# Automatic Extraction of High-Voltage Power Transmission Objects from UAV Lidar Point Clouds
## 3 Method
### Feature Calculation  
In order to extract the transmission objects, different features of PLs and pylons, i.e., dimensional features (eigenvalue-based) and distribution features (point-based) of the point clusters were utilized. The distribution features consisted of height features (e.g., local digital elevation model (DEM), digital surface model (DSM), and height difference) and density features.  
**Feature calculation in 2D grids**: The terrain where power transmission lines are constructed is generally uneven. Nevertheless, power pylon points normally have large height differences and continuous vertical distributions, and their height values tend to be high [67]. These properties of distribution are not affected by the terrain and surrounding objects, providing a strong basis for pylon identification.  
Considering a grid as a unit, features of point data in each grid were calculated, including DEM, DSM, and height-difference. Among them, DEM and DSM were obtained directly through statistical analysis of the point cloud. The height difference was calculated by subtracting DEM from DSM. Notice that the PL points extracted earlier from the corresponding point cloud data should be separated out when the grid-based DSM features are computed.  
DEM reflects the distribution of topographic relief in the mapping area. The adverse impact of topography fluctuation on pylon extraction can be suppressed by normalizing the DSM using DEM. Normalized DSM (nDSM) reflects the local height differences within the point cloud data. Because of the large height difference of HV towers, the pylons are easily visible in nDSM.  
**3D feature calculation:** According to [PERSON] et al. [41] and [PERSON] et al. [27], PL points have the properties of local linearity and consistency of local convergence, which can be used to distinguish PLs from other objects. In Figure 3, these dimensional features can be intuitively observed. Points in each 2D grid were first clustered based on Euclidean distance, then the voxels in each cluster were taken as a basic unit to calculate the dimensional features of points. By computing the covariance matrix [7] and the eigenvalues of all points in the clustered voxels, the linear, planar, and spherical features were  
Figure 2: Voxels colored by height: (**a**) voxel blocks including power lines (PLs); (**b**) voxel blocks including a pylon; (**c**) voxel blocks including no power transmission objects.  
derived. The linear structure of a point set was determined by comparing the three values a\({}_{\text{1D}}\), a\({}_{\text{2D}}\), and a\({}_{\text{3D}}\), calculated as:  
\[\text{a}_{\text{1D}}=\frac{\sqrt{\lambda_{1}}-\sqrt{\lambda_{2}}}{\sqrt{\lambda_ {1}}},\ \ \ \text{a}_{\text{2D}}=\frac{\sqrt{\lambda_{2}}-\sqrt{\lambda_{3}}}{\sqrt{\lambda_ {1}}},\ \ \ \text{a}_{\text{3D}}=\frac{\sqrt{\lambda_{3}}}{\sqrt{\lambda_{1}}}\, \tag{3}\]  
where \(\lambda_{1}\), \(\lambda_{2}\), \(\lambda_{3}(\lambda_{1}>\lambda_{2}>\lambda_{3})\)[68] refer to the eigenvalues of the covariance matrix of each point set.  
**Height distribution:** By analyzing the patterns shown in Figure 4, it can be obviously seen that the relative height and local linearity are features able to distinguish PLs from other objects. The clustering distance is indicated by the distance calculated by the height distribution feature. The value is the minimum height gap from an overhead PL to the ground objects in a span (the space between two adjacent pylons). Using the height distribution histogram (Figure 4b) of a test dataset in Figure 4a, where the points above 13 m are highlighted, the gap was fixed at the height of about 8 m. The gap between the first and the last peak was considered similar to the height of the top area of a tower, named as the head of the tower.  
Figure 4: _Cont._  
Figure 3: Parts of the point cloud of transmission line from unmanned aerial vehicle (UAV) data (colored by height): (**a**) side view; (**b**) top view.