# Fully-Automated Power Line Extraction from Airborne Laser Scanning Point Clouds in Forest Areas

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## Abstract

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## 1. Introduction

^{2}to the current data density of approximately 55 points per m

^{2}. The objects’ levels of detail are markedly different according to the point density variation. Many classification methodologies have been developed according to different point densities. For example, Axelsson (1999) [2] utilized ALS data with a density of eight points/m

^{2}for power line detection. He presented a classification method of power lines by looking for parallel and linear 2D structures based on the Hough transformation method and utilizing a 2D line equation for line extraction. Melzer and Briese (2004) [3] proposed a method for power line extraction and modelling from ALS by using 2D Hough transformation and 3D catenary curve fitting methods. The density of ALS data was at that time up to 10 points/m

^{2}. Clode and Rottensteiner (2005) [6] detected trees and power lines from less than one point per m

^{2}point cloud in Sydney. First and last pulse return differences were applied. McLaughlin (2006) [7] used ALS data with an average point spacing of 1.2 m–2.4 m on a power line. Based on these data, he presented a supervised method to classify the power lines. Liu et al. (2009) [8] detected power lines with a 2D gray-level image, the intensity of laser return and an improved Hough transform. Jwa et al. (2009) [9] introduced a voxel-based piecewise line detector (VPLD) approach for automatic power line reconstruction using a density of five points/m

^{2}ALS data. Liang et al. (2011) [10] used the random sample consensus (RANSAC) method to determine which points belong to a line. Kim and Sohn (2011) [11] used RANSAC, minimum description length and principal component analysis in feature extraction and random forests as a classification technique for a test dataset with a density of 30 points per m

^{2}. Sohn et al. (2012) [12] proposed that using a Markov random field (MRF) classifier would delineate the spatial context of linear and planar features, as in a graphical model for power line and building classification. The test data were at a density of 16 points/m

^{2}. Kim and Sohn (2013) [5] proposed a point-based supervised random forest method for five utility corridor object classification from an ALS point cloud set with a density of 25–30 points/m

^{2}. Based on the above literature review, the methods for power line detection can be summarized into two types: line-shape-based detection methods (e.g., RANSAC and 2D Hough transformation [2,3,8,10,13]) and supervised classification methods [7,9,11,12]. Line-shape-based detection methods incur a relatively high computational cost, especially for a large area dataset. Each point must be calculated to determine whether it belongs to a line. Therefore, some researchers [9,14] have proposed piece-wise line detection to improve the efficiency. However, because the detected results are usually pieces of lines, the correct topographic relations must be calculated between the turn points. For supervised classification methods, a large training dataset is required to achieve the desired results. In addition, unbalance sampling will lead to an increased rate of misclassification.

## 2. Materials and Methods

#### 2.1. Data Resources and Test Fields

^{2}. These point clouds contain georeferenced 3D coordinates (X, Y and Z) in an ETRS-TM35FIN coordinate system: X towards the east, Y referring to the north and Z upwards.

^{2}to 300 × 500 m

^{2}. Figure 2 displays the locations of the six study areas on a 1:40,000 topographic map. The two areas indicated in red in Figure 1 represent Areas 3 and 4 in Figure 2.

**Figure 2.**Illustration of the study areas on an aerial image (from the Finnish National Land Survey). The numbers on the map indicate the IDs of the test fields.

#### 2.2. Methods

**Figure 3.**Method for power line extraction. Red frame: steps in the statistical analysis; green frame: steps in the image-based processing.

^{2}. Algorithm 1 is divided into three parts: statistical analysis (Steps 1, 2 and 3), image analysis (Steps 4 and 5) and power line extraction (Step 6). Statistical analysis aims to identify power line candidates. Table 2 lists the European regulations regarding power line overhead heights. It can be observed that the minimum heights of power lines above the ground vary according to the voltages. However, the minimum height cannot be less than 5.2 m. Considering the possible curvatures and ages of the power lines (possibly not completely vertical to the ground), we set a height threshold above ground (Ht = 4 m) to separate the data into two sectors. This separation was performed by gridding the data in the xy plane and, from each grid, extracting the points that are 4 m higher than or equal to the ground ({Pij} ∈ Pu). The rest of the data are in group Pl. The power line candidates are selected from the point set “Pu”. The selection standards of the candidates are as follows:

^{2}, when the number of power line points is smaller than the square root of 2 × the density of the points, they are selected as power lines. That is, the candidate points are distributed along the diagonal of a square.

