# Registration of Airborne LiDAR Point Clouds by Matching the Linear Plane Features of Building Roof Facets

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Point Cloud Registration by Matching Plane Features of Building Roof Facets

#### 2.1. Principle and Flowchart of Proposed Method

#### 2.2. Calculating the Normal Vectors of Building Roof Facets

#### 2.3. Model Parameters Estimation Using Common Building Features

#### 2.3.1. Rotation Matrix Calculation

#### 2.3.2. 3D Translation Calculation

## 3. Experiments

#### 3.1. Details of Datasets and the Selected Corresponding Roofs

^{2}. The case area is near the airport of Zhoushan; therefore, buildings here were very simple. Flat roofs and gable roofs are two main roof types included in the dataset. The difference between two trajectories’ point is relative large. A preliminary evaluation of difference of two trajectories point cloud is about 25 m on average.

#### 3.2. Selection of Building Roofs for Registration

#### 3.3. Estimation of Transformation Parameters

- ■
- Parameters comparison for the first case

- ■
- Parameters comparison for the second case

#### 3.4. Accuracy Evaluation

#### 3.4.1. Accuracy Evaluation by Checkpoints

#### 3.4.2. Accuracy Evaluation by Overlap Zones

#### 3.5. Error Sensitivity Evaluation of Proposed Method

^{−12}to 1 × 10

^{−6}rapidly. However, as the random error increased from 0.001 m to 0.100 m, the components difference decreased slowly (from about 1 × 10

^{−6}to 1 × 10

^{−4}). From the last column of above table, the shift parameter difference is relevant with the scope of the random errors. Once the scope of random error is relatively small, the difference of the 3D shift parameter is low.

#### 3.6. Visualization of the Matched Point Cloud

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

LiDAR | Light Detection and Ranging |

OSM | Open Street Map |

ICP | Iterative Cloest Point |

RANSAC | Random Sample Consensus |

LMS | Least Median of Squares estimators |

LS | Least Square |

RMSE | root mean squared error |

## References

- Brenner, C. Building reconstruction from images and laser scanning. Int. J. Appl. Earth Obs. Geoinform.
**2005**, 6, 187–198. [Google Scholar] [CrossRef] - Shan, J.; Toth, C.K. Topographic Laser Scanning and Ranging: Principles and Processing; Taylor and Francis Group: Boca Raton, FL, USA, 2008; p. 590. [Google Scholar]
- Vosselman, G.; Maas, H.G. Airborne and Terrestrial Laser Scanning; Taylor and Francis Group: Boca Raton, FL, USA, 2010; p. 320. [Google Scholar]
- Scaioni, M. On the estimation of rigid-body transformation for TLS registration. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2012**, 39, 601–606. [Google Scholar] [CrossRef] - Besl, P.; McKay, N. A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell.
**1992**, 14, 239–256. [Google Scholar] [CrossRef] - Chen, Y.; Medioni, G. Object modelling by registration of multiple range images. Image Vis. Comput.
**1992**, 10, 145–155. [Google Scholar] [CrossRef] - Masuda, T.; Yokoya, N. A robust method for registration and segmentation of multiple range images. Comput. Vis. Image Underst.
**1995**, 61, 295–307. [Google Scholar] [CrossRef] - Cheng, L.; Tong, L.; Li, M.; Liu, Y. Semi-Automatic registration of airborne and terrestrial laser scanning data using building corner matching with boundaries as reliability check. Remote Sens.
**2013**, 5, 6260–6283. [Google Scholar] [CrossRef] - Zhong, L.; Tong, L.; Chen, Y.; Wang, Y.; Li, M.; Cheng, L. An automatic technique for registering airborne and terrestrial LiDAR data. In Proceedings of the 21st International Conference on Geoinformatics, Kaifeng, China, 20–22 June 2013.
- Wu, H.B.; Scaioni, M.; Li, H.Y.; Li, N.; Lu, M.F.; Liu, C. Feature-constrained registration of building point clouds acquired by terrestrial and airborne laser scanners. J. Appl. Remote Sens.
**2014**, 8, 083587. [Google Scholar] [CrossRef] - Li, X.; Guskov, I. Multiscale features for approximate alignment of point-based surfaces. In Proceedings of the Third Eurographics Symposium on Geometry Processing (SGP), Vienna, Austria, 4–6 July 2005; pp. 217–226.
- Alba, M.; Barazzetti, L.; Scaioni, M.; Remondino, F. Automatic registration of multiple laser scans using panoramic RGB and intensity images. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2011**, 33, 6. [Google Scholar] [CrossRef] - Weinmann, M.; Hinz, S.; Jutzi, B. Fast and automatic image-based registration of TLS data. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, S62–S70. [Google Scholar] [CrossRef] - Bae, K.; Lichti, D. A method for automated registration of unorganized point clouds. ISPRS J. Photogramm. Remote Sens.
**2008**, 63, 36–54. [Google Scholar] [CrossRef] - Crosilla, F.; Visintini, D.; Sepic, F. Reliable automatic classification and segmentation of laser point clouds by statistical analysis of surface curvature values. Appl. Geomat.
**2009**, 1, 17–30. [Google Scholar] [CrossRef] - Hansen, W.; Gross, H.; Thoennessen, U. Line-based registration of terrestrial and aerial LiDAR data. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2008**, 37 B3a, 161–166. [Google Scholar] - Cheng, L.; Wu, Y.; Tongm, L.; Chenm, Y.; Li, M.C. Hierarchical registration method for integration of airborne and vehicle LiDAR data. Remote Sens.
**2015**, 7, 13921–13944. [Google Scholar] [CrossRef] - He, B.; Lin, Z.; Li, Y.F. An automatic registration algorithm for the scattered point clouds based on the curvature feature. Opt. Laser Technol.
**2012**, 46, 53–60. [Google Scholar] [CrossRef] - Dold, C.; Brenner, C. Registration of terrestrial laser scanning data using planar patches and image data. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2006**, 36, 78–83. [Google Scholar] - Wu, H.B.; Li, H.Y.; Liu, C.; Yao, L.B. Feature-based registration between terrestrial and airborne point cloud assisted by topographic maps. J. Tongji Univ. (Nat. Sci.)
**2015**, 43, 462–467. (In Chinese) [Google Scholar] - Armenakis, C.; Gao, Y.; Sohn, G. Semi-automatic co-registration of photogrammetric and LiDAR data using buildings. In Proceedings of the 2012 XXII ISPRS Congress on ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Melbourne, Australia, 5 August–1 September 2012; Volume 1–3, pp. 13–18.
- Yu, F.; Xiao, J.X.; Funkhouser, T. Semantic Alignment of LiDAR Data at City Scale. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 8–10 June 2015; pp. 1722–1731.
- Fan, H.C.; Yao, W.; Fu, Q. Segmentation of sloped roofs from airborne LiDAR point clouds using ridge-based hierarchical decomposition. Remote Sens.
**2014**, 6, 3284–3301. [Google Scholar] - Zhang, X.; Zang, A.; Agam, G.; Chen, X. Learning from synthetic models for roof style classification in point clouds. In Proceedings of the 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Dallas, TX, USA, 4–7 November 2014; pp. 263–270.

