# A Heuristic Method for Power Pylon Reconstruction from Airborne LiDAR Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Related Work

**Data-driven:**Generally, data-driven reconstruction methods adopt a bottom-up strategy. They firstly extract basic features, such as planes, lines, or points, and then through a combination of features and their topological relations, a complete model is reconstructed. In buildings, reconstruction usually contains two key processes: building roof edge segmentation and topological reconstruction [1]. Since plane features of buildings are more stable than point or line features, for complex roof structures with high-density point cloud data, methods based on plane segmentation is first adopted, such as ridge or edge-based and voxel-based region growing [10,11], cross-line element growth (CLEG) [12], RANSAC [13,14], classification or feature clustering [15,16,17,18]; then, point or line features are obtained by intersection of plane features. Reconstruction results of data-driven methods are not limited by the integrity of the model library, and they theoretically allow the generation of a model in any shape [19]. Data-driven methods provide accurate descriptions of simple objects when the data are complete. For example, Laefer and Truong-Hong [20] introduced a method to automatically identify structural steel members and generate their geometry from a terrestrial LiDAR data for building information modeling (BIM) usage. Experiments shows that the 3D model can be derived by assembling the 3D sub-models of all individual members. However, deviations or reconstruction failures will occur when raw data are sparse, noisy or partially occluded [21]. To overcome this problem, more and more multi-platform and multi-view data are fused to improve data integrity. For example, Kedzierski and Fryskowska [22,23] integrated data from different laser scanning technologies, such as terrestrial and airborne, to reconstruct buildings more precisely.

**Model-driven:**Contrary to data-driven methods, model-driven methods use a top-down strategy, which is based on a predefined model library. There are two key steps for model-driven methods: (1) the optimal model matching between existing models in the predefined library and the original data; and (2) the appropriate parameter estimation of the optimal selected model. For most model-driven building reconstruction methods, there is a common assumption that a building is a collection of roof primitives, such as gable roofs and hipped roofs [24]. Several Monte Carlo Simulation approaches, such as RJMCMC [25,26], have been adopted to solve model parameters and great potential has been shown in object reconstruction. Model-driven methods are known to be robust with respect to data quality and suitable for large scenes [2]. Because topological relations of models are predefined in the model library, it is advantageous for low-density point cloud data, and it can guarantee topological correctness of reconstructed models [1]. For example, Cheng et al. [27] proposed a full framework to reconstruct multilayer interchange bridge. An interchange bridge was firstly divided into structure units; then its obscured structures was detected and restored; finally, by modeling each structure unit, the interchange bridge was reconstructed. However, the reconstruction results are limited by the integrity of the predefined model library [9], and it is can be quite time-consuming, especially when large amounts of parameters need to be estimated.

**Hybrid-driven:**Because of the complexity in structure and diversity in shape, it is hard to meet the reconstruction requirements of complex objects by merely using either data-driven or model-driven methods. Therefore, hybrid approaches combining both data-driven and model-driven strategies have been put forward in recent years. Construction constraints (e.g., coplanarity, symmetry and parallelism) are brought into the process of object reconstruction to optimize models. For example, Xiong et al. [28] introduced flexible building primitives for 3D building modeling. In this method, the point cloud of buildings was firstly segmented into roof patches, and then through combining the predefined building primitives, buildings could be well reconstructed. Kwak and Habib [29] developed a framework for fully-automated building model generation where the building’s approximate boundary was firstly generated by a data-driven method and then integrated by a model-based processing strategy. Zheng et al. [9] proposed a hybrid approach for generating Level of Detail 2 (LoD2) building models. Buildings could be completely and correctly reconstructed through this method by assembling basic models. Cabaleiro et al. [4] proposed a method for the detection and automatic 3D modeling of metal frame connections from LiDAR data. In their method, the information of connections was firstly extracted, and then through a parametric model of connections, the geometric model of the frame could be completed. Compared with the single reconstruction strategy, hybrid approaches combine both advantages: on the one hand, it is more flexible than model-driven methods; on the other hand, it is more robust than data-driven methods.

