# Supervised Classification of Power Lines from Airborne LiDAR Data in Urban Areas

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

^{2}) and lower part area (which is referred to as LP Dataset, 800 × 100 m

^{2}) from a large LiDAR scene that covers the study site (Figure 2). The power lines in these datasets are urban distribution lines. The point density is ~3.4 points/m

^{2}. For both UL Dataset and LP Dataset, ground truth is available in the form of a manual point-wise labelling of the power line class. An overview of the number of labelled 3D points for power lines is given in Table 1.

#### 2.2. Power Line Candidate Filtering

#### 2.2.1. Ground Points and Non-Ground Points Filtering

#### 2.2.2. Power Line Corridor Direction Construction

#### 2.3. Local Neighborhood Selection

#### 2.3.1. Neighborhood Type Determination

- a spherical neighborhood is formed by all 3D points within a sphere around point P, which is parameterized with a fixed radius,
- a vertical cylindrical neighborhood is formed by all 3D points within a vertical cylindrical whose axis vertically passes through point P and whose radius is fixed,
- a k nearest neighborhood is formed by the $\mathrm{k}\in \mathrm{N}$ nearest neighbors of considered point P, the k is its parameter, and
- a slant cylindrical neighborhood is formed by all 3D points with a slant cylindrical whose radius is fixed and whose axis passes through considered point P along with the direction of power line corridor.

#### 2.3.2. Neighborhood Scale Selection

#### 2.4. Spatial Structural Feature Extraction

#### 2.5. SVM Classification

#### 2.6. Experiments

## 3. Results

#### 3.1. Single-Scale and Multi-Scale Neighborhoods

#### 3.2. Different Neighborhood Types

## 4. Discussion

^{2}) of our LiDAR data is relatively low relative to the ones reported in published research, for which some can reach up to 150 points/m

^{2}[7]. Despite of these challenges, our method can still achieve high classification accuracy.

#### 4.1. Influence of Power Line Corridor Direction

#### 4.2. Benefit of Power Line Neighborhood Selection

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Visualization of the experimental datasets. (

**a**) the whole large urban LiDAR scene around the campus of the University of Hawaii; (

**b**) the UL (upper left area) Dataset from the blue rectangle in (

**a**); (

**c**) the LP (lower part area) Dataset from the red rectangle in (

**a**). The linear objects of red to orange points are power lines.

**Figure 3.**Visualization of power line candidate filtering process. (

**a**) raw LiDAR point cloud; (

**b**) non-ground points; (

**c**) the detected power line 2D corridor direction in XOY plane: the green lines are extracted by Hough transform and the red line is the power line corridor direction constructed by RANSAC algorithm; (

**d**) power line candidate points filtered by power line corridor direction: the red points are true power line points, the blue ones are the power line candidate filtering results.

**Figure 4.**Visualization of the four different neighborhood types. The black dashed arrow line represents power line corridor direction; the green sphere is the spherical neighborhood of p1 (radius is 5 m); the blue cylinder is the vertical cylindrical neighborhood of p1 (radius is 3 m); blue ‘o’ points are k nearest points of p2 (k = 15); the yellow sphere is k nearest neighborhood of p2 (contains the 15 ‘o’ points); the red cylinder is slant cylindrical neighborhood of p2 (radius is 3 m, height is 12 m, symmetry axis is the corridor direction).

**Figure 5.**Visualization of the experiment results for power line classification of UL Dataset. (

**a**) is the whole area results in XOY plane involving the raw LiDAR point cloud, power line candidate points, true power line points and classified power line points; (

**b**) is the local magnification of the blue dashed ellipse area in (

**a**) in power line corridor direction; (

**c**) is the whole area results in 3D view; (

**d**) is the local magnification of the blue dashed ellipse area in (

**c**).

**Figure 6.**Visualization of the experiment results for power line classification of LP Dataset. (

**a**) is the whole area results in XOY plane involving the raw LiDAR point cloud, power line candidate points, true power line points and classified power line points; (

**b**) is the local magnification of the blue dashed ellipse area in (

**a**) in power line corridor direction; (

**c**) is the whole area results in 3D view; (

**d**) is the local magnification of the blue dashed ellipse area in (

**c**).

Class | UL Dataset | LP Dataset |
---|---|---|

Ground | 48,070 | 136,891 |

Building | 24,348 | 48,574 |

Vegetation | 19,532 | 73,523 |

Power line | 1519 | 6858 |

Others (billboard, etc.) | 4475 | 2516 |

Total | 97,944 | 268,362 |

Feature Class | Formal Definition | Computing Method |
---|---|---|

Geometric features | Normalized eigenvalues | ${\mathrm{e}}_{i}=\frac{{\lambda}_{i}}{{{\displaystyle \sum}}^{\text{}}\lambda}\text{}i\in \left\{1,2,3\right\}$ |

Linearity | ${L}_{\lambda}=\frac{{\lambda}_{1}-{\lambda}_{2}}{{\lambda}_{1}}$ | |

