# Quantifying Multi-Scale Performance of Geometric Features for Efficient Extraction of Insulators from Point Clouds

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## Abstract

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## 1. Introduction

- Applying multi-scale features to provide significant representations of shape and structure information, mitigating the impact of noise and similarity on extraction accuracy.
- Introducing the EWM to quantify the multi-scale performance of geometric features, producing robust results.
- Developing an automatic data-driven method to extract insulators from pylons with various shapes and sizes, where tension and suspension insulators can be distinguished as well.

## 2. Relate Works

#### 2.1. Insulator Extraction

#### 2.2. Multi-Scale Feature Fusion

## 3. Materials and Methods

#### 3.1. Datasets

#### 3.2. Methodology

#### 3.2.1. Pylon Head Segmentation

#### 3.2.2. Feature Construction

#### 3.2.3. Quantification of Multi-Scale Feature

#### 3.2.4. Optimize Extraction of Enlarged Perspective

## 4. Results and Analysis

#### 4.1. Parameters Analysis

#### 4.2. Pylon Head Segmentation

#### 4.3. Insulator Extraction

## 5. Discussion

#### 5.1. Influences Come from Possible Conditions

#### 5.2. Advantages of Multi-Scale Neighborhood

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Pylon point clouds. (

**a**–

**g**) T-type pylons; (

**h**,

**i**) O-type pylons; and (

**j**) a portal pylon. Suspension insulators are colored in red and tension insulators are colored in blue.

**Figure 4.**Process of pylon head segmentation. (

**a**) Process of the pylon extraction. First floor: PTC point clouds, second floor: continuous vertical distribution, and third floor: height difference of point clouds in each sparse grid. (

**b**) Head segmentation according to its aspect ratio.

**Figure 6.**Region erosion and growing: (

**a**) candidate insulator point clouds, (

**b**) point clouds after erosion operation, and (

**c**) point clouds after growing operation.

**Figure 8.**The cases of poor results. (

**a**) The missing insulator case and (

**b**) the high similarity case.

**Figure 9.**The proposed method applied to various conditions: (

**a**) the sparse point density of pylons, (

**b**) the unusual pylons, and (

**c**) the complex environment. Suspension insulators are colored in red and tension insulators are colored in blue. Misidentified suspension insulators are marked in green circles and misidentified tension insulators are marked in blue circles.

**Figure 10.**Performance evaluation of single-scale and multi-scale features. Description: R

_{opt,λ}represents the optimal neighborhood and R

_{multi}represents the multi-scale neighborhood.

Pylon | Length (m) | Width (m) | Height (m) | Number of SIs | Number of TIs |
---|---|---|---|---|---|

a | 13.32 | 10.66 | 29.77 | 2 | 6 |

b | 14.48 | 10.10 | 44.59 | 3 | 12 |

c | 8.7 | 4.5 | 45.10 | 6 | 12 |

d | 23.43 | 14.48 | 53.87 | 6 | 6 |

e | 14.15 | 9.58 | 34.20 | 3 | 6 |

f | 13.41 | 5.09 | 24.41 | 2 | 6 |

g | 12.49 | 12.46 | 44.97 | 6 | / |

h | 9.56 | 6.30 | 37.25 | 3 | / |

i | 16.06 | 7.64 | 40.65 | 3 | / |

j | 1.28 | 13.85 | 23.24 | 3 | / |

**Table 2.**The designed features. The first column represents the feature categories, the second column represents the features, the third column listed the equations on how to compute these features, the fourth column represents applied features in TIs extraction, and the fifth column represents applied features in SIs extraction.

Category | Feature | Equation | TIs | SIs |
---|---|---|---|---|

Eigenvalue features | Minimum eigenvalue (ME) | ${\lambda}_{3}$ | ✓ | |

Planarity (PL) | $({\lambda}_{2}-{\lambda}_{3})/{\lambda}_{1}$ | ✓ | ||

Linearity (LI) | $({\lambda}_{1}-{\lambda}_{2})/{\lambda}_{1}$ | ✓ | ||

Surface variation (SV) | ${\lambda}_{3}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | ✓ | ||

PCA1 | ${\lambda}_{1}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | ✓ | ||

PCA2 | ${\lambda}_{2}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | ✓ | ✓ | |

Verticality (VE) | $1-\left|\overrightarrow{(0,0,1)}\u2022\overrightarrow{{V}_{1}}\right|$ | ✓ | ||

Density features | Point density (PD) | $num(\mathrm{points})$ | ✓ | |

Projection features | Width (WI) | ${Y}_{\mathrm{max}}-{Y}_{\mathrm{min}}$ | ✓ | |

Length–width Sum (LS) | $({X}_{\mathrm{max}}-{X}_{\mathrm{min}})+({Y}_{\mathrm{max}}-{Y}_{\mathrm{min}})$ | ✓ |

Pylon | Accuracy of SIs | Accuracy of TIs | Pylon | Accuracy of SIs | Accuracy of TIs | |
---|---|---|---|---|---|---|

Recall (%) | 79.48 | 86.99 | 98.68 | 94.41 | ||

Precision (%) | 98.39 | 96.56 | 60.01 | 97.30 | ||

F1-score (%) | 87.93 | 91.52 | 74.63 | 95.83 | ||

Recall (%) | 79.47 | 86.98 | 96.03 | / | ||

Precision (%) | 98.39 | 94.61 | 96.53 | / | ||

F1-score (%) | 87.93 | 90.63 | 96.27 | / | ||

Recall (%) | 65.96 | 93.21 | 93.30 | / | ||

Precision (%) | 100.00 | 98.52 | 97.92 | / | ||

F1-score (%) | 79.49 | 95.79 | 95.55 | / | ||

Recall (%) | 86.60 | 92.04 | 92.25 | / | ||

Precision (%) | 99.31 | 99.82 | 100.00 | / | ||

F1-score (%) | 92.52 | 95.78 | 95.97 | / | ||

Recall (%) | 84.23 | 86.24 | 94.99 | / | ||

Precision (%) | 100.00 | 99.23 | 89.30 | / | ||

F1-score (%) | 91.45 | 92.28 | 92.05 | / |

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## Share and Cite

**MDPI and ACS Style**

Tang, J.; Tan, J.; Du, Y.; Zhao, H.; Li, S.; Yang, R.; Zhang, T.; Li, Q.
Quantifying Multi-Scale Performance of Geometric Features for Efficient Extraction of Insulators from Point Clouds. *Remote Sens.* **2023**, *15*, 3339.
https://doi.org/10.3390/rs15133339

**AMA Style**

Tang J, Tan J, Du Y, Zhao H, Li S, Yang R, Zhang T, Li Q.
Quantifying Multi-Scale Performance of Geometric Features for Efficient Extraction of Insulators from Point Clouds. *Remote Sensing*. 2023; 15(13):3339.
https://doi.org/10.3390/rs15133339

**Chicago/Turabian Style**

Tang, Jie, Junxiang Tan, Yongyong Du, Haojie Zhao, Shaoda Li, Ronghao Yang, Tao Zhang, and Qitao Li.
2023. "Quantifying Multi-Scale Performance of Geometric Features for Efficient Extraction of Insulators from Point Clouds" *Remote Sensing* 15, no. 13: 3339.
https://doi.org/10.3390/rs15133339