# The Extraction of Street Curbs from Mobile Laser Scanning Data in Urban Areas

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

## 3. Method

#### 3.1. Classification

_{S}scales, for each point in the scene, we can obtain an eigenvector that describes the local dimension features of the point cloud around that feature point at multiple scales.

#### 3.2. Extraction Algorithm

#### 3.2.1. Intensity Filtering

- Compute the normalized intensity histogram. Let ${n}_{i}$ be the value of the i-th histogram bin, and let M be the number of road points; then, the normalized intensity (${p}_{i}$) is:$${p}_{i}=\frac{{n}_{i}}{M}$$
- The cumulative sum $P\left(k\right)$ is the probability that a LiDAR point belongs to the range $\left[0,k\right]$ and is calculated as:$$P\left(k\right)={{\displaystyle \sum}}_{i=0}^{k}{p}_{i}$$
- Compute the cumulative mean intensity $m\left(k\right)$ in the range $\left[0,k\right]$:$$m\left(k\right)={{\displaystyle \sum}}_{i=0}^{k}i{p}_{i}$$
- The global cumulative mean ${m}_{G}$ is the mean intensity of the whole histogram, where $L$ is the number of possible intensity values that the LiDAR can record:$${m}_{G}={{\displaystyle \sum}}_{i=0}^{L-1}i{p}_{i}$$
- Compute the global intensity variance ${\sigma}_{G}^{2}$:$${\sigma}_{G}^{2}={{\displaystyle \sum}}_{i=0}^{L-1}{\left(i-{m}_{G}\right)}^{2}{p}_{i}$$
- The local variance ${\sigma}_{L}^{2}$ is the variance of a specific intensity:$${\sigma}_{L}^{2}\text{}=\text{}\frac{{m}_{G}P\left(k\right)-m\left(k\right)}{P\left(k\right)\left(1-P\left(k\right)\right)}$$
- The threshold T is the value of k that maximizes ${\sigma}_{L}^{2}$:$$T=\underset{0\le k\le R-1}{\mathrm{argmax}}{\sigma}_{L}^{2}\left(k\right)$$

#### 3.2.2. Elevation Filtering

#### 3.2.3. Slope Filtering

_{slope}is the slope of two consecutive points, S

_{T}is a given slope threshold, and D

_{i}is the elevation difference of a point and its neighbor. D

_{min}and D

_{max}are the minimum and maximum thresholds, respectively.

_{slope}gets a slope greater than S

_{T}, it means that the point has reached a possible curb. If the height difference D

_{i}near the curb candidate is within the range of [D

_{min}, D

_{max}], the curb candidate will be marked as a curb; otherwise, it will be marked as a non-curb point.

#### 3.3. Curb Refinement

_{0}, P

_{1,}and P

_{2}. The reconnection process can be written as a problem of finding the three control points of the Bézier curve. Points P

_{0}and P

_{2}are the start and endpoints of the smooth area respectively.

^{2}P

_{0}+ 2(1 − t)tP

_{1}+ t

^{2}P

_{2}, t∈[0,1]

_{1}is in the middle of P

_{0}and P

_{2}. If the curb to be reconnected is not collinear, place P

_{1}at the intersection of the two-point tangent projection lines of P

_{0}and P

_{2}. The non-collinear area of the curb produces a parabolic segment.

#### 3.4. Curb Clustering

_{RBNN}= {{x

_{i}, y

_{i}, d

_{xi,yi}|d

_{xi,yi}≤ r}

## 4. Data Acquisition

## 5. Analysis and Discussion

#### 5.1. Visual Examples of the Obtained Results in Classification Process

#### 5.2. Visual Examples of the Obtained Results of Curb Extraction

#### 5.3. Quantitative Evaluation

#### 5.4. Comparison with Other Methods

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The classification algorithm of the scene elements based on their 3D geometrical properties across multiple scales.

**Figure 3.**Multiscale dimensionality classification [28].

**Figure 7.**Decision tree for preliminary geometric classification [33].

**Figure 8.**Schematic diagram of curb refinement on unconnected boundaries. (

**a**) The curb which connected by a straight area. (

**b**) The curb which connected by a curve fitting area.

**Figure 9.**KNN classification. (a), (b) and (c) means that the classification results of KNN are different under different K values.