Planarity | ${P}_{\lambda}=\frac{{\lambda}_{2}-{\lambda}_{3}}{{\lambda}_{1}}$ | |

Scattering | ${S}_{\lambda}=\frac{{\lambda}_{3}}{{\lambda}_{1}}$ | |

Distributional features | Omnivariance | ${O}_{\lambda}=\sqrt[3]{{\mathsf{\lambda}}_{1}{\mathsf{\lambda}}_{2}{\mathsf{\lambda}}_{3}}$ |

Sum | ${{\displaystyle \sum}}^{\text{}}\lambda ={\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}$ | |

Changing of curvature | ${C}_{\lambda}=\frac{{\lambda}_{3}}{{\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}}$ | |

Radius of local neighborhood | ${\gamma}_{\mathrm{p}}=dist\left({p}_{0}-{p}_{max}\right)$ | |

Density of point set $\mathcal{P}$ | ${D}_{P}=\raisebox{1ex}{$num\left({p}_{i}\right)$}\!\left/ \!\raisebox{-1ex}{$\frac{4}{3}\pi {r}_{P}^{3}$}\right.$ | |

Delta of point set $\mathcal{P}$ in Z axis | ${\mathsf{\Delta}}_{Z}=ma{x}_{Z}-mi{n}_{Z}$ |

**Table 3.**$\mathit{PREC}$ , $\mathit{REC}$, $\mathit{QUA}$ (in %) and $T$ (in s) for different neighborhood scales and two datasets.

Scale | UL Dataset | LP Dataset | ||||||
---|---|---|---|---|---|---|---|---|

$\mathit{PREC}$ | $\mathit{REC}$ | $\mathit{QUA}$ | $\mathit{T}$ | $\mathit{PREC}$ | $\mathit{REC}$ | $\mathit{QUA}$ | $\mathit{T}$ | |

${N}_{1\mathrm{m}}$ | 74.12 | 41.74 | 36.23 | 126 | 79.17 | 58.59 | 50.76 | 1029 |

${N}_{3\mathrm{m}}$ | 82.28 | 68.80 | 59.92 | 82 | 93.59 | 63.88 | 61.20 | 935 |

${N}_{5\mathrm{m}}$ | 95.19 | 85.91 | 82.33 | 48 | 96.55 | 75.85 | 73.85 | 921 |

${N}_{7\mathrm{m}}$ | 95.98 | 91.11 | 87.76 | 44 | 91.99 | 89.59 | 83.11 | 882 |

${N}_{9\mathrm{m}}$ | 94.38 | 91.84 | 87.08 | 52 | 93.06 | 91.08 | 85.28 | 942 |

${N}_{11\mathrm{m}}$ | 94.65 | 89.73 | 85.40 | 64 | 95.92 | 82.52 | 79.72 | 886 |

${N}_{all}$ | 97.89 | 94.73 | 92.84 | 131 | 97.98 | 96.85 | 94.95 | 1220 |

**Table 4.**$\mathit{PREC}$ , $\mathit{REC}$, $\mathit{QUA}$ (in %) and $T$ (in s) for different neighborhood types and two datasets.

Type | UL Dataset | LP Dataset | ||||||
---|---|---|---|---|---|---|---|---|

$\mathit{PREC}$ | $\mathit{REC}$ | $\mathit{QUA}$ | $\mathit{T}$ | $\mathit{PREC}$ | $\mathit{REC}$ | $\mathit{QUA}$ | $\mathit{T}$ | |

$S{P}_{all}$ | 97.89 | 94.73 | 92.84 | 131 | 97.98 | 96.85 | 94.95 | 1220 |

$V{C}_{all}$ | 97.47 | 96.25 | 93.89 | 152 | 98.19 | 97.42 | 95.70 | 767 |

$KN$ | 86.88 | 58.85 | 54.05 | 116 | 87.88 | 79.01 | 71.31 | 1513 |

$S{C}_{all}$ | 97.44 | 97.83 | 95.38 | 18 | 98.83 | 98.25 | 97.12 | 98 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Chen, Q.; Liu, L.; Zheng, D.; Li, C.; Li, K.
Supervised Classification of Power Lines from Airborne LiDAR Data in Urban Areas. *Remote Sens.* **2017**, *9*, 771.
https://doi.org/10.3390/rs9080771

**AMA Style**

Wang Y, Chen Q, Liu L, Zheng D, Li C, Li K.
Supervised Classification of Power Lines from Airborne LiDAR Data in Urban Areas. *Remote Sensing*. 2017; 9(8):771.
https://doi.org/10.3390/rs9080771

**Chicago/Turabian Style**

Wang, Yanjun, Qi Chen, Lin Liu, Dunyong Zheng, Chaokui Li, and Kai Li.
2017. "Supervised Classification of Power Lines from Airborne LiDAR Data in Urban Areas" *Remote Sensing* 9, no. 8: 771.
https://doi.org/10.3390/rs9080771