#### 1.2. Contribution

#### 1.3. Overview

## 2. Methodology

#### 2.1. Preprocessing

#### 2.2. Pylon Decomposition Based on Statistical Analysis

#### 2.3. Pylon Body Reconstruction Based on a Data-Driven Strategy

#### 2.3.1. Extraction and Segmentation of Corner Points

#### 2.3.2. Corner Line Fitting Based on RANSAC

_{1}(x

_{1}, y

_{1}, z

_{1}) and P

_{2}(x

_{2}, y

_{2}, z

_{2}) are randomly selected, as shown in Figure 5a. The equation of the 3D line L calculated by the two points is as Equation (1):

#### 2.4. Pylon Head Reconstruction Based on a Model-Driven Strategy

#### 2.4.1. 3D Parametric Model Library of Pylon Heads

_{3}can be inferred by Equation (2) according to geometric relations, while L

_{3}can be inferred by Equation (3) according to collinearity (in Figure 7a).

_{1}and l

_{2}can be obtained. Then, according to their collinearity, the head width of the side view can be derived.

#### 2.4.2. Pylon Head Type Recognition by Shape Context

_{1}, p

_{2}, p

_{3}, …, p

_{n}} on each contour of shapes, as shown in Figure 8a,b, and compute the shape context of each point p

_{i}. The shape context of p

_{i}is defined as the relative coordinates of the remaining n − 1 points. For simplicity, the relative coordinates are replaced with the number of points in each sector of the target template which is shown in Figure 8c. N concentric circles are established at logarithmic intervals in the region where the current point p

_{i}is the center and R is the radius, and the region is divided into M bins in a circumferential direction.

_{i,j}is the matching cost between point i and point j, h

_{i}(k) is the p

_{i}’s shape histogram of points, h

_{j}(k) is the q

_{j}’s shape histogram of models, k = {1, 2, 3, …, K}, and K = M × N.

#### 2.4.3. Optimizations

_{0}= 1), and the decreasing cooling schedule Ti is required as ${\mathrm{lim}}_{i\to \infty}{T}_{i}=0$ [8]. As shown in Figure 9, with the temperature T

_{i}cooling, the probability of accepting worse solutions explored in the search space will decrease. When the temperature T is low enough, the target distribution $p(x)$ eventually tends to be global optimal as it can jump out the local optimal solution with high probability.

_{i}, the homogeneous Markov transition kernel mixes quickly enough, then convergence to the set of global maxima of $p(x)$ is ensured for an appropriate sequence T

_{i}. To cool the temperature T quickly, an exponential cooling schedule is chosen. Combining the Gibbs energy and the MH sampler, the detailed procedure of simulated annealing is shown in the Appendix A.

## 3. Experimental Data

^{2}, and the points amount is 43,879,821, including six power pylons. The point density of the example area is about 500 pts/m

^{2}on average.

## 4. Results

#### 4.1. Decomposition Results of Different Pylon Types

#### 4.2. Precision of Pylon Body Reconstruction

_{i}, the ratio of inliers r

_{i}, and the fitting residual ${\delta}_{i}$ of each leg i between the fitted line and inliers of extracted corner points are calculated. The fitting residual ${\delta}_{i}$ is defined as Equation (11):

_{k}to the fitting line L, and n is the number of inliers.

#### 4.3. Recognition of Pylon Head Type

#### 4.4. Precision of Pylon Head Reconstruction

_{ave}and maximum distance D

_{max}between the reconstructed head model and the original point cloud are, respectively, calculated according to Equations (12) and (13).

_{i}, q

_{i}) is the distance from the model key points p

_{i}to the corresponding closest point q

_{i}of the original pylon point cloud, and n is the number of model key points.

_{ave}of four pylon heads is 0.196 m on average, while the maximum distance D

_{max}of the four pylon heads is 0.333 m.

#### 4.5. Efficiency of Pylon Head Reconstruction

_{p}(mentioned in Section 2.3.1), the head size of original point cloud, the number of points ncount, and the time consumption Time are calculated. Table 8 shows the reconstruction time of the 12 pylons, which is sorted by Time.

