# Automatic Extraction of High-Voltage Power Transmission Objects from UAV Lidar Point Clouds
## 3 Method
### Reconstruction of Power Transmission Components
#### 3.5.2 Modeling of pylons Based on Tower Center Localization
Since the optimization process of the energy model was non-convex, the towers were reconstructed by energy optimization using Markov chain Monte Carlo (MCMC) [PERSON] et al. (2018). **Insulator modeling:** Insulator reconstruction was achieved by insulator matching based on a region growing method. In most cases, it was fixed to a tower model [PERSON] et al. (2018). Generally, insulator points were determined by contextual search and then clustered [PERSON] et al. (2018). The insulator candidate points were searched within several successive adjacent vertical profiles in the principle direction of the PL \begin{table}
\begin{tabular}{l l} \hline \hline
**Input: HV Towers in Grids \(M^{\text{c}}\).** \\ \hline \multicolumn{2}{l}{Output: coordinates of HV tower centers} \\ \hline \multirow{2}{*}{1.} & Divide points \(\text{C}_{\text{i}}\) in \(\text{M}_{\text{i}}^{\text{c}}\) into layers at a certain height gap (2 m). Calculate center points P of all layers. Take two adjacent layers (\(\text{Pi},\text{ Pi}+1\)) as a pair, calculate \(\text{d}_{\text{rc}}\) and \(\theta_{\text{rc}}\). \\ \hline \multirow{2}{*}{2.} & Query the maximum \(\text{d}_{\text{Mrc}}\) from \(\{\text{d}_{\text{rc}}\}\); if \(\text{d}_{\text{Mrc}}>0.5\) m, then compute the e passing through \(\text{p}_{0}\) (another center point) and e and repeat this process to \(\text{p}_{\text{c}}\). \\ \hline \multirow{2}{*}{3.} & Vote for the one, \(\text{p}_{r}\) or \(\text{p}_{c}\), with larger \(\theta_{\text{rc}}\) when each \(\theta_{\text{rc}}\) is calculated. Delete the one with more votes from the two center points \(\text{p}_{r}\) and \(\text{p}_{c^{\prime}}\) and delete all \(\text{d}_{\text{rc}}\) and \(\theta_{\text{rc}}\) values relating to it, then go back to step 2. \\ \hline \multirow{2}{*}{4.} & If \(\text{d}_{\text{Mrc}}>0.5\) m, return the average coordinate values of the remaining center points \(coord_{\text{avg}}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The tower center coordinate calculation algorithm. Figure 12: The pylon reconstruction: (**a**) pylon modeling; (**b**) the diagram for insulator searching; (**c**) the reconstruction of the labeled insulators. (Figure 12b). In fact, insulator model construction was accompanied by the processes of line fitting and region growing along the vertical profile. The midpoint of the insulator point cloud was taken as the modeling center. For transversal insulators (points in the red ellipse in Figure 12a), the points located along the PL from its end until the center of the nearest tower were marked as insulator points. When the growth and fitting of the whole PL was completed, the insulator points on the corresponding line were also searched out. The yellow dots in Figure 12b were the centers of insulators. Note that the two (in the dashed ellipse) on the top were removed, as there was no insulator along the shielded wire. Finally, corresponding types of insulator models were added to the tower model.