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City3D: Large-Scale Building Reconstruction from Airborne LiDAR Point Clouds

Jin Huang, Jantien Stoter, Ravi Peters, Liangliang Nan

arXiv:2201.10276v2cs.CVcs.GR

TL;DR

Airborne LiDAR often misses building walls, complicating reconstruction of compact 3D models. City3D infers vertical planes and uses them in an extended polygonal reconstruction framework. The method reports plausible reconstructions across varied data and RMSE values from 0.04 m to 0.26 m, and releases a 20k-building dataset.

  • Problem

    Airborne LiDAR point clouds typically omit vertical walls, while sparse and noisy structural cues complicate topologically correct reconstruction of complex buildings.

    Source: §1 · p. 2

  • Method

    City3D infers vertical planes from airborne LiDAR and extends hypothesis-and-selection polygonal surface reconstruction with roof preferences and building-specific hard constraints.

    Source: §1 · p. 2, §3.2 · p. 5, §3.3 · p. 7

  • Results

    RMSE for the evaluated buildings ranges from 0.04 m to 0.26 m, and reconstructions are visually plausible across varied structures and point-cloud conditions.

    Source: §4.2 · pp. 9, 11

  • Takeaways & Limitations

    The released dataset contains airborne LiDAR point clouds and reconstructed 3D models for 20k real-world buildings.

    Source: §4.2 · p. 13

    The planar-primitive implementation cannot reconstruct buildings with curved surfaces.

    Source: §5 · p. 17

Abstract

from arXiv · show

We present a fully automatic approach for reconstructing compact 3D building models from large-scale airborne point clouds. A major challenge of urban reconstruction from airborne LiDAR point clouds lies in that the vertical walls are typically missing. Based on the observation that urban buildings typically consist of planar roofs connected with vertical walls to the ground, we propose an approach to infer the vertical walls directly from the data. With the planar segments of both roofs and walls, we hypothesize the faces of the building surface, and the final model is obtained by using an extended hypothesis-and-selection-based polygonal surface reconstruction framework. Specifically, we introduce a new energy term to encourage roof preferences and two additional hard constraints into the optimization step to ensure correct topology and enhance detail recovery. Experiments on various large-scale airborne LiDAR point clouds have demonstrated that the method is superior to the state-of-the-art methods in terms of reconstruction accuracy and robustness. In addition, we have generated a new dataset with our method consisting of the point clouds and 3D models of 20k real-world buildings. We believe this dataset can stimulate research in urban reconstruction from airborne LiDAR point clouds and the use of 3D city models in urban applications.

1. Introduction

Large-scale urban applications need accurate, compact building models, but airborne LiDAR often omits walls and provides sparse cues for complex structures. The paper infers vertical planes and extends polygonal surface reconstruction to recover building models from these data.

1. Introduction

  • The target is high-accuracy, compact 3D building models for large-scale urban applications, while prior airborne-LiDAR approaches often compromise accuracy and geometric detail.Urban models support visualization, simulation, navigation, and entertainment.Source: §1 · pp. 1–2
  • Missing vertical walls, cluttered scenes, and sparse, noisy structural cues make large-scale reconstruction from airborne LiDAR challenging.Buildings’ vertical walls are typically not captured, while complex structures create ambiguity about topologically correct models.Source: §1 · p. 2
  • The method uses building footprints to separate instances, infers vertical planes from incomplete point clouds, and constrains polygonal surface reconstruction with those planes.Inferred planes are treated as walls connecting piecewise planar roofs to the ground; outer walls can also be extruded from footprints.Source: §1 · p. 2
  • The framework extends hypothesis-and-selection reconstruction with a roof-preference energy term and hard constraints for topology and detail recovery.The paper also introduces optimal transport to extract polylines from 2D bounding contours when inferring vertical planes.Source: §1 · p. 2

2. Related Work

Prior work addresses roof primitives, footprints, and polygonal surface assembly, but airborne LiDAR often lacks a complete set of planar primitives. This paper extends a hypothesis-and-selection reconstruction method with building-specific energy and constraints.