Abbreviation | Description |
---|---|

P(x, y, z) | 3D point cloud; |

P_{ij} | A set of point in a grid (i, j), with 3D coordinates (X_{ij}, Y_{ij}, Z_{ij}); |

Pl_{ij} | A set of point lower than a certain height threshold; |

Pu_{ij} | A set of point in a grid (i, j) greater than or equal to a certain height threshold; |

Z_{min} | The minimum height value in a grid; each grid has its minimum height; |

H_{t} | The height threshold for the lowest power line in a regulation; |

numOfPoints_g | The number of the points in a grid; |

P_{density} | The density of a point cloud, points/m^{2}; |

Z_{bij} | The height value of a point in a bin (produced by a height histogram) of a grid (i, j); |

Z_{bmin} | The minimum height value of a point in a bin of a grid (i, j); |

numOfPoints_b | The number points in a bin; |

P_{bij} | The points in a bin of a grid (i, j); |

paraArea_min | The minimum area of a single region of a binary image that can be considered a power line; |

paraArea_max | The maximum area of a single region of a binary image that can be considered a power line; |

paraLength | The length of the major axis of one region in a binary image; |

paraShape | Eccentricity of a single region in a binary image, which means that “1” is a line and “0” is a circle; |

sizeP | Pixel size of a binary image. |

Algorithm 1 Power Line Detection | |

1: Grid the dataset {P(x, y, z)}, e.g., grid = 1 m * 1 m. {P} = {P_{11}} + {P_{12}} + {P_{13}} +...... + {P_{ij}} | |

2: {P_{ij}} ={Pl_{ij}} + {Pu_{ij}}, where P_{ij} (Z_{ij} − Z_{min} < H_{t}) ∈ Pl_{ij}, P_{ij} (Z_{ij} − Z_{min} >= H_{t}) ∈ Pu_{ij} | |

3: Power line candidate points are selected from {Pu_{ij}} | |

if (Z_{ij} − Z_{min} <= 0.5) | (numOfPoints_g <= sqrt (2 * P_{density})), then | |

P_{ij}∈ {candidates}, | |

else | |

if Z_{ij} − Z_{min} > 0.5, then | |

using histogram analyzing the height distribution with (for example) a 1 m interval, {P_{ij}} = {bin} | |

if only one bin has points, the others are empty, then | |

P_{bij }∈ {candidates}, | |

else | |

if (Z_{bij} −Z_{bmin } <= 0.5) & (numOfPoints_b >= sqrt (P_{density})), then | |

P_{bij} (Z_{bij} − Z_{bmin }<= 0.5) ∈ {candidates}, | |

end if | |

end if | |

end if | |

end if | |

4: Transfer {candidates} to a raster image I_{(m,n)} by using their X, Y coordinates and predefined | |

if a raster is not empty, then | |

it is set to 1 | |

else it is set to 0 | |

end if | |

5: Image regions are labelled: I = R_{1}+R_{2}+R_{3}+......+R_{k}, where R_{1}, R_{2}, R_{3},.... R_{k }are the labelled image regions | |

if area of R_{k} > paraArea_min & area of R_{k} <= paraArea_max & length of major axis of R_{k} > paraLength | |

& Eccentricity of R_{k} > paraShape, then | |

accepts as {2Dpower lines} | |

end if | |

6: Transfer {2Dpower lines} to {3Dpower lines} by reverse processing of step (4) |

**Table 2.**Regulations for the heights of power lines [22].

Schedule 2 Minimum Height Above Ground of Overhead Lines | Regulation 17 (2) | |||
---|---|---|---|---|

Column 1 | Column 2 | Column 3 | ||

Nominal Voltages | Over Roads | Other Locations | ||

Not exceeding 33,000 volts | 5.8 meters | 5.2 meters | ||

Exceeding 33,000 volts, but not exceeding 66,000 volts | 6 meters | 6 meters | ||

Exceeding 66,000 volts, but not exceeding 132,000 volts | 6.7 meters | 6.7 meters | ||

Exceeding 132,000 volts, but not exceeding 275,000 volts | 7 meters | 7 meters | ||

Exceeding 275,000 volts, but not exceeding 400,000 volts | 7.3 meters | 7.3 meters |

^{2}. Figure 4b is the power line candidates. It can be observed that after statistical analysis, the power lines became more visible. Moreover, as the number of points was considerably reduced, the subsequent processing became more efficient. Figure 4c is a binary image that was transferred from Figure 4b. After the image was filtered by the area size, length and shape, the result yielded Figure 4d: a power line image. This 2D power line image was transferred to 3D power lines (see Figure 4e) using the same parameters as in Figure 4b to Figure 4c. Figure 5 shows another example of the power line extraction in Area 5. It can be observed that the shape of the power lines is different from that in Figure 4. By applying image processing technology, the power lines were distinguished from their surroundings. This figure also illustrates the entire process. The explanation is the same as that presented for Figure 4.

