# Hierarchical Registration Method for Airborne and Vehicle LiDAR Point Cloud

^{1}

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## Abstract

**:**

## 1. Introduction

**Figure 1.**An example of “point city” with registered airborne and vehicle LiDAR points. (

**a**) Airborne LiDAR points; (

**b**) Vehicle LiDAR points; (

**c**) Building X in “point city” (blue points: airborne data, green points: vehicle data); (

**d**) Building Y in “point city” (blue points: airborne data, green points: vehicle data).

## 2. Method

#### 2.1. Coarse Registration with 3D Road Networks

#### 2.1.1. 3D Road Networks from Airborne LiDAR

#### 2.1.2. Coarse Registration with 3D Road Networks

_{i}, i = 0,1,2,…,μ} and PB = {PB

_{i}, i = 0,1,2,…,v}, with their corresponding road networks being RA = {RA

_{i}, i = 0,1,2,…,m}and RB = {RB

_{i}, i = 0,1,2,…,n}, respectively. The coarse registration of airborne and vehicle LiDAR with road networks is conducted as follows:

_{1}.

_{1}and R

_{1}to convert the road networks RB. The converted road network RC = {RC

_{i}, i = 0,1,2,…,n} is obtained.

_{1}and R

_{2}refer to road segments selected from road networks RA and RC, respectively. Starting from Endpoint NA

_{0}of Segment R

_{1}, draw 3D section planes at an interval θ. The section plane is drawn as a circle with its radius set according to the positioning precision of extracted road networks. If precise road networks are provided, a small radius is set and vice versa. As for each node point (e.g., NA

_{0}and NA

_{1}), if it intersects with the other road segments, record the reciprocal of the distance between the foot point and intersection point as the matching rate $pme=\{\begin{array}{c}1/{d}_{i},\text{\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}}{d}_{i}>0.1\\ 10,\text{\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}}{d}_{i}\le 0.1\end{array}$, in which ${d}_{i}$ represents the distance of nodes NA

_{i}and NB

_{i}. Otherwise, pme = 0. If several roads intersect with a section plane leading to pme

_{1}, pme

_{2},…, pme

_{n}, then the largest matching rate is regarded as its matching rate. As for road segments R

_{1}and R

_{2}, the matching rate is $lme={\displaystyle \sum _{i=1}^{k}\frac{1}{{d}_{i}}}$, where k is the number of nodes in R

_{1}. The final matching rate between two road networks is $tme={\displaystyle \sum _{j=1}^{m}lm{e}_{j}}$, where m is the number of road segments in RA.

_{i}, i = 0,1,2,…,v}.

_{i}, i = 0,1,2,…,m} and MC = {MC

_{i}, i = 0,1,2,…,n}, respectively. The least mean square (LMS) method is used to calculate the registration relationships between set MA and set MC. The acquired registration transformational matrices R and T are used to transform the LiDAR points. Finally, the coarse registration is finished.

**Figure 3.**Coarse registration of 3D road networks. (

**a**) Airborne road networks and intersections; (

**b**) Vehicle road networks and intersections; (

**c**) Matching rate of two single road segments from 3D road networks.

#### 2.2. Fine Registration with 3D Building Contours

#### 2.2.1. 2D Building Contours from Vehicle LiDAR

- (1)
- Elevation difference filtering.

- (2)
- Height value accumulation.

**Figure 4.**Theory of height value accumulation. (

**a**) A sample of building roofs; (

**b**) A sample of height value accumulation; (

**c**) Height histogram; (

**d**) Extraction of elevation range of building contours.

**Projecting points to 2D grids**.

_{i}and calculate the point number N

_{i}of each grid.

**Calculating the elevation range**.

_{min}, Z

_{max}) with the highest point and lowest point in the point cloud. Set a small interval as Z

_{s}and divide the elevation range, getting the set S = {S

_{j}, j = 1,2,…,n}, where n = (Z

_{max}−Z

_{min})/Z

_{s}.

**Height value accumulation**.

_{i}is within the interval S

_{j}; then the accumulation value Acc

_{j}is recalculated as Acc

_{j}= Acc

_{j}+ N

_{i}, and the height histogram is shown in Figure 4c.

**Obtaining the elevation range interval of buildings**.

- (3)
- 2D contour extraction.