**Figure 10.**The difference between KNN and RBNN in cluster ability. Subfigure (

**a**) shows the data set with 2 clusters and 1 outlier, (

**b**) shows 1-NN graph yielding 6 clusters, (

**c**) shows 2-NN graph yielding 1 cluster and subfigure (

**d**) displays RBNN graph yielding 2 clusters and 1 outlier.

**Figure 13.**The visual results of multiscale dimensionality criterion classification: (

**a**) Front-view images before classification; (

**b**) Front-view images after classification; (

**c**) Oblique view images before classification; (

**d**) Oblique view images after classification; (

**e**) Enlarged display of the classification results in (

**a**); (

**f**) Enlarged display of the classification results in (

**b**); (

**g**) Enlarged display of the classification results in (

**c**); (

**h**) Enlarged display of the classification results in (

**d**).

**Figure 14.**Extraction results of the vegetation covering the curbs. (

**a**,

**b**) Two detail views of study sites; (

**c**) Original point cloud; (

**d**) Street-level imagery of the studied area overlapped by segmented curbs; (

**e**) The result of curb extraction by proposed method.

**Figure 15.**Extraction results of curved curbs. (

**a**,

**b**) Two detail views of study sites; (

**c**–

**e**) Point cloud of the studied area overlapped by segmented curbs; (

**f**) The result of curb extraction by proposed method.

**Figure 16.**Extraction results of occlusion curbs. (

**a**,

**e**) Two detail views of study sites; (

**b**,

**f**) The result of curb extraction by proposed method; (

**c**,

**g**) Original point cloud; (

**d**,

**h**) Point cloud of the studied area overlapped by segmented curbs.

**Figure 17.**The extraction results compared with other methods. (

**a**,

**e**) Proposed method in our study sites; (

**b**) Yang’s extraction results in our study sites; (

**c**) Kumar’s extraction results in our study sites; (

**d**) Zhang’s extraction results in our study sites; (

**f**) Sun’s extraction results in our study sites.

Intensity | Medium | Object Classification |
---|---|---|

1–100 | Asphalt, concrete | Street, bridge |

100–300 | Paint coat | Road marking line |

>300 | Vegetation | Grass, tree |

Medium | Average Intensity | Max. | Min. | STD |
---|---|---|---|---|

Asphalt | 49.193 | 157 | 9 | 7.817983 |

Building | 70.120 | 255 | 3 | 52.15585 |

Grass | 57.954 | 116 | 1 | 10.68206 |

Concrete | 14.150 | 138 | 0 | 7.989562 |

Left Edges | Right Edges | |
---|---|---|

Length of reference (Manual extraction according to field survey) | 1691.2 | 1623.7 |

Minimum (m) | 0 | 0 |

Maximum (m) | 0.179 | 0.112 |

Mean (m) | 0.023 | 0.011 |

Median (m) | 0.015 | 0.009 |

Horizontal RMSE (m) | 0.142 | 0.060 |

Vertical RMSE (m) | 0.071 | 0.014 |

Buffer Width (m) | Completeness (%) | Correctness (%) | ||
---|---|---|---|---|

Left Edges | Right Edges | Left Edges | Right Edges | |

0.1 | 88.3 | 88.5 | 87.9 | 90.6 |

0.2 | 93.7 | 94.2 | 94.9 | 96.4 |

0.3 | 98.5 | 98.7 | 98.8 | 98.6 |

0.5 | 99.2 | 99.8 | 99.6 | 99.7 |

Kumar (2013) | Yang (2013) | Sun (2019) | Zhang (2018) | Proposed Method | |||
---|---|---|---|---|---|---|---|

Left Edges | Right Edges | Left Edges | Right Edges | ||||

Completeness (%) | 96.5 | 65.4 | 95.13 | 95.1 | 93 | 99.2 | 99.8 |

Correctness (%) | 100 | 63.8 | 98.09 | 95 | 92.5 | 99.6 | 99.7 |

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**MDPI and ACS Style**

Zhao, L.; Yan, L.; Meng, X.
The Extraction of Street Curbs from Mobile Laser Scanning Data in Urban Areas. *Remote Sens.* **2021**, *13*, 2407.
https://doi.org/10.3390/rs13122407

**AMA Style**

Zhao L, Yan L, Meng X.
The Extraction of Street Curbs from Mobile Laser Scanning Data in Urban Areas. *Remote Sensing*. 2021; 13(12):2407.
https://doi.org/10.3390/rs13122407

**Chicago/Turabian Style**

Zhao, Leyang, Li Yan, and Xiaolin Meng.
2021. "The Extraction of Street Curbs from Mobile Laser Scanning Data in Urban Areas" *Remote Sensing* 13, no. 12: 2407.
https://doi.org/10.3390/rs13122407