# Extraction of Urban Road Boundary Points from Mobile Laser Scanning Data Based on Cuboid Voxel

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Relevant Works

## 3. Methodology

#### 3.1. Point Cloud Voxelization

_{min}, X

_{max}], [Y

_{min}, Y

_{max}], and [Z

_{min}, Z

_{max}], respectively. Therein, (X

_{max}, Y

_{max}, Z

_{max}) and (X

_{min}, Y

_{min}, Z

_{min}) denote the maximum and minimum values of the point cloud in the three directions, respectively. The number of voxels in each direction of the X-, Y-, and Z-axes obtained by point cloud voxelization is determined as follows:

_{i}, C

_{i}, and H

_{i}, respectively. For fast indexing, the row, column, and vertical coding of each voxel is weighted and summed to reduce the index coding from 3D to 1D. The coding varies from voxel to voxel, and the coding of the voxel where points within the same voxel are located remains the same.

_{i}, Y

_{i}, Z

_{i}) represents the coordinates of the current point.

#### 3.2. Extracting Candidate Road Curb Points

#### 3.2.1. Normal Vector of Voxels

_{1}, λ

_{2}, and λ

_{3}) of the matrix M were obtained by singular value decomposition, satisfying λ

_{1}≥ λ

_{2}≥ λ

_{3}≥ 0. The eigenvector corresponding to the minimum eigenvalue λ

_{3}was the normal vector of the voxel. Then, the included angle α between the normal vector of the voxel and the Z-axis was calculated. If α > Th_a, then the current voxel was an initial candidate road curb voxel where Th_a is the threshold of the included angle.

_{i}is the coordinates of a point in the current voxel, k is the quantity of points contained in the current voxel, and $\overline{p}$ represents the centroid of all points in the current voxel.

#### 3.2.2. Linear Dimension of Voxels

_{1}, λ

_{2}, and λ

_{3}) solved in Section 3.2.1. Unnikrishnan et al. [39] normalized the three eigenvalues to obtain the three-dimensional features α

_{1D}, α

_{2D}, and α

_{3D}that could quantitatively describe the spatial distribution pattern of point clouds.

_{1D}≈ 1, α

_{2D}≈ 0, and α

_{3D}≈ 0. When the point cloud is planarly distributed, its dimensional features are α

_{1D}≈ 0, α

_{2D}≈ 1, and α

_{3D}≈ 0. When the point cloud is scattered, its dimensional features are α

_{1D}≈ 0, α

_{2D}≈ 0, and α

_{3D}≈ 1. Given that the points in the curb voxel were linearly distributed, the voxels meeting Formula (5) in the initial candidate voxels were reserved as candidate voxels where Th_e is the threshold for the linear dimension.

#### 3.3. Determining the Final Curb Point

#### 3.3.1. Reflection Intensity Constraint of Surface Features

#### 3.3.2. Noise Point Elimination

## 4. Experimental Results and Analysis

#### 4.1. Experimental Data

_{1}between the left and right adjacent points on the same scanning line was 0.06 m, the distance d

_{2}between the front and rear adjacent points was 0.06 m, and the height difference h between the points at the curb was 0.01 m. The diagrams of d

_{1}, d

_{2}, and h are shown in Figure 10. Data 2, Data 3, and Data 4 are from an open-source IQmulus & TerraMobilita competition dataset, where roads have their widths changed and contain curved roads and different types of intersections. Three sets of data contain a total of 12, 20, and 30 million points, with a total length of about 210, 420, and 620 m, respectively, and an average slope of about 2%. After manual measurement, the average distance d

_{1}between left and right adjacent points on the same scanning line was 0.006 m, the distance d

_{2}between front and rear adjacent points was 0.06 m, and the height difference h between points at the curb was 0.01 m. In comparison with Data 1, the latter three point cloud data had a higher point cloud density. Four sets of data were urban internal road environments, including high-rise buildings, border trees, fences, streetlamps, and other urban ancillary facilities. The data were stored in ply format and contained attribute information of X, Y, Z, and intensity points.