#### 2.2.2. 2D Building Contours from Airborne LiDAR

#### 2.2.3. Extraction of 3D Building Contours

- (1)
- Projection and division of points.

- (2)
- Points clustering.

- (3)
- 3D contour fitting.

**Figure 5.**Contour segmentation using point elevation. (

**a**) A sample of a projected 2D contour; (

**b**) A sample of 3D contour segments.

#### 2.2.4. Fine Registration with 3D Building Contours

_{i}, i = 1,2,…,m} and LB = { LB

_{i}, i = 1,2,…,n}, respectively. The fine registration with building contours are as follows:

**(A) Searching for conjugate contours**

_{1}, LA

_{2}, LB

_{1}, and LB

_{2}. The following conditions should be met: (a) $\{\begin{array}{c}lAng\le Thr{e}_{ang}\\ lDist\le Thr{e}_{dist}\\ lDif\le Thr{e}_{dif}\end{array}$, where $lAng=\mathrm{arccos}(\frac{\overrightarrow{{l}_{1}}\xb7\overrightarrow{{l}_{2}}}{\left|\overrightarrow{{l}_{1}}\right|\xb7\left|\overrightarrow{{l}_{2}}\right|})$ is the angle between the straight lines in which the two contours are located, $lDist=\text{|}\frac{(\overrightarrow{{l}_{1}}\times \overrightarrow{{l}_{2}})\xb7\overrightarrow{{P}_{1}{P}_{2}}}{|\overrightarrow{{l}_{1}}\times \overrightarrow{{l}_{2}}|}\text{|}$ is the distance between the straight lines in which the two contours are located, $lDif=|\text{|}\overrightarrow{{l}_{1}}\text{|}-\text{|}\overrightarrow{{l}_{2}}\text{|}|$ is the length difference of the two contours. $\overrightarrow{{l}_{1}}$ and $\overrightarrow{{l}_{2}}$ refer to the directions of the two contours. (b) LA

_{1}and LB

_{1}are neither parallel nor coplanar, nor are LA

_{2}and LB

_{2}. (c) The angles and distances between LA

_{1}and LB

_{1}equal those between LA

_{1}and LB

_{1}.

^{T}= I. In this study, spatial vectors are first obtained with the 3D building contours. Assuming that the unit vectors corresponding to two pairs of conjugate contours are v and w, we get equation:

_{x}, b

_{y}, b

_{z}) are the vector components of b, and (L

_{x}, L

_{y}, L

_{z}) are those of L. Then the parameter vector x can be approximated by using the following linear least squares estimation.

_{x}, d

_{y}, d

_{z}as the variables.

**(B) Fine registration with reliable conjugate contours**

- (1)
- Selection of reliable conjugate contours.

**Selecting contours by angle**.

_{i}, i = 0,1,2,…,k}. Group the angles in α and calculate the total number of conjugate contours in each group. If the group with the largest number of contours reaches a certain percent of the total contours, the contours in the group are considered as reliable ones. Otherwise, join other groups of segment pairs until the proportion of matched pairs is more than a certain threshold. Here the percent threshold is set according to the overall precision of extracted building contours.

**Selecting contours by distance**.

- (2)
- Fine registration.

#### 2.3. Summary of Threshold Parameters

_{min}/5, where W

_{min}= 5 m is the minimum width of road) for obtaining 3D road networks.

_{dif}) is set to 5 m according to the width of a lane.

Method | Parameter | Scale | Setting Basis | |
---|---|---|---|---|

Coarse registration with road networks | Extraction of three dimensional (3D) road networks | Radius of small circle | 1 m·W/4 | Calculation |

Determination of matching rate | Interval of 3D section planes | 1 m | Empiric | |

The radius of section plane | 60 m | Data source | ||

Fine registration with building contours | Extraction of two dimensional (2D) building contours from vehicle LiDAR | 2D regular grid | 1 m × 1 m | Data source |

Elevation difference | 15 m | Data source | ||

Elevation interval Z_{s} | 4–5 times the average point spacing | Empiric | ||

Extraction of 3D building contours | Elevation difference | 2 × D × I | Calculation | |

