# Shiftable Leading Point Method for High Accuracy Registration of Airborne and Terrestrial LiDAR Data

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## Abstract

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## 1. Introduction

## 2. Related Work

#### 2.1. Review on Registration of LiDAR Data from the Same Platform

#### 2.1.1. Registration of Multi-Scan Terrestrial LiDAR Data

#### 2.1.2. Registration of Airborne LiDAR Strips

#### 2.2. Review of the Registration of Airborne and Terrestrial LiDAR Data

## 3. Method

#### 3.1. Extraction of Building Corners from Airborne and Terrestrial LiDAR Data

**Figure 1.**Building corner extraction from airborne and terrestrial LiDAR data. (

**a**) Extracted building corners (red points) and contours (black lines) from airborne LiDAR data; (

**b**) extracted building corners (green points) and contours (black lines) from terrestrial LiDAR data.

#### 3.2. Initial Matching of Terrestrial and Airborne Corners

_{0}, y

_{0}, z

_{0}are the transition elements along axis X, axis Y and axis Z.

_{i}, i = 0, 1, 2, …, u} and B = {B

_{i}, i = 0, 1, 2, …, v}, respectively. Then, the initial matching of corners is conducted as follows.

- (1)
- Select three points from point set A and B, respectively; then, compute translation matrix T and rotation matrix R with the six-parameter model.
- (2)
- All points in B are converted using translation matrix T and rotation matrix R, to obtain C = {C
_{i}, i = 0, 1, 2, …, v}. Seek the closest point C_{closet}in C for each point A_{i}in A. If the distance from A_{i}to C_{closet}is smaller than the determined distance threshold, the two points are considered to be matched points. If point C_{closet}is the closest point for both point A_{1}and point A_{2}in A, compare distance A_{1}C_{cloest}and distance A_{2}C_{cloest}; the set of points that are closest together are considered to be successfully matched. Record the successfully matched point pairs in this transformation relationship as MA = {MA_{i}, i = 1, 2, …, n} and MB = {MB_{i}, i = 1, 2, …, n}. - (3)
- Repeat a, b and select the transformation matrix R
_{i}and T_{i}with the greatest number of matching pairs. - (4)
- For each group of R
_{i}and T_{i}, calculate the distance between the corresponding elements in MA and MB. The transformation relationship with the smallest distance is regarded as the best. - (5)
- The initial matching of corners is obtained after all points in B have been converted by resorting to the best transformation matrix R
_{1}and T_{1}(Figure 2; green circles are terrestrial corners, and black triangles are airborne corners).

**Figure 2.**Initial matching results of airborne corners (black triangles) and terrestrial corners (green circles).

#### 3.3. Shiftable Leading Point Method for Improvement of the Geometric Accuracy of Registration

**Figure 3.**Basis for the shiftable leading point method. (

**a**) Example of extracted airborne corners (green pentagons refer to true airborne corners; black triangles refer to airborne corners; red straight lines refer to error vectors, which are amplified 10 times); (

**b**) example of unevenly distributed corners (green pentagons refer to true airborne corners; black triangles refer to airborne corners).

**Figure 4.**A shiftable leading point method (airborne corners: red circles; terrestrial corners: green circles; leading point: yellow triangles). (

**a**) Original airborne and terrestrial corners; (

**b**) airborne and terrestrial corners after registration; (

**c**) generated leading points from airborne corners; (

**d**) shift of a leading point; (

**e**) registration of leading points and terrestrial corners; (

**f**) transformation of airborne corners with the registration matrix in (e); (

**g**) change of the geometric error of leading points and terrestrial corners with iterations.

_{i}, i = 0, 1, 2, …, n} and the terrestrial corners as U = {U

_{i}, i = 0, 1, 2, …, n}. The shiftable leading point method operates as follows.

- (1)
- Register P and U using the least squares algorithm, and obtain a rotation matrix R and a translation matrix T, with which the airborne corners P are transformed as Q = {Q
_{i}, i = 0, 1, 2, …, n} (there is no leading point shift in the first iteration). - (2)
- Calculate the three-dimensional spatial distance between conjugate points among point set P and its corresponding point set U, and obtain a one-dimensional distance matrix D = {D(U
_{i},Q_{i}), i = 0, 1, 2, … n}. Calculate the overall position error of conjugate points $Err={{\displaystyle \sum}}_{i=1}^{n}{D}_{i}$; the iteration is stopped if Err_{current }> thresh × Err_{pre}, where Err_{current}is the current position error, thre is a threshold and Err_{pre}is the former position error. - (3)
- Seek the maximum distance in D and find its corresponding points U
_{max}and Q_{max}in point sets U and Q, respectively. Shift leading point Q_{max}to the corresponding terrestrial corner U_{max}. Point set P is modified as P = {P_{1}, P_{2}, …, P_{max}, …, P_{n}}. - (4)
- Repeat procedures (1)–(3) until the iteration stops during Procedure (2). The final transformation matrix is used to register airborne and terrestrial LiDAR points, thus finishing the registration procedure.