Footprint extraction

  • The method relies on footprint data to extract building instances from large point clouds and can also be used for footprint extraction.Footprints represent building outer-wall geometry projected onto the ground plane.Source: §2 · p. 3

Roof primitive extraction

  • Roof primitives are commonly extracted with RANSAC or region growing; this paper uses an existing region-growing method for its simplicity and robustness.The cited region-growing method is Rabbani et al..Source: §2 · p. 3

Footprint extraction

  • Footprint methods project points to a grid or use rooftop contours, with simplification and directional regularization used to shape outlines.The paper detects contours from a projected-point heightmap, then regularizes polylines by orientation clustering and adjustment.Source: §2 · pp. 3–4

Building surface reconstruction

  • Primitive-assembly methods hypothesize polyhedral cells or polygonal faces from detected planes, then extract a compact mesh, but complete primitive sets remain challenging to obtain from airborne LiDAR.Other reconstruction approaches include TIN simplification, topology-controlled contouring, inferred primitives for missing walls, and template-based models limited by predefined shapes.Source: §2 · p. 4
  • The paper extends a general hypothesis-and-selection polygonal reconstruction method with a novel energy term and hard constraints for building topology and detail.The target buildings have piecewise-planar roofs connected to the ground by vertical walls.Source: §2 · p. 4

3. Methodology

The method reconstructs building models by inferring missing vertical planes from airborne LiDAR data and selecting hypothesized faces in an extended surface-reconstruction framework. It adds building-specific roof preferences and hard constraints to guide that optimization.

3.1. Overview

  • Given point clouds and building footprints, the pipeline extracts each building’s points and reconstructs a compact polygonal model.The inputs are airborne LiDAR data and corresponding footprints; the outputs are 2-manifold, watertight models.Source: §3.1 · p. 4
  • The method extends PolyFit by using inferred vertical planes and adding a roof-preference energy term and hard constraints for topology and detail recovery.The model is obtained by optimizing over hypothesized building faces.Source: §3.1 · p. 5

3.2. Inferring Vertical Planes

  • Vertical walls are inferred by extracting height variations from a rasterized height map, converting contours into closed polylines, and extruding them into planes.A TIN is rasterized to form the height map, and optimal transport extracts the polylines.Source: §3.2 · pp. 5–6
  • The polyline simplification limits contour deviation by a distance threshold and minimizes increases in transport cost, stopping when no vertex can be removed or the cost tolerance is exceeded.An edge-filtering step removes small groups of undesirable edges caused by noise and outliers.Source: §3.2 · p. 6
  • Clustering and adjustment regularize noisy polylines using parallelism, collinearity, and orthogonality; adjustment can also align segments with footprint edges.Near-collinear and near-orthogonal segments are made exactly collinear and orthogonal using a 20° angle threshold; regularization improves outline regularity and reduces complexity.Source: §3.2 · pp. 6–7, Figure 3 · p. 6

3.3. Reconstruction

  • Face hypotheses are formed by intersecting roof planes and cropping the resulting faces with outer vertical planes, connecting roof boundaries to inferred walls.The method also uses vertical planes inferred from the point cloud as hard constraints.Source: §3.3 · p. 7
  • The objective combines data fitting, which favors faces supported by more points, with model complexity, which favors simple planar structures, and a roof preference for higher faces.The roof preference addresses cases with multiple roof layers by preferring a higher roof face over one beneath it.Source: §3.3 · p. 7
  • Two hard constraints require a single roof layer and apply a face prior that selects the highest-confidence face derived from each planar segment.Face confidence is measured by supporting-point count; the face prior resolves ambiguities between near-coplanar, nearby faces and preserves finer details.Source: §3.3 · pp. 7–8, Figure 4 · p. 8

4. Results and Evaluation

City3D reconstructs compact building models across large airborne point-cloud datasets, including scenes with varying density, noise, and missing data. Comparisons report higher reconstruction accuracy than 2.5D Dual Contouring, PolyFit, and BAG3D, alongside practical runtime and limitations for complex buildings.