Angle difference | 20° | Empiric | ||

Fine registration | Angle threshold Thre_{ang} | 5° | Empiric | |

Distance threshold Thre_{dist} | 5 m (width of a lane) | Calculation | ||

Length difference Thre_{dif} | 10 m | Empiric |

## 3. Experiments and Analysis

#### 3.1. Experimental Data

**Figure 7.**Experimental data. (

**a**) Airborne LiDAR data; (

**b**) Vehicle LiDAR data; (

**c**) Vehicle trajectory path.

#### 3.2. Coarse Registration with 3D Road Networks

**Figure 8.**Coarse registration with road networks. (

**a**) Airborne road network (black lines); (

**b**) Vehicle road network (red lines); (

**c**) Registered road networks.

#### 3.3. Fine Registration with 3D Building Contours

#### 3.3.1. Extraction of 3D Building Contours

**Figure 9.**Building contour extraction of Area A. (

**a**) Vehicle LiDAR data; (

**b**) Elevation difference filtering; (

**c**) Height value accumulation; (

**d**) Vehicle building contours; (

**e**) Airborne LiDAR data; (

**f**) RIMM for buildings; (

**g**) Airborne building contours.

#### 3.3.2. Fine Registration with 3D Building Contours

**Figure 10.**Fine registration with building contours in Area A. (

**a**) Result of coarse registration; (

**b**) Result after using the conjugate contours; (

**c**) Result of fine registration by only using conjugate contours in (

**b**), and all airborne contours (black lines) are retained for visualization.

#### 3.4 Result and Analysis

#### 3.4.1 Visual Evaluation

**Figure 11.**Registration result of Area A using the proposed method. (

**a**) Registration result in Area A; (

**b**) Details of VA; (

**c**) Details of VB; (

**d**) Details of VC; (

**e**) Details of VD.

#### 3.4.2 Evaluation on Horizontal Accuracy with Building Contours

**Figure 12.**Evaluation on horizontal accuracy using building contours of Area A (left) and Area B (right). (

**a**) Result of coarse registration; (

**b**) Result by using the conjugate contours; (

**c**) Result of fine registration (all airborne contours are retained for visualization); (

**d**) ICP refined result.

Method | Transect Distance (m) | Line Angle (°) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Average | Max | Average | Max | ||||||||||

A | B | A | B | A | B | A | B | ||||||

Coarse registration | 17.44 | 7.43 | 21.03 | 12.68 | 0.95 | 0.88 | 1.7 | 2.1 | |||||

Searching result | 2.53 | 1.59 | 4.30 | 3.79 | 0.82 | 0.69 | 1.6 | 1.3 | |||||

Fine registration | 0.73 | 0.63 | 1.90 | 1.73 | 0.32 | 0.48 | 1.2 | 1.1 | |||||

ICP refined result | 1.52 | 5.27 | 2.55 | 11.23 | 0.47 | 0.72 | 1.5 | 1.9 |

#### 3.4.3. Evaluation on Vertical Accuracy with Common Ground Points

**Figure 13.**Location of common ground points. (

**a**) Common ground points of Area A; (

**b**) Common ground points of Area B.

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

A/B | A/B | A/B | ||||

Coarse registration | 0.92/1.08 | 1.17/1.33 | 0.97/0.84 | |||

Searching result | 0.46/0.59 | 0.63/0.92 | 0.50/0.68 | |||

Fine registration | 0.39/0.43 | 0.50/0.75 | 0.42/0.36 | |||

ICP result | 0.37/0.46 | 0.61/0.72 | 0.28/0.21 |

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Cheng, L.; Wu, Y.; Tong, L.; Chen, Y.; Li, M.
Hierarchical Registration Method for Airborne and Vehicle LiDAR Point Cloud. *Remote Sens.* **2015**, *7*, 13921-13944.
https://doi.org/10.3390/rs71013921

**AMA Style**

Cheng L, Wu Y, Tong L, Chen Y, Li M.
Hierarchical Registration Method for Airborne and Vehicle LiDAR Point Cloud. *Remote Sensing*. 2015; 7(10):13921-13944.
https://doi.org/10.3390/rs71013921

**Chicago/Turabian Style**

Cheng, Liang, Yang Wu, Lihua Tong, Yanming Chen, and Manchun Li.
2015. "Hierarchical Registration Method for Airborne and Vehicle LiDAR Point Cloud" *Remote Sensing* 7, no. 10: 13921-13944.
https://doi.org/10.3390/rs71013921