**Figure 4.**Spatial distributions of the selected buildings. (

**a**) Selected buildings of first case; and (

**b**) selected buildings for the second case.

**Figure 5.**Typical roof types adopted in this paper. (

**a**) Type-1: flat roof; (

**b**) Type-2: slope roof; and (

**c**) Type-3: gabled roof.

Parameters | Method | Value |
---|---|---|

$\left(\Delta x,\Delta y,\Delta \mathrm{z}\right)$ | Proposed method | $\left(-0.840,-2.109,0.351\right)$ |

ICP | $\left(-1.286,-2.391,0.358\right)$ | |

LS | $\left(-0.827,-1.941,0.370\right)$ | |

R | Proposed method | $\left[\begin{array}{ccc}1.00231078858& 0.0151900835& 0.0002490458\\ 0.0042444902& 0.9990222473& 0.0006161759\\ -0.0001060228& 0.0000582398& 1.0000560232\end{array}\right]$ |

ICP | $\left[\begin{array}{ccc}0.9999526948& -0.0097251967& -0.0001690211\\ 0.0097250337& 0.9999522693& -0.0009395809\\ 0.0001781506& 0.0009378928& 0.9999995443\end{array}\right]$ | |

LS | $\left[\begin{array}{ccc}0.9998695268& -0.0138030552& 0.0083907681\\ 0.0137186482& 0.9998555364& 0.0100351809\\ -0.0085280720& -0.0099187616& 0.9999144414\end{array}\right]$ |

Parameters | Method | Value |
---|---|---|

$\left(\Delta x,\Delta y,\Delta \mathrm{z}\right)$ | Proposed method | $\left(-31.430,-7.947,-0.139\right)$ |

ICP | $\left(-23.635,41.723,0.104\right)$ | |

LS | $\left(-24.209,-0.156,0.353\right)$ | |

R | Proposed method | $\left[\begin{array}{ccc}0.9999034331& -0.0001935506& 0.0005516807\\ -0.0002691125& 0.9999946061& 0.0001537416\\ 0.0009099559& 0.0001823840& 0.9999401501\end{array}\right]$ |

