# Newly Designed Identification Scheme for Monitoring Ice Thickness on Power Transmission Lines
## 4 Ice Thickness Calculation Using 3D Measurement  
The principal indicator of an ice disaster is ice thickness. This section describes a method for ice thickness measurement based on our proposed iced transmission line identification scheme. After obtaining the key point through the point-matching algorithm to find similar key points, the key point is used as a reference point in determining 3D coordinates. Figure 14 illustrates the flowchart of the ice thickness calculation. Figure 13: An example of the labeling used in this research. (**a**) Unlabeled object; (**b**) The process of labeling ‘1’ on the current pixel; (**c**) the mask is scanned at the next unlabeled pixel (2, 0); (**d**) The process of labeling ‘2’; (**e**) the mask is scanned at the next unlabeled pixel (3, 0); (**f**) The process of labeling ‘2’ and expanded the labeling area; (**g**) The mask is scanned at the next unlabeled pixel (1, 1); (**h**) Pixels are labeled with ‘1’ because the diagonals of adjacent pixels (0, 0) are already labeled with ‘1’; (**i**) The process of labeling area expanded; (**j**) The labeled areas ‘1’ and ‘2’ intersect; (**k**) The mask is scanned at the next unlabeled pixel (2, 1); (**l**) The eight connected neighboring pixels have their labels updated. This process begins with determining the intrinsic and extrinsic camera parameters through calibration. This initialization aims to investigate the relationship between 3D world coordinates and 2D image coordinates, which will later be utilized as a reference for determining the 3D point at each key point. This paper uses [PERSON]'s calibration methods [28]. The calibration process provides the internal parameters of the camera, such as focal length and distortion factor, as well as the external parameters, including the rotation matrix and translation matrix. The calibration process is shown in Figure 15. Multiple sets of calibration images can be captured by adjusting the relative positions of the camera and the plane target. The method assumes an ideal pinhole camera model and quickly solves the mapping matrix between the target and image planes using the equations established by the calibration images. The internal and external camera parameters are then obtained by matrix decomposition. Finally, all the obtained linear parameters and the simultaneous addition of lens distortion parameters undergo optimization searches to obtain the optimal solution for all parameters. After setting up the camera parameters, the next step is linear triangulation. Binocular stereo vision relies on the disparity value of the same point in different viewing angle images to calculate the depth value using the triangulation principle, i.e., the projection points \(p_{1}\) and \(p_{2}\) of a specific point P on the left and right image pairs in space. The camera structure parameters are used to calculate the 3D space coordinates of point P.  
As shown in Figure 16, it is assumed that the left camera coordinate system \(O-xyz\) is located at the origin of the world coordinate without rotation, the image coordinate system is \(O_{l}-x_{l}y_{l}\), and the effective focal length is \(f_{l}\). The right camera coordinate system is \(O_{r}-x_{r}y_{r}\)\(z_{r}\), and the image coordinate system is \(O_{r}-x_{r}y_{r}\). The effective focal length is  
Figure 14: The flowchart of the ice thickness calculation. Figure 15: The flowchart of [PERSON]’s camera calibration method. \(f_{r}\), and the relationship between the left and right camera coordinate systems and their corresponding image coordinate systems can be obtained from the camera perspective transformation model:  
\[ \begin{bmatrix}x_{l}\\ y_{l}\\ 1\end{bmatrix} =\frac{1}{s_{l}} \begin{bmatrix}f_{l}&0&0\\ 0&f_{l}&0\\ 0&0&1\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix} . \tag{24}\]  
\[ \begin{bmatrix}x_{r}\\ y_{r}\\ 1\end{bmatrix} =\frac{1}{s_{r}} \begin{bmatrix}f_{r}&0&0\\ 0&f_{r}&0\\ 0&0&1\end{bmatrix}\begin{bmatrix}x_{r}\\ y_{r}\\ z_{r}\end{bmatrix}