# Bridge Displacements Monitoring Method Based on Pixel Sequence
## 4 Experimental Results and Analysis
### Edge Detection Effectiveness
#### 4.2.2 DoG Algorithm for Edge Extraction  
Common edge detection operators include Sobel, Prewitt, and Canny operators. These operators are mainly used to locate edges based on changes in grayscale values in the image. The Canny operator performs non-maximum suppression and double thresholding after grayscale detection, making it less susceptible to noise compared to other operators and, thus, widely applicable in various scenarios. However, in many scenarios, the results obtained by the aforementioned operators cannot be directly used. The edge extraction performed on the ROI region identified earlier yields the following results (Figures 15-17):  
Figure 14: The result of the Region of Interest (ROI) selection.  
Figure 13: Grayscale image using the weighted averaging method.  
The above results indicate that common operators cannot accurately extract the edges of the beam under the experimental conditions, highlighting the significant limitations of traditional operators.  
Figure 16: The result of the Prewitt operator.  
Figure 17: The result of the Sobel operator.  
Figure 15: The result of the Canny operator.  
In the novel edge detection algorithm proposed in this paper, the grayscale image undergoes initial processing through Gaussian filtering at two distinct scales. This involves the generation of the saliency map using Gaussian filtering with different standard