# An Entropy-Weighting Method for Efficient Power-Line Feature Evaluation and Extraction from LiDAR Point Clouds

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Datasets

#### 2.2. Features and Significance

#### 2.3. Feature Weights Determined by Entropy-Weighting Method

#### 2.4. Feature Evaluation

## 3. Experiments and Analysis

#### 3.1. Evaluation Metrics

#### 3.2. Parameters Sensitivity Analysis

#### 3.3. Results and Analysis

^{3}) being inaccurately removed. Furthermore, there are some fracture PTL points that were filtered as noises during the clustering step. Benefitting from the excellent performance of feature evaluation, there were no vegetation, ground or building points extracted as PTLs in the four datasets. The HGS feature evaluation determines the number of subsequent points involved in the calculation of complex features. Thus, the evaluation threshold parameter is an important factor that affects the efficiency of the algorithm. Due to the steep terrain, we set a more relaxed evaluation threshold to ensure that there was no loss of power-line accuracy in Dataset 1. Thus, the efficiency of Dataset 3 was the lowest (0.9 million points/s). The highest efficiency was from Dataset 4 (5.9 million points/s). In urban areas, the terrain is flat, and more non-PTL objects can be filtered by HGS feature evaluation.

#### 3.4. Comparative Study

## 4. Discussion

#### 4.1. Influence of Feature Weighting on PTL Extraction

#### 4.2. Real-Time PTLs Extraction by EWFE

^{2}to 42 pts/m

^{2}). The point density of different time intervals can be different. At the edge of the data, the PTL density dropped to a fairly low range (within 5 pts/m

^{2}). We used the same implementation environment and laptop with the experiments in Section 3.3. After extracting, we combined five copies (total 10 s, 200 frames) of data as a block to display the intuitive extraction effect and calculate efficiency. Figure 13 shows a portion of blocks which came from Dataset 3. The same effect can be observed in other blocks and datasets.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Test datasets. (

**a**) Nanchong 220 kV (Dataset 1), (

**b**) Mianyang 500 kV (Dataset 2), (

**c**) Sanmenxia 220 kV (Dataset 3) and (

**d**) Wuhan 110 kV (Dataset 4). The zoomed pictures show part of the four datasets.

**Figure 4.**The voxels with different types of scenes. (

**a**) Voxels with pylons and PTLs; (

**b**) voxels with vegetation and PTLs.

**Figure 5.**Feature significance. The values of SSFs were normalized into three levels: high, medium and low: (

**a**) Original point clouds with categories; (

**b**–

**g**) the different performances of the HGS, VRR, HA, SV, LI and CC features. The orange represents high performance, where the point clouds are on a high level. The yellow represents points on medium level. The gray represents points on low level.

**Figure 6.**A schematic diagram of tower detection. The $h$ represents the HGS of point clouds in the moving window, and $d$ represents the biggest height gap in the moving window.

**Figure 7.**An example of the entropy-weighting feature evaluation. Different color represents different evaluation level. The grey represents the evaluation values under 0~0.6, the orange represents the evaluation values under 0.6~0.8 and the red represents the evaluation values under 0.8~1.

**Figure 8.**The optimization effect of the adaptive entropy weights switching. (

**a**) The extraction results before and after adaptive weights with a steel pipe tower; (

**b**) the extraction results before and after adaptive weights with a cat-head tower.

**Figure 9.**Performance testing for different empiric parameters. The other parameters were set as in Table 4. (

**a**) The accuracy of the minimum length of line; (

**b**) the accuracy of the evaluation threshold.

**Figure 10.**Extracted results. (

**a**–

**d**) represent the qualitative results of Dataset 1–4, respectively. The extracted PTL points were labelled with red color. The zoomed pictures show the extraction effects of pylon connections or complex scenes.

**Figure 11.**Examples of error extraction in the four datasets. (

**a**) The drainage lines which were labelled as PTLs in Dataset 1; (

**b**) error extraction in Dataset 4.

**Figure 12.**The comparison of the evaluation metrics of the rule-based extraction, AWFE and the proposed EWFE extraction methods.

**Figure 13.**The results of sequential blocks (each block includes 10 s, 200 frames data). The average time consumption of processing 20 frames is labelled in the bottom right corner.