4.2. Reconstruction Results

  • Reconstructions across AHN3, DALES, and Vaihingen were visually plausible despite varied building structures, point densities, noise, outliers, and missing data.The method reconstructed more than 20,000 buildings; AHN3 and Vaihingen footprints supported segmentation and wall extrusion, while DALES instance labels supported segmentation.Source: §4.1 · p. 8, §4.2 · p. 9, Figure 5 · p. 10
  • For the buildings evaluated in Table 1, RMSE ranged from 0.04 m to 0.26 m, and most reconstructions took less than 30 seconds.A complex building took 42 minutes; the paper attributes this to many candidate faces and a large optimization problem.Source: §4.2 · p. 11, Table 1 · p. 12, Figure 7 · p. 13
  • The method releases a dataset of 20,000 buildings with reconstructed 3D models and corresponding airborne LiDAR point clouds.Source: §4.2 · p. 13

4.3. Parameters

  • The reported settings fix distance and transportation-cost tolerances and energy weights, while rasterization resolution varies by dataset.The resolution is 0.20 m for AHN3, 0.15 m for DALES, and 0.25 m for Vaihingen.Source: §4.3 · p. 13

4.4. Comparisons

  • The proposed method achieved the highest reconstruction accuracy among 2.5D Dual Contouring and PolyFit on AHN3, DALES, and Vaihingen, averaging 4.9 seconds per building.It produced the most plausible 3D models and used an order of magnitude fewer faces than 2.5D Dual Contouring. PolyFit still failed to reconstruct some walls and performed poorly in recovering geometric details.Source: §4.4 · pp. 13–14
  • Across four regions comprising 1,113 BAG3D buildings, our models showed higher accuracy than BAG3D in the quantitative comparison, with both methods using AHN3 point clouds as input.Source: §4.4 · p. 14, Table 3 · p. 15

4.5. With vs. Without Footprint

  • With footprint data, the method extrudes footprint polygons to form vertical planes, then intersects them with planes extracted from point clouds before optimization.Without footprints, it infers vertical planes from roof points; this can slightly increase reconstruction errors.Source: §4.5 · p. 15, Figure 10 · p. 16

4.6. Reconstruction Using Point Clouds with Vertical Planes

  • For point clouds containing detectable walls, such as those reconstructed from drone images, detected vertical planes can replace inferred planes.This adaptation skips the vertical-plane inference step.Source: §4.6 · p. 15, Figure 11 · p. 16

5. Conclusions and Future Work

City3D reconstructs large-scale urban buildings from airborne LiDAR by inferring vertical planes that are commonly missing. The framework uses planar primitives, so curved building surfaces remain outside its current capability.

5. Conclusions and Future Work

  • Inferring vertical planes is an effective reconstruction strategy, while the roof-preference energy and hard constraints support topologically correct and accurate models.Outer planes become exterior walls; inner planes split roof planes and form necessary inner walls.Source: §5 · p. 17
  • The current framework uses planar primitives and cannot handle buildings with curved surfaces.The authors propose extending the strategy to other primitives, including spheres, cylinders, or parametric surfaces.Source: §5 · p. 17

Abbreviations

The manuscript uses three abbreviations: LiDAR, TIN, and RMSE.

Abbreviations

  • LiDAR means Light Detection and Ranging, TIN means Triangular Irregular Network, and RMSE means Root Mean Square Error.Source: Abbreviations · p. 17

Appendix A. The Complete Formulation

The formulation selects an optimal subset of hypothesized building faces using data-fitting, model-complexity, and roof-preference energies. Constraints govern roof layers, face adjacency, and face selection priors.

Appendix A. The Complete Formulation

  • The objective combines data fitting, model complexity, and roof preference to select the optimal subset of hypothesized faces.Data fitting measures fit to the input point cloud; model complexity encourages large planar structures to avoid defects from noise and outliers.Source: Appendix A · pp. 17–18
  • The roof-preference term favors higher roof faces when a building has multiple roof layers.The authors note this can occur with semi-transparent or overhung roofs.Source: Appendix A · p. 18
  • Three constraints require a single roof layer, two adjacent faces per edge, and selection of the highest-confidence face from each planar segment.The adjacency constraint makes the final model watertight and manifold; the face prior resolves near-coplanar, close-face ambiguity to preserve finer details.Source: Appendix A · p. 18
  • The selected faces, indicated by binary variables set to 1, form the building's final surface model.Source: Appendix A · p. 18

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