## 5. Discussion

#### 5.1. Robustness to Noise of Pylon Body Reconstruction

#### 5.2. Influence Factors of Pylon Head Reconstruction

#### 5.2.1. Key Points Extraction

_{ave}between the reconstructed models and the original point cloud increase from 0.176 m to 0.244 m, while the maximum distance D

_{max}increases from 0.274 m to 0.435 m, showing that the quality of reconstructed model also decreases. Thus, the alpha value should be selected carefully to capture the detail of head contour while not introducing non-contour points.

#### 5.2.2. Data Loss

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Detailed Procedure of Simulated Annealing Algorithm

Input: space X, original state x_{0}, initial temperature T, iteration number N at each temperature and the cooling rate γ |

While T > T_{min} |

{ |

For i = 0 to N |

sample x* according to $q({x}^{*}|{x}_{i})$ in space X |

if $A({x}_{i},{x}^{*})=\mathrm{min}\{1,\frac{{p}^{\frac{1}{\mathrm{Ti}}}({x}^{*})}{{p}^{\frac{1}{\mathrm{Ti}}}({x}_{i})}\}$ > random (0, 1) |

x_{i+1} = x*; |

else |

x_{i+1} = x_{i}; |

T = T*γ; |

} |

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**Figure 2.**Definition of the 3D pylon coordinate system: (

**a**) the front view of a pylon; and (

**b**) the vertical view.

**Figure 3.**Pylon decomposition based on statistical analysis: (

**a**,

**e**) the original point cloud of extracted pylons, and the red planes are the waist plane; (

**b**,

**c**,

**f**,

**g**) statistical analysis results on density and length histogram, respectively; and (

**d**,

**h**) decomposition results.

**Figure 4.**Extraction and segmentation of corner points: (

**a**) layering results of the original pylon body point cloud; (

**b**) contour points of one bin extracted by convex hull algorithm (

**c**) simplified corner points; and (

**d**) segmentation results of four subsets which are colored in different color.

**Figure 5.**Pylon body reconstruction based on RANSAC: (

**a**) corner points of one subset; (

**b**) corner line fitting result of one subset; (

**c**) fitting results of four corner lines; and (

**d**) refined results of the pylon body. The original point cloud is colored in black.

**Figure 6.**3D parametric model library of pylon heads. The parameters are specified as the feature height, feature length and feature width. (

**a**) Model 1; (

**b**) Model 2; (

**c**) Model 3; (

**d**) Model 4.

**Figure 8.**Point sampling and its shape context for pylon head type recognition: (

**a**) the sampled edge of pylon head point; (

**b**) the sampled edge points of head model; and (

**c**) the target template used to compute the shape context of point p

_{i}.

**Figure 11.**Original point cloud data of four typical pylons. (

**a**) pylon of Type 1; (

**b**) pylon of Type 2; (

**c**) pylon of Type 3; (

**d**) pylon of Type 4.

**Figure 12.**Filled mages of Pylon 3, Models 2 and 4: (

**a**) the image of Pylon 3’s head points; (

**b**) the image of Model 2; and (

**c**) the image of Model 4.

**Figure 13.**Four typical pylon reconstruction results. The pylon body reconstruction results are colored in blue, while the pylon head reconstruction results are colored in yellow. (

**a**,

**b**), (

**c**,

**d**), (

**e**,

**f**) and (

**g**,

**h**) are the reconstructed model of Type 1, Type 2, Type 3 and Type 4, respectively.

**Figure 14.**Comparison of the pylon body reconstruction in two situations: (

**a**) the top view of the pylon with vegetation points effect; and (

**b**) the same pylon without vegetation points effect.

**Figure 15.**Key point extraction and head reconstruction result: (

**a**–

**c**) the extraction results of alpha = 1 m, 0.5 m, and 0.1 m, respectively; and (

**d**–

**f**) the corresponding head reconstruction results.

**Figure 16.**Pylon reconstruction results: (

**a**) the result of the head without data loss; (

**b**) the head with some data loss; and (

**c**) the head data with whole sections of the structure missing.

Type | Unknown Parameters | Known Parameters |
---|---|---|

Model 1 | H_{1} H_{2} L_{1} L_{2} | Length Height tdx tdy H_{3} L_{3} |

Model 2 | H_{1} H_{2} H_{3} H_{4} L_{1} L_{2} L_{3} | Length Height tdx tdy H_{5} H_{6} L_{4} L_{5} L_{6} L_{7} |