**Figure 4.**The complete power line process in Area 4. (

**a**) Airborne laser scanning (ALS) point cloud (3D); (

**b**) power line candidate selection (3D); (

**c**) binary image of (b) (2D); (

**d**) after binary image filtering: power line image (2D); (

**e**) extracted power lines (3D).

**Figure 5.**Power line extraction in Area 5. (

**a**) ALS point cloud (3D); (

**b**) power line candidates (3D); (

**c**) binary image of (b) (2D); (

**d**) after binary image filtering: power line image (2D); (

**e**) extracted power lines (3D).

## 3. Results and Discussions

**Figure 6.**Power line extraction in Area 1. (

**Left**) ALS point cloud; (

**Right**) the result of power line extraction.

**Figure 7.**Power line extraction in Area 2. (

**Left**) ALS point cloud; (

**Right**) the result of power line extraction.

**Figure 8.**Power line extraction in Area 3. (

**Left**) ALS point cloud; (

**Right**) the result of power line extraction.

**Figure 9.**Power line extraction in Area 6. (

**Left**) ALS point cloud; (

**Right**) the result of power line extraction.

Area ID | Parameters | Number of Points of ALS (point) | Length of Power Lines (m) | Detected Number of Power Lines (point) | Run Time (s) |
---|---|---|---|---|---|

1 | Pdensity = $\sqrt{55}$ paraArea_min = 100 paraArea_max =1000 paraLength = 70 paraShape = 0.96 sizeP = 0.6 | 3,130,155 | 166.13 | 2348 | 530.47 |

2 | Pdensity = $\sqrt{55}$ paraArea_min = 80 paraArea_max = 1000 paraLength = 35 paraShape = 0.96 sizeP = 0.60 | 2,874,851 | 269.45 | 3409 | 309.45 |

3 | Pdensity = $\sqrt{55}$ paraArea_min = 100 paraArea_max = 1000 paraLength = 100 paraShape = 0.92 sizeP = 0.70 | 3,602,719 | 464.03 | 6790 | 530.50 |

4 | Pdensity = $\sqrt{55}$ paraArea_min = 100 paraArea_max = 1000 paraLength = 70 paraShape = 0.9 sizeP = 0.60 | 3,130,116 | 188.76 | 3295 | 523.09 |

5 | Pdensity = $\sqrt{55}$ paraArea_min = 100 paraArea_max = 1000 paraLength = 100 paraShape = 0.93 sizeP = 0.60 | 4,781,564 | 380.29 | 7157 | 606.19 |

6 | Pdensity = $\sqrt{55}$ paraArea_min = 70 paraArea_max = 1000 paraLength = 60 paraShape = 0.99 sizeP = 0.70 | 2,197,719 | 298.50 | 3028 | 167.20 |

Area ID | Test Outcome (points) | Reference Data (points) | Commission (points) | Omission (points) | True Points (points) |
---|---|---|---|---|---|

1 | 2348 | 2249 | 173 | 74 | 2175 |

2 | 3409 | 3256 | 216 | 63 | 3193 |

3 | 6790 | 6377 | 509 | 96 | 6281 |

4 | 3295 | 3183 | 175 | 63 | 3120 |

5 | 7157 | 6681 | 585 | 109 | 6572 |

6 | 3028 | 2901 | 175 | 48 | 2853 |

Total | 26,027 | 24,647 | 1833 | 453 | 24,194 |

Area ID | Commission Error (%) | Omission Error (%) | Correctness (%) |
---|---|---|---|

1 | 7.37 | 3.29 | 92.63 |

2 | 6.34 | 1.93 | 93.66 |

3 | 7.50 | 1.51 | 92.50 |

4 | 5.31 | 1.98 | 94.69 |

5 | 8.17 | 1.63 | 91.83 |

6 | 5.78 | 1.65 | 94.22 |

Average | 6.74 | 2.00 | 93.26 |

## 4. Conclusions

^{2}. By applying our algorithms, the power lines were detected with an average accuracy of 93.26%. These findings are comparable with the latest results for non-forest areas. The advantages of our method are as follows:

## Acknowledgements

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Zhu, L.; Hyyppä, J.
Fully-Automated Power Line Extraction from Airborne Laser Scanning Point Clouds in Forest Areas. *Remote Sens.* **2014**, *6*, 11267-11282.
https://doi.org/10.3390/rs61111267

**AMA Style**

Zhu L, Hyyppä J.
Fully-Automated Power Line Extraction from Airborne Laser Scanning Point Clouds in Forest Areas. *Remote Sensing*. 2014; 6(11):11267-11282.
https://doi.org/10.3390/rs61111267

**Chicago/Turabian Style**

Zhu, Lingli, and Juha Hyyppä.
2014. "Fully-Automated Power Line Extraction from Airborne Laser Scanning Point Clouds in Forest Areas" *Remote Sensing* 6, no. 11: 11267-11282.
https://doi.org/10.3390/rs61111267