Scanner Type Site | UAV-LiDAR | Vehicle-Borne LiDAR | ||
---|---|---|---|---|

Sanmenxia | Mianyang | Chongqing | Wuhan | |

Platform | UAV | UAV | UAV | Vehicle |

Voltage type (kV) | 220 | 500 | 500 | 110 |

Length (km) | 6.73 | 0.95 | 3.04 | 1.52 |

Vehicle speed (m/s) | 5 | 5 | 5 | 8 |

Point density (pts/m^{2}) | 415 | 399 | 215 | 685 |

Point mutual distance (cm) | 0.24 | 0.25 | 0.46 | 0.14 |

Total points (millions) | 167.32 | 19.96 | 51.82 | 68.80 |

Power-line points (thousands) | 1569.04 | 450.51 | 1039.3 | 371.15 |

Terrain | Mountain, steep | Rural, flat | Mountain, steep | City, flat |

**Table 2.**The designed features. The first column represents the feature category, the second column represents the feature formal definition name, the third column represents the abbreviation of the feature, and the fourth column is the equation for calculating the feature.

Category | Formal Definition | Description | Symbol Abbreviation | Equation |
---|---|---|---|---|

Height features | Height above Ground Surface | Distance to the lowest point | ${H}_{\mathrm{G}}$ | ${H}_{\mathrm{G}}=Z-{Z}_{\mathrm{ground}}$ |

Vertical Range | Points height in voxels | ${V}_{\mathrm{R}}$ | ${V}_{\mathrm{R}}=({Z}_{\mathrm{max}}-{Z}_{\mathrm{min}})$ | |

Vertical Range Ratio | Ratio of vertical range to length | ${V}_{\mathrm{RR}}$ | ${V}_{\mathrm{RR}}=({Z}_{\mathrm{max}}-{Z}_{\mathrm{min}})/l$ | |

Height Below | Distance to the highest point | ${H}_{\mathrm{B}}$ | ${H}_{\mathrm{B}}={Z}_{\mathrm{max}}-Z$ | |

Height Above | Distance to the lowest point | ${H}_{\mathrm{Ab}}$ | ${H}_{\mathrm{Ab}}=Z-{Z}_{\mathrm{min}}$ | |

Eigenvalue features | Sum | Sum of eigenvalues | ${S}_{\mathrm{U}}$ | ${S}_{\mathrm{U}}={\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}$ |

Anisotropy | The uniformity of points | ${A}_{\mathrm{N}}$ | ${A}_{\mathrm{N}}=({\lambda}_{1}-{\lambda}_{3})/{\lambda}_{1}$ | |

Horizontal Angle | The horizontal angle of points | ${H}_{\mathrm{A}}$ | ${H}_{\mathrm{A}}=\left\{\begin{array}{c}{180}^{\circ}-\theta (\theta \ge {90}^{\circ})\\ {90}^{\circ}-\theta (\theta <{90}^{\circ})\end{array}\right.$ | |

Surface Variation | The surface roughness of points | ${S}_{\mathrm{V}}$ | ${S}_{\mathrm{V}}={\lambda}_{3}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | |

Linearity | The linearity of points | ${L}_{\mathrm{I}}$ | ${L}_{\mathrm{I}}=({\lambda}_{1}-{\lambda}_{2})/{\lambda}_{1}$ | |

Curvature Change | The extent of curvature change | ${C}_{\mathrm{U}}$ | ${C}_{\mathrm{U}}={\lambda}_{1}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | |

Density features | Planarity | The planarity of points | ${P}_{\mathrm{L}}$ | ${P}_{\mathrm{L}}=({\lambda}_{2}-{\lambda}_{3})/{\lambda}_{1}$ |

Density of Point Set | The number of points within the radius | ${D}_{\mathrm{P}}$ | ${D}_{\mathrm{P}}=\frac{3}{4}\cdot \frac{num(r)}{\pi {r}^{3}}$ | |

Density Ratio | The ratio of density in projection plane | ${D}_{\mathrm{R}}$ | ${D}_{\mathrm{R}}=\frac{3}{4r}\cdot \frac{num(3D)}{num(2D)}$ |

**Table 3.**An example of entropy weight and final weight calculation of two samples from the Sanmenxia 220 kV data (Dataset 1). Sample 1 is of the PTLs which are away from pylons. Sample 2 is of the PTLs close to pylons.

Feature | Weights | |
---|---|---|

Sample 1 | Sample 2 | |

HGS | 1 | 1 |

VRR | 0.21 | 1 |

HA | 0.11 | 0.12 |

SV | 0.30 | 0.07 |

LI | 0.14 | 0.28 |

CC | 0.24 | 0.53 |

**Table 4.**Parameter setting for the proposed EWFE algorithm. The first column represents the parameter’s name, the second column represents the abbreviation of the parameter, the third column represents the parameter’s thresholds suggested for the EWFE algorithm, and the last column represents the parameter’s setting sources.