Model 3 | H_{1} H_{3} H_{4} H_{5} H_{6} L_{1} L_{2} L_{5} L_{9} | Length Height tdx tdy H_{2} H_{7} L_{3} L_{4} L_{5} L_{6} L_{7} L_{8} |

Model 4 | H_{1} H_{2} H_{3} L_{1} L_{2} | Length Height tdx tdy H_{4} H_{5} L_{3} L_{4} L_{5} |

ALS System | Flying Height | Horizontal Distance | Flying Speed | Scanning Speed | Rate | Accuracy | Data Density |
---|---|---|---|---|---|---|---|

RIEGL VUX-1 | 50 m above the powerline | 30 m to the powerline | 30 km/h | 200 lines/s | 550 khz | 10 mm | 500 pts/m^{2} |

Accuravy | Type 1 | Type 2 | Type 3 | Type 4 |
---|---|---|---|---|

dh (m) | 0.08 | 0.06 | 0.10 | 0.07 |

Correctness | 90% | 90% | 100% | 100% |

T | N_{1} | r_{1} (%) | ${\mathit{\delta}}_{1}$ (m) | N_{2} | r_{2} (%) | ${\mathit{\delta}}_{2}$ (m) | N_{3} | r_{3} (%) | ${\mathit{\delta}}_{3}$ (m) | N_{4} | r_{4} (%) | ${\mathit{\delta}}_{4}$ (m) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 163 | 40 | 0.008 | 207 | 74 | 0.005 | 180 | 37 | 0.016 | 197 | 63 | 0.011 |

