(2) Edge detection

Figure 5 shows that there is still background noise in the image and the objectives and background of the segmentation image have low contrast. Thus, the modified Canny operator edge detection algorithm is selected to trace boundaries of objects through extraction of information about attributes of endpoints of edges, in particular orientation and neighborhood relationships [19,20]. In the algorithm, the image is smoothed by Gaussian filter which is used to determine the adjustable parameters based on the characteristics of the image. Most of the background is divided according to the information of the image edge for reducing imprecise background and objective. Then, the image edge can be detected by using Canny operator. The image processing result is shown in Figure 6.

**Figure 6.** The comparison diagram of the original image and the binarization image and the image after edge detection processing. (**a**) Original image. (**b**) Binarization image. (**c**) Image after edge detection processing.

The modified Canny algorithm is used to calculate the amplitude of the gradient through the directional derivatives for pixels of the image G(i,j) in the selected neighborhood. Equations (3)–(9) are as follows:

The calculation of the *X* directional derivative:

$$G\_x(i,j) = F(i+1,j) - F(i-1,j) \tag{3}$$

The calculation of the *Y* directional derivative:

$$G\_{\mathcal{Y}}(i,j) = F(i,j+1) - F(i,j-1) \tag{4}$$

The calculation of the 45◦ directional derivative:

$$G\_{45}(i,j) = F(i+1, j+1) - F(i-1, j-1) \tag{5}$$

The calculation of the 135◦ directional derivative:

$$G\_{135}(i,j) = F(i-1,j+1) - F(i+1,j-1) \tag{6}$$

The calculation of the first partial derivatives:

$$E\_{\mathbf{x}} = G\_{\mathbf{x}}(i, j) + \frac{G\_{45}(i, j) + G\_{135}(i, j)}{2} \tag{7}$$

$$E\_y = G\_y(i, j) + \frac{G\_{45}(i, j) - G\_{135}(i, j)}{2} \tag{8}$$

The calculation of the gradient magnitude:

$$A(i,j) = \sqrt{E\_{\mathbf{x}}^2 + E\_{\mathbf{x}}^2} \tag{9}$$

#### (3) Region growth method

After obtaining the improved Canny edge detection images, the icing thickness can be obtained by calculating the difference between the edge of the non-iced insulator image and the edge of the iced insulator image. Besides, in order to obtain the icicles and air gap parts of the ice-covered insulators' image for identifying the icing degree of the insulators more accurately, this paper determines the location of icicles by using the regional growth method, the schematic diagram as shown in Figure 7.

**Figure 7.** Regional growth method diagram.

Regional growth corresponds to the process of development of a set of pixels and regions extend to a larger area. Each pixel of the edge of the non-ice shed parts of ice-covered insulators is set as the seed pixel, which is used as the starting point of growth. By inspecting the pixel value of all direction point of neighborhoods, when the pixel value of neighborhood point is the same as the pixel value of seed point, this point is defined as a new seed point. The neighborhood point will be searched continuously until it cannot satisfy the above condition. Due to the fact that the direction of the edge region of the iced insulators image is downward, the point of the top directional can be eliminated. After the process of regional growth method, it can be considered that the selected points are the tip of icicle, and then it separates the tip of icicle part and the air gaps according to the location point of the tip of icicle.

The distance between the tip of icicle and the edge of insulator is considered the air gap length. However, the pixel value of the air gap length obtained by the Canny edge detection image method needs to be transformed in millimeters for further accurate calculation. However, the air gap length cannot be used as the only parameter to indicate the icing degree of insulators because of it is impacted by the di fferent insulator models and angles of camera recording. Thus, the icing degree is indicated by the Rg (the ratio of the air gap length to the insulator length) for avoiding the influence of these factors. Then, we can establish the relationship between the icing degree and the Rg.

#### **4. Analyze the Results of Characteristic Extraction**

The results of ice thickness, icicle length, and Rg are as shown in Table 2.


**Table 2.** The results of ice thickness, icicle length, and Rg.

As shown in Table 2, it can be found that non-uniformity distribution of ice accretion on the surface of insulators and the ice is mainly accumulated on the windward side of insulators. When the cold room maintains the ambient temperature at −12 ◦C, the low-temperature droplets frozen on the surface of insulator sheds under the experimental condition. The ice thickness shows the nonlinear increasing tendency on the sheds of insulators during the process of ice accumulation. From 0 min to 20 min, the ice thickness increased slowly, only 7 mm. While from 30 min to 50 min, ice thickness increased 64 mm, the increment is about 9 times higher than the former, which indicates that the ice layer grew rapidly and the insulators' icing degree became more serious during this period.

The variation of icicle length and Rg during ice accretion regime is shown in Figure 8. The super-cooled droplet formed ice, and simultaneously, the test voltage produced joule heat which can cause the melting and dripping of accreted ice. Hence, the ice accreted on the insulators is a dynamically varying phenomenon. However, each shed of the ice-covered insulators shows an obvious decreasing tendency of the variation of icicle length and Rg because of the serious degree of icing e ffect. Note that the icicle length of the second unit of insulators slightly decreases and Rg slightly increases between 20 min and 30 min. In this period, leakage current generated by heat energy can cause the melting of icicles and can even make some of them fall down to the ground. Although the electric field distortion of the insulator surface will increase further and the thermal e ffect of the arc discharge will have a negative influence on the ice accumulation, the freezing influence of precipitated droplets dominates the shed surface so the ice layer can maintain growth and the icicle length can keep increasing and Rg still can decrease at this time. Therefore, the variations of icicle length and Rg correspond well to the ice accretion process, which can be used to judge the risk of the icing degree.

**Figure 8.** The variation of icicle length and Rg during the ice accretion regime.

In addition, from the HV (high voltage) electrode to the ground side, the shed separation between cap-and-pin insulators is significantly reduced by the increasing of icicles. Because the super-cooled droplet was subjected to the e ffect of gravity, the ice bridging condition of the bottom side of the insulator string units are heavy. At 30 min, the average ice thickness just reaches 24 mm, the value of the Rg between the second unit and the fifth unit of the ice-covered insulators is more than 40%, the first unit of ice-covered insulators Rg is 0%, which indicates the icing degree from the first unit to HV electrode is extremely serious. At 50 min, the first unit and the third unit are fully bridged. While the fourth and fifth units are without complete bridging, the value of Rg is 37.8 and 45.7% respectively. Meanwhile, the partial arcs constantly burn at the air gaps, which inhibits the growth of the icicles. Finally, the ice growth rate and the melting rate will reach a balance state that causes these units to be unable to be bridged completely. By analyzing the icing degree of every unit of the insulator string, we can evaluate the hazards of ice-covered insulators accurately.

In this way, through the independent analysis of the icing degree of di fferent insulator sheds, the icing degree of insulators can be evaluated more accurately, which avoids the simple generalization of icing conditions of di fferent types of insulators under the same environmental conditions, enhances the detailed judgment of the icing degree of insulators, and reduces the estimation error of the icing degree.

Because most of the transmission lines are exposed in the field, the monitoring equipment also needs to be exposed in the field for a long time, which will inevitably be a ffected by severe weather such as strong wind, high temperature, and rainstorms. There are still a series of problems in security protection, energy consumption, wireless communication, data encryption, and video image compression. In short, there will be some obstacles to the implementation of the method in this paper, but this is mainly a technical problem. With the development of science and technology, these obstacles will be solved one by one. At the same time, when dealing with di fferent background noise, we can improve the denoising method. We can judge the type of noise by intelligent algorithms and select the corresponding denoising method automatically. The practical application of this method needs further research.
