# A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds

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^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Building Contours Generation

^{2}).

#### 2.2. Graph-Based Localized Contour Tree Construction

**A**as the root node, which has the lowest height value. Then, the adjacent contour

**B**is identified and added as the child node of contour

**A**. This iterative process continues until the highest contour F is included as the leaf node. Finally, the single building leads to a single-branch contour tree. Similarly, for a multi-story composite building, as shown in Figure 1c, a multi-branch contour tree (Figure 1d) is established through the contour tree construction. As shown in Figure 1d, the multi-branch contour tree is composed of a root node (

**A1**), six internal nodes (

**A2**,

**B1**,

**B2**,

**B3**,

**B4**, and

**C1**) and two terminal nodes (

**B5**and

**C2**).

**A2**has two child nodes

**B1**and

**C1**, representing a separation relationship in the sense of topological representation. The sub-tree rooted at

**B1**is a monotonous structure, representing a part of the building. Similarly, the sub-tree rooted at

**C1**is also a part of the building. Besides, the sub-tree

**A1**–

**A2**is also a part of the building, which represents the base of the building. Therefore, the building in Figure 1c can be separated into three different components:

**A1**–

**A2**,

**B1**–

**B5**, and

**C1**–

**C2**. Clearly, the local contour tree can capture and emulate the spatial and topological structure of buildings nicely.

#### 2.3. Bipartite Graph Matching

#### 2.4. Building Model Reconstruction

**B0**and

**C0**in Figure 3a) in the gap. The shape of the virtual contour is the same as the nearest neighbor contour at a higher height value, while the contour value of the virtual contour is set as same as the most adjacent neighbor contour at a lower height value. As shown in Figure 3a, the virtual contour

**B0**has the same shape as contour

**B1**and its contour value is identical to the height value of contour

**A2**. By adding the virtual contour, the gap can be filled (see Figure 3b). So far, we can get a complete and unbroken 3D building model by connecting all the individual parts of the building together.

#### 2.5. Implementation

## 3. Experiment

#### 3.1. Study Area and Data

^{®}3D Analyst Toolbox (Environmental Systems Research Institute, Redlands, CA, USA). The LiDAR point cloud data extracted from the ASCII file is in the map projection of Shanghai local coordinate system and referenced to the horizontal datum-D_Beijing_1954. The study area consists of 15,940,136 sampling points, covering an area of 4,184,300 m

^{2}with an average point density of approximately 4 points/m

^{2}. Figure 5 shows the 3D georeferenced point clouds of the study area.

#### 3.2. Results

## 4. Discussion

#### 4.1. Performance

#### 4.2. Tuning of Algorithm Parameters

#### 4.3. Limitations

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Illustration of graph-based localized contour tree representation of buildings: (

**a**) contour representation of a single building; (

**b**) a single-branch contour tree representation of the building shape shown in (

**a**); (

**c**) contour representation of a multi-layers building; and (

**d**) a multi-branch contour tree representation of the building shape shown in (

**c**).

**Figure 2.**Bipartite graph matching: (

**a**) two consecutive contours; (

**b**) sets of nodes in two consecutive contours; (

**c**) resulting matchings between the two sets of nodes in (

**b**); and (

**d**) the surface model.

**Figure 3.**Virtual contours: (

**a**) the existing gap and virtual contour; (

**b**) a complete model by filling the gap.

**Figure 4.**Geographical location and high-resolution aerial photograph of the Lujiazui region in Shanghai, China.

**Figure 6.**Reconstructed building models for the Lujiazui region: (

**A**) the 3D building models for area A; (

**B**) the 3D building models for area B; and (

**C**) the 3D building models for area C.

**Figure 7.**Results on selected buildings: (

**a**) and (

**e**) are the building point clouds; (

**b**) and (

**f**) are the outdoor scene pictures; (

**c**) and (

**g**) are the contours in 3D scene; and (

**d**) and (

**h**) are the reconstructed building models.

No./${\mathit{d}}_{\mathit{i}}$ | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 5.0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

#1 | 0.39 | 0.41 | 0.42 | 0.43 | 0.43 | 0.52 | 0.65 | 0.96 | 0.98 | 0.99 | 1.04 | 1.07 | 1.10 | 1.44 | 1.84 |

#2 | 0.33 | 0.35 | 0.35 | 0.36 | 0.36 | 0.37 | 0.39 | 0.39 | 0.43 | 0.45 | 0.59 | 0.72 | 0.97 | 1.02 | 1.43 |

#3 | 0.49 | 0.49 | 0.50 | 0.52 | 0.54 | 0.57 | 0.60 | 0.67 | 0.77 | 0.91 | 1.03 | 1.57 | 2.22 | 3.28 | 4.05 |

#4 | 0.28 | 0.29 | 0.29 | 0.37 | 0.42 | 0.42 | 0.48 | 0.54 | 0.67 | 0.79 | 0.90 | 1.28 | 2.00 | 2.93 | 4.42 |

#5 | 0.17 | 0.19 | 0.20 | 0.22 | 0.28 | 0.30 | 0.30 | 0.32 | 0.39 | 0.44 | 0.51 | 0.70 | 1.32 | 1.97 | 2.56 |

#6 | 0.26 | 0.28 | 0.30 | 0.31 | 0.31 | 0.43 | 0.46 | 0.47 | 0.59 | 0.65 | 0.67 | 0.81 | 1.70 | 2.23 | 3.19 |

No./$\mathit{n}$ | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 250 | 300 | 350 | 400 | 500 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

#1 | 0.66 | 0.51 | 0.45 | 0.44 | 0.44 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 | 0.43 |

#2 | 0.82 | 0.67 | 0.59 | 0.51 | 0.42 | 0.41 | 0.39 | 0.39 | 0.37 | 0.37 | 0.36 | 0.36 | 0.36 | 0.35 | 0.35 |

#3 | 0.93 | 0.81 | 0.74 | 0.69 | 0.67 | 0.60 | 0.58 | 0.57 | 0.57 | 0.56 | 0.55 | 0.54 | 0.52 | 0.51 | 0.51 |

#4 | 1.23 | 1.05 | 1.01 | 0.98 | 0.79 | 0.77 | 0.76 | 0.68 | 0.60 | 0.55 | 0.45 | 0.42 | 0.40 | 0.38 | 0.38 |

#5 | 0.51 | 0.46 | 0.44 | 0.43 | 0.41 | 0.39 | 0.35 | 0.32 | 0.32 | 0.31 | 0.28 | 0.28 | 0.24 | 0.22 | 0.21 |

#6 | 0.47 | 0.36 | 0.33 | 0.32 | 0.32 | 0.32 | 0.32 | 0.32 | 0.32 | 0.32 | 0.31 | 0.31 | 0.31 | 0.31 | 0.31 |

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**MDPI and ACS Style**

Wu, B.; Yu, B.; Wu, Q.; Yao, S.; Zhao, F.; Mao, W.; Wu, J. A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds. *Remote Sens.* **2017**, *9*, 92.
https://doi.org/10.3390/rs9010092

**AMA Style**

Wu B, Yu B, Wu Q, Yao S, Zhao F, Mao W, Wu J. A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds. *Remote Sensing*. 2017; 9(1):92.
https://doi.org/10.3390/rs9010092

**Chicago/Turabian Style**

Wu, Bin, Bailang Yu, Qiusheng Wu, Shenjun Yao, Feng Zhao, Weiqing Mao, and Jianping Wu. 2017. "A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds" *Remote Sensing* 9, no. 1: 92.
https://doi.org/10.3390/rs9010092