# Newly Designed Identification Scheme for Monitoring Ice Thickness on Power Transmission Lines
## 3 New Scheme for Iced Transmission Line Identification
### Image De-Noising  
Figure 4 shows the block diagram of image de-noising. Based on the block diagram in Figure 4, the input data from this system is the PTLI image that has been restored in color. The color-corrected image still contains noise, so a filter is needed to remove noise and retain critical information in the image. If the image color restoration stage focuses on lighting and color restoration, this stage focuses on filtering out image noise. After the PTLI image data is prepared, the image containing noise will be restored. Then the output from this system is a de-noising image while maintaining the edges of the transmission line. The Gaussian smoothing concept focuses on filter coefficients enhanced in this method by relative pixel intensities. This method obtains the resulting image pixel values from the weighted average of neighboring pixels through a convolution process. The smaller the pixel's spatial weight, the greater the pixel distance to the central pixel analysis in an image, and vice versa. The more significant the difference in intensity between two pixels, the smaller the photometric weight, so the contribution to the weighting is small. Three parameters control this filter method: kernel dimension, standard deviation to control factors of spatial weighting, and standard deviation to control factors of photometric weighting.  
Figure 4: The block diagram of image de-noising.  
Spatial weighting in this filter means giving weight to pixels according to the distance between them and those that are the center of analysis in the image. Spatial weight (WS) is the realization of measuring spatial proximity in a Gaussian function that calculates the spatial distance between pixels using Euclidean distance. The calculation of the spatial weight for each pixel is shown in Equation (9).  
\[\begin{array}{l}W_{s}[x,u]=\exp\left\{\frac{-d^{2}[x],[x,u]}{2\sigma^{2}s} \right\}.\\ \qquad\qquad=\exp\left\{\frac{-u^{2}}{2\sigma^{2}s}\right\}\end{array} \tag{9}\]  
With:  
\(W_{s}[x,u]\): Spatial weight of each pixel in the kernel;  
\(x\qquad\): Kernel midpoint (\(w\) (\(0\), \(0\)));  
\(u\qquad\): Neighboring elements in the kernel;  
\(\sigma_{s}\qquad\): Standard deviation for spatial weighting.  
Meanwhile, photometric weighting means that the weighting of pixels is based on the difference between the pixel's intensity and the intensity of those that are the center of analysis in the image. Photometric weight (WR) is the realization of measuring the difference in intensity based on the photometric similarity in the Gaussian function, which measures the difference in intensity between pixels using the Euclidean distance. The calculation of the photometric weight at each pixel is shown in the following equation:  
\[\begin{array}{l}W_{s}[x,u]=\exp\left\{\frac{-d^{2}[\{g[x],g[x-u]\}]}{2\sigma ^{2}R}\right\}\\ \qquad\qquad=\exp\left\{\frac{-\{g[x],g[x-u]\}^{2}}{2\sigma^{2}R}\right\}. \end{array} \tag{10}\]  
With:  
\(W_{s}[x,u]\): Photometric weight per pixel in the kernel;  
\(x\qquad\): Kernel midpoint (\(w\)(\(0\), \(0\)));  
\(u\qquad\): Neighboring elements in the kernel;  
\(g[x]\qquad\): Pixels, which are the center of analysis in degraded images;  
\(g[x-u]\): Neighboring pixels of pixel \(g\) [\(x\)];  
\(\sigma_{R}\qquad\): Standard deviation for photometric weighting.  
The two weights (spatial and photometric) are normalized to one weight value \((W)\) as in Equation (11).  
\[W[x,u]=W_{s}[x,u]*W_{R}[x,u]. \tag{11}\]  
After weighting the pixels, the resulting pixel values can be found in Equation (12).  
\[f[x]=\frac{\sum_{u=-N}^{N}W[x,u]g[x-u]}{\sum_{u=-N}^{N}W[x,u]}. \tag{12}\]  
With:  
\(W[x,u]\): Neighboring weight values in the \(W\) weight matrix;  
\(f[x]\quad\): Calculated pixel value.