Phase | Parameters | Symbol | Values | Sources |
---|---|---|---|---|

Weight calculation | Ratio of vertical range to length | ${V}_{\mathrm{RR}}$ | [0, 0.15], [0, 0.25], [0, 0.3] | Standard |

Radius for neighbor search (m) | $K$ | 3 | Significance analysis | |

Horizontal angle threshold scope | $\left[{H}_{\mathrm{min}},{H}_{\mathrm{max}}\right]$ | [0°, 30°] | Significance analysis | |

Surface variation threshold scope | $\left[{S}_{\mathrm{min}},{S}_{\mathrm{max}}\right]$ | [2, 6] | Significance analysis | |

Curvature scope | $\left[{C}_{\mathrm{min}},{C}_{\mathrm{max}}\right]$ | [0.02, 0.06] | Significance analysis | |

Linearity threshold scope | $\left[{L}_{\mathrm{min}},{L}_{\mathrm{max}}\right]$ | [0.8, 1] | Significance analysis | |

Feature evaluation | The HGS evaluation threshold (m) | ${E}_{\mathrm{HGS}}$ | 8, 10, 12 | Standard |

The other features evaluation threshold | ${E}_{\mathrm{t}}$ | 0.6, 0.7, 0.8 | Empiric | |

Refinement | Minimum length of line (m) | ${l}_{\mathrm{min}}$ | 6, 8, 10 | Empiric |

Dataset | Recall (%) | Precision (%) | F (%) | Efficiency (Million Points/s) |
---|---|---|---|---|

Dataset 1 | 98.8 | 98.3 | 98.6 | 2.8 |

Dataset 2 | 99.9 | 99.5 | 99.7 | 1.8 |

Dataset 3 | 99.3 | 98.4 | 98.9 | 0.9 |

Dataset 4 | 99.2 | 97.6 | 98.4 | 5.9 |

Dataset | Total Points | Feature Evaluation | Clustering | Original PTLs | |
---|---|---|---|---|---|

HGS | The Other Features | ||||

Dataset 1 | 167,325 | 2960 | 1611 | 1577 | 1569 |

Dataset 2 | 19,938 | 784 | 454 | 452 | 450 |

Dataset 3 | 58,427 | 2343 | 1368 | 1065 | 1055 |

Dataset 4 | 68,800 | 674 | 382 | 377 | 371 |

Dataset | Total Time Consumption (s) | Feature Evaluation (s) | Clustering (s) | Efficiency (Million Points/s) | |
---|---|---|---|---|---|

Height Features | Eigenvalue Features | ||||

Dataset 1 | 80.01 | 9.25 | 68.56 | 2.2 | 2.1 |

Dataset 2 | 9.5 | 1.47 | 7.36 | 0.67 | 2.1 |

Dataset 3 | 62.52 | 8.62 | 52.8 | 1.1 | 0.97 |

Dataset 4 | 10.48 | 3.33 | 7.01 | 0.5 | 6.3 |

Dataset | Proposed Method | Zhang’s Method | Jaehoon’s Method | ||||||
---|---|---|---|---|---|---|---|---|---|

Recall | Precision | F | Recall | Precision | F | Recall | Precision | F | |

Dataset 1 | 98.8 | 98.3 | 98.6 | 96.1 | 93.1 | 94.6 | 95.8 | 95.1 | 95.5 |

Dataset 2 | 99.9 | 99.5 | 99.7 | 97.3 | 94.8 | 96.0 | 97.6 | 97.1 | 97.3 |

Dataset 3 | 99.3 | 98.4 | 98.9 | 95.4 | 91.8 | 93.6 | 94.2 | 92.7 | 93.5 |

Dataset 4 | 99.2 | 97.6 | 98.4 | \ | \ | \ | 94.2 | 90.8 | 92.3 |

Proposed Method | Zhang’s Method | Jaehoon’s Method | |
---|---|---|---|

Computation rate | 2.85 | 1.4 (>1.1) | 1.2 (1.46) |

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**MDPI and ACS Style**

Tan, J.; Zhao, H.; Yang, R.; Liu, H.; Li, S.; Liu, J.
An Entropy-Weighting Method for Efficient Power-Line Feature Evaluation and Extraction from LiDAR Point Clouds. *Remote Sens.* **2021**, *13*, 3446.
https://doi.org/10.3390/rs13173446

**AMA Style**

Tan J, Zhao H, Yang R, Liu H, Li S, Liu J.
An Entropy-Weighting Method for Efficient Power-Line Feature Evaluation and Extraction from LiDAR Point Clouds. *Remote Sensing*. 2021; 13(17):3446.
https://doi.org/10.3390/rs13173446

**Chicago/Turabian Style**

Tan, Junxiang, Haojie Zhao, Ronghao Yang, Hua Liu, Shaoda Li, and Jianfei Liu.
2021. "An Entropy-Weighting Method for Efficient Power-Line Feature Evaluation and Extraction from LiDAR Point Clouds" *Remote Sensing* 13, no. 17: 3446.
https://doi.org/10.3390/rs13173446