation

BibTeX

@inproceedings{kim2026delaunay,
  title        = {Delaunay Canopy: Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph},
  author       = {Kim, Donghyun and Kim, Chanyoung and Kwon, Youngjoong and Hwang, Seong Jae},
  booktitle    = {European Conference on Computer Vision (ECCV)},
  year         = {2026}
}