1 | 148 | 58 | 0.006 | 185 | 65 | 0.007 | 93 | 84 | 0.006 | 133 | 81 | 0.005 |

1 | 120 | 83 | 0.007 | 210 | 71 | 0.005 | 172 | 48 | 0.010 | 209 | 77 | 0.007 |

2 | 132 | 37 | 0.022 | 211 | 76 | 0.004 | 196 | 66 | 0.007 | 149 | 39 | 0.014 |

2 | 128 | 74 | 0.005 | 171 | 81 | 0.007 | 84 | 56 | 0.008 | 140 | 61 | 0.014 |

2 | 188 | 71 | 0.008 | 210 | 74 | 0.008 | 121 | 48 | 0.022 | 200 | 42 | 0.015 |

3 | 115 | 50 | 0.013 | 217 | 57 | 0.011 | 196 | 54 | 0.011 | 201 | 46 | 0.015 |

3 | 112 | 57 | 0.012 | 234 | 60 | 0.003 | 227 | 48 | 0.010 | 175 | 31 | 0.022 |

3 | 248 | 58 | 0.006 | 414 | 69 | 0.007 | 360 | 50 | 0.005 | 398 | 44 | 0.010 |

4 | 91 | 80 | 0.007 | 131 | 74 | 0.007 | 107 | 83 | 0.005 | 142 | 58 | 0.019 |

4 | 131 | 44 | 0.016 | 293 | 52 | 0.007 | 286 | 41 | 0.013 | 327 | 41 | 0.013 |

4 | 204 | 48 | 0.008 | 269 | 45 | 0.013 | 188 | 49 | 0.023 | 179 | 34 | 0.010 |

Pylon Body | Type | The Front Plane (m) | The Side Plane (m) |
---|---|---|---|

1 | 1 | 0.061 | 0.052 |

2 | 1 | 0.041 | 0.062 |

3 | 1 | 0.037 | 0.056 |

4 | 2 | 0.038 | 0.090 |

5 | 2 | 0.059 | 0.074 |

6 | 2 | 0.048 | 0.080 |

7 | 3 | 0.153 | 0.075 |

8 | 3 | 0.064 | 0.109 |

9 | 3 | 0.134 | 0.071 |

10 | 4 | 0.053 | 0.090 |

11 | 4 | 0.028 | 0.051 |

12 | 4 | 0.020 | 0.050 |

Model 1 | Model 2 | Model 3 | Model 4 | Type | |
---|---|---|---|---|---|

Pylon 1 | 0.240 | 0.153 | 0.035 | 0.097 | 3 |

Pylon 2 | 0.047 | 0.068 | 0.105 | 0.117 | 1 |

Pylon 3 | 0.078 | 0.028 | 0.120 | 0.037 | 2 |

Pylon 4 | 0.121 | 0.070 | 0.098 | 0.024 | 4 |

Pylon | Ncount | D_{ave} (m) | D_{max} (m) |
---|---|---|---|

1 | 333 | 0.176 | 0.274 |

2 | 440 | 0.231 | 0.283 |

3 | 995 | 0.253 | 0.578 |

4 | 320 | 0.122 | 0.202 |

Pylon | Type | Np | Head Size (Length × Width × Height) | Ncount | Time (s) |
---|---|---|---|---|---|

1 | 1 | 4 | 14.2 m × 7.9 m × 10.4 m | 15,114 | 6 |

2 | 1 | 4 | 13.0 m × 9.2 m × 10.5 m | 22,315 | 6 |

3 | 1 | 4 | 13.9 m × 8.7 m × 10.0 m | 12,520 | 6 |

4 | 4 | 5 | 11.0 m × 5.5 m × 12.5 m | 3152 | 6 |

5 | 4 | 5 | 11.1 m × 4.7 m × 12.5 m | 4272 | 7 |

6 | 4 | 5 | 11.0 m × 5.4 m × 12.7 m | 5095 | 7 |

7 | 2 | 7 | 14.0 m × 5.4 m × 12.7 m | 5762 | 10 |

8 | 2 | 7 | 13.7 m × 5.5 m × 13.0 m | 3619 | 11 |

9 | 2 | 7 | 13.7 m × 6.4 m × 13.0 m | 5008 | 12 |

10 | 3 | 9 | 17.9 m × 4.4 m × 28.8 m | 12,821 | 23 |

11 | 3 | 9 | 19.0 m × 7.5 m × 29.5 m | 14,080 | 24 |

12 | 3 | 9 | 21.7 m × 14 m × 29.0 m | 28,331 | 28 |

N_{1} | r_{1} (%) | ${\mathit{\delta}}_{1}$ (m) | N_{2} | r_{2} (%) | ${\mathit{\delta}}_{2}$ (m) | N_{3} | r_{3} (%) | ${\mathit{\delta}}_{3}$ (m) | N_{4} | r_{4} (%) | (m) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 163 | 40 | 0.008 | 207 | 74 | 0.005 | 180 | 37 | 0.016 | 197 | 63 | 0.011 |

2 | 120 | 83 | 0.006 | 207 | 73 | 0.007 | 168 | 50 | 0.009 | 207 | 74 | 0.008 |

Alpha (m) | Ncount | D_{ave} (m) | D_{max} (m) |
---|---|---|---|

1 | 333 | 0.176 | 0.274 |

0.5 | 439 | 0.177 | 0.322 |

0.1 | 1077 | 0.244 | 0.435 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, R.; Jiang, W.; Huang, W.; Xu, B.; Jiang, S.
A Heuristic Method for Power Pylon Reconstruction from Airborne LiDAR Data. *Remote Sens.* **2017**, *9*, 1172.
https://doi.org/10.3390/rs9111172

**AMA Style**

Zhou R, Jiang W, Huang W, Xu B, Jiang S.
A Heuristic Method for Power Pylon Reconstruction from Airborne LiDAR Data. *Remote Sensing*. 2017; 9(11):1172.
https://doi.org/10.3390/rs9111172

**Chicago/Turabian Style**

Zhou, Ruqin, Wanshou Jiang, Wei Huang, Bo Xu, and San Jiang.
2017. "A Heuristic Method for Power Pylon Reconstruction from Airborne LiDAR Data" *Remote Sensing* 9, no. 11: 1172.
https://doi.org/10.3390/rs9111172