## 4. Experiment and Analysis

#### 4.1. Experimental Data

**Figure 5.**Experimental data. (

**a**) Airborne LiDAR data; (

**b**) terrestrial LiDAR data (collected by nine terrestrial survey stations manually registered based on targets).

#### 4.2. Evaluation of Building Contour and Corner Extraction

Actual Number | Correct Number | Incorrect Number | Missing Number | Correctness | Completeness | |
---|---|---|---|---|---|---|

Airborne contours | 99 | 79 | 4 | 20 | 95.2% | 79.8% |

Terrestrial contours | 36 | 33 | 0 | 3 | 100% | 91.7% |

**Figure 6.**Building corner extraction from airborne and terrestrial LiDAR data. (

**a**) Evaluation of extracted building contours from airborne LiDAR data; (

**b**) extracted airborne corners; (

**c**) evaluation of extracted building contours from terrestrial LiDAR data; (

**d**) initial registration results of airborne corners and terrestrial corners.

Average Error (m) | Max Error (m) | RMSE (m) | |
---|---|---|---|

Airborne corners | 0.91 | 2.15 | 1.08 |

Terrestrial corners | 0.13 | 0.19 | 0.14 |

#### 4.3. Change of Error between Leading and Terrestrial Point Pairs during Iterations

**Figure 7.**Geometric error of leading points and referenced points. (

**a**) Geometric error of leading points (black triangles) and referenced points (green circles) by using FC (fixed corner, without the shiftable leading point) (red lines represent error vectors, which are amplified 10 times); (

**b**) geometric error of leading points (black triangles) and referenced points (green circles) by using RC (RANSAC; removed points in the box); (

**c**) geometric error of leading points and referenced points by using SC (shifted corner, with the shiftable leading point), after the 10th iteration; (

**d**) change of the geometric error of leading points and referenced points with iterations by using SC.

Average Error (m) | Max Error (m) | RMSE (m) | |
---|---|---|---|

FC | 0.93 | 1.94 | 1.06 |

RC | 0.61 | 1.30 | 0.41 |

SC | 0.31 | 0.51 | 0.34 |

#### 4.4. Evaluation of Geometric Accuracy of LiDAR Data Registration

#### 4.4.1. Visual Check

**Figure 8.**Comparison of the registration of airborne and terrestrial LiDAR data. (

**a**) Registration results by using SC; (

**b**–

**e**) differences of Labels A, B, C and D, respectively.

#### 4.4.2. Evaluation with Common Sections

**Figure 9.**Evaluation with common sections. (

**a**) Positions of the sections; (

**b**) section A by using FC; (

**c**) section A by using RC; (

**d**) section A by using SC; (

**e**) section B by using FC; (

**f**) section B by using RC; (

**g**) section B by using SC.

#### 4.4.3. Quantitative Analysis using Common Building Contours

**Figure 10.**Geometric precision evaluation by using common building boundaries. (

**a**) The registered boundaries from airborne (red) and terrestrial (green) LiDAR data by using FC; (

**b**) the registered boundaries from airborne and terrestrial LiDAR data by using RC; (

**c**) the registered boundaries from airborne and terrestrial LiDAR data by using SC; (

**d**) length of transect lines.

**Table 4.**Evaluation of the geometric precision of LiDAR data registration using building boundaries.

Transect Distance (m) | Angle (Degree) | |||||
---|---|---|---|---|---|---|

Average | Max | RMSE | Average | Max | RMSE | |

FC | 0.81 | 1.73 | 0.95 | 0.75 | 2.80 | 0.95 |

RC | 0.49 | 0.96 | 0.38 | 0.71 | 1.89 | 0.60 |

SC | 0.31 | 0.89 | 0.37 | 0.44 | 1.30 | 0.53 |

#### 4.4.4. Quantitative Analysis using Common Ground Points

**Table 5.**Evaluation of the geometric precision of LiDAR data registration using common ground points.

Average | Max | RMSE | |
---|---|---|---|

FC | 0.51 | 0.82 | 0.56 |

RC | 0.43 | 0.62 | 0.38 |

SC | 0.26 | 0.46 | 0.30 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Cheng, L.; Tong, L.; Wu, Y.; Chen, Y.; Li, M.
Shiftable Leading Point Method for High Accuracy Registration of Airborne and Terrestrial LiDAR Data. *Remote Sens.* **2015**, *7*, 1915-1936.
https://doi.org/10.3390/rs70201915

**AMA Style**

Cheng L, Tong L, Wu Y, Chen Y, Li M.
Shiftable Leading Point Method for High Accuracy Registration of Airborne and Terrestrial LiDAR Data. *Remote Sensing*. 2015; 7(2):1915-1936.
https://doi.org/10.3390/rs70201915

**Chicago/Turabian Style**

Cheng, Liang, Lihua Tong, Yang Wu, Yanming Chen, and Manchun Li.
2015. "Shiftable Leading Point Method for High Accuracy Registration of Airborne and Terrestrial LiDAR Data" *Remote Sensing* 7, no. 2: 1915-1936.
https://doi.org/10.3390/rs70201915