#### 4.2. Parameter Setting

#### 4.3. Experimental Results

#### 4.4. Quantitative Results

#### 4.5. Comparative Analysis of Different Methods

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Voxelization using different types of voxel at the road curb: (

**a**) original point cloud; (

**b**) cubic voxelization; (

**c**) cuboid voxelization.

**Figure 4.**Schematic of point distribution in the voxels of different surface features: (

**a**) Schematic of the roadway voxel; (

**b**) Schematic of the road curb voxel. Notes: The red dotted squares represent the planes obtained by plane fitting with the internal points in each voxel.

**Figure 5.**Voxelization results of different ground object point using cuboid voxels in this study: (

**a**) Roadway point cloud voxelization; (

**b**) Road curb point cloud voxelization. Notes: The red box represents that the location is in a road curb voxel, and the points within it are road curb points.

**Figure 6.**Ground points obtained by CSF method. Notes: The black rectangular area represents the bottom of street trees amd the blue rectangular area is the bottom of fences.

**Figure 14.**Extraction results of road curb points by the proposed method: (

**a**) Road curb points extracted in Data 1; (

**b**) Road curb points extracted in Data 2; (

**c**) Road curb points extracted in Data 3; (

**d**) Road curb points extracted in Data 4.

**Figure 15.**Schematic of fractures in the curb point extraction result: (

**a**) Sparsely distributed curb points; (

**b**) Vehicle occlusion.

Parameter | Parameter Value |
---|---|

Voxel sizes step_x, step_y, and step_z/m | 0.3, 0.3, 0.02 |

Included angle threshold Th_a/° | 60 |

Linear dimension threshold Th_e | 0.1 |

Intensity range Th_ i | [−12, −10] |

Searching radius Th_epx | 0.3 |

Point number threshold in the cluster Th_Minpts | 6 |

Dataset | Left | Right | Total | |||
---|---|---|---|---|---|---|

LS/m | LD/m | RS/m | RD/m | TS/m | TD/m | |

Data 1 | 674.2 | 534.7 | 580.5 | 469.4 | 1254.7 | 1004.1 |

Data 2 | 204.9 | 162.5 | 216.8 | 177.3 | 421.7 | 339.8 |

Data 3 | 433.3 | 304.9 | 391.9 | 370.3 | 825.2 | 675.2 |

Data 4 | 661.6 | 524.7 | 581.2 | 478.9 | 1242.8 | 1003.6 |

Dataset | TP/m | FP/m | FN/m | Precision/% | Recall/% | Quality/% |
---|---|---|---|---|---|---|

Data 1 | 1004.1 | 27.8 | 250.6 | 97.3 | 80.0 | 78.3 |

Data 2 | 339.8 | 24.3 | 81.9 | 93.3 | 80.6 | 76.2 |

Data 3 | 675.2 | 34.4 | 150.0 | 95.2 | 81.8 | 78.5 |

Data 4 | 1003.6 | 94.6 | 239.2 | 91.4 | 80.8 | 75.0 |

**Table 4.**Comparative analysis of the results of different algorithms for road curb extraction based on data in Figure 9b.

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Dong, X.; Liu, G.
Extraction of Urban Road Boundary Points from Mobile Laser Scanning Data Based on Cuboid Voxel. *ISPRS Int. J. Geo-Inf.* **2023**, *12*, 426.
https://doi.org/10.3390/ijgi12100426

**AMA Style**

Wang J, Dong X, Liu G.
Extraction of Urban Road Boundary Points from Mobile Laser Scanning Data Based on Cuboid Voxel. *ISPRS International Journal of Geo-Information*. 2023; 12(10):426.
https://doi.org/10.3390/ijgi12100426

**Chicago/Turabian Style**

Wang, Jingxue, Xiao Dong, and Guangwei Liu.
2023. "Extraction of Urban Road Boundary Points from Mobile Laser Scanning Data Based on Cuboid Voxel" *ISPRS International Journal of Geo-Information* 12, no. 10: 426.
https://doi.org/10.3390/ijgi12100426