ICP | $\left[\begin{array}{ccc}1& -0.0000000017& -0\\ 0.0000000042& 1& -0\\ 0.0000000791& 0.0000000393& 1\end{array}\right]$ | |

LS | $\left[\begin{array}{ccc}0.99999688564& 0.0021268808& 0.0013057830\\ -0.0021220269& 0.9999908760& -0.0037074001\\ -0.0013136563& 0.0037046177& 0.9999922750\end{array}\right]$ |

Index | Average | Minimum | Maximum |
---|---|---|---|

Proposed method | 0.964 | 0.195 | 1.628 |

ICP method | 2.190 | 0.046 | 4.690 |

LS method | 1.668 | 0.300 | 2.504 |

Class (m) | # Points | Percentage (%) | Cumulative Percentage (%) |
---|---|---|---|

0.00–0.05 | 4002 | 72.47 | 72.47 |

0.05–0.10 | 812 | 14.70 | 87.17 |

0.10–0.15 | 427 | 7.73 | 94.90 |

0.25–0.20 | 229 | 4.14 | 99.04 |

0.20–0.25 | 43 | 0.77 | 99.81 |

0.25–0.30 | 8 | 0.14 | 99.95 |

0.30–0.35 | 1 | 0.01 | 99.96 |

Class (m) | Points | Percentage (%) | Cumulative Percentage (%) |
---|---|---|---|

0.00–0.10 | 3763 | 56.71% | 56.71% |

0.10–0.20 | 1803 | 27.17% | 83.89% |

0.20–0.30 | 508 | 7.66% | 91.54% |

0.30–0.40 | 176 | 2.65% | 94.20% |

0.40–0.50 | 127 | 1.91% | 96.11% |

0.50–0.60 | 74 | 1.12% | 97.23% |

0.60–0.70 | 48 | 0.72% | 97.95% |

0.70–0.80 | 38 | 0.57% | 98.52% |

0.80–0.90 | 42 | 0.63% | 99.16% |

0.90–1.00 | 27 | 0.41% | 99.56% |

1.00–1.10 | 29 | 0.44% | 100.00% |

Scope of Random Error (m) | Rotation Matrix Difference | 3D Shift Parameter Difference (m) |
---|---|---|

[−0.000, 0.000] | $\left[\begin{array}{ccc}6E-13& 2E-12& 1E-12\\ -3E-12& -7E-13& -4E-12\\ -2E-13& 3E-13& 2E-13\end{array}\right]$ | $\left(\begin{array}{c}0.000\\ 0.000\\ 0.000\end{array}\right)$ |

[−0.001, 0.001] | $\left[\begin{array}{ccc}3E-6& -3E-6& 1E-6\\ -1E-5& -2E-6& -4E-6\\ -1E-6& 5E-7& 7E-7\end{array}\right]$ | $\left(\begin{array}{c}0.000\\ 0.000\\ 0.000\end{array}\right)$ |

[−0.025, 0.025] | $\left[\begin{array}{ccc}-1E-4& 3E-4& 1E-4\\ 9E-4& 4E-4& 1E-4\\ 8E-6& -1E-4& -4E-5\end{array}\right]$ | $\left(\begin{array}{c}-0.044\\ -0.011\\ -0.006\end{array}\right)$ |

[−0.050, 0.050] | $\left[\begin{array}{ccc}2E-4& 5E-4& -7E-4\\ 6E-4& -7E-4& -6E-4\\ 8E-6& -4E-4& -1E-5\end{array}\right]$ | $\left(\begin{array}{c}-0.015\\ -0.005\\ -0.006\end{array}\right)$ |

[−0.100, 0.100] | $\left[\begin{array}{ccc}1E-4& -2E-3& 5E-4\\ 3E-3& 1E-3& 8E-4\\ -4E-5& 4E-4& 1E-5\end{array}\right]$ | $\left(\begin{array}{c}0.190\\ 0.035\\ 0.049\end{array}\right)$ |

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**MDPI and ACS Style**

Wu, H.; Fan, H.
Registration of Airborne LiDAR Point Clouds by Matching the Linear Plane Features of Building Roof Facets. *Remote Sens.* **2016**, *8*, 447.
https://doi.org/10.3390/rs8060447

**AMA Style**

Wu H, Fan H.
Registration of Airborne LiDAR Point Clouds by Matching the Linear Plane Features of Building Roof Facets. *Remote Sensing*. 2016; 8(6):447.
https://doi.org/10.3390/rs8060447

**Chicago/Turabian Style**

Wu, Hangbin, and Hongchao Fan.
2016. "Registration of Airborne LiDAR Point Clouds by Matching the Linear Plane Features of Building Roof Facets" *Remote Sensing* 8, no. 6: 447.
https://doi.org/10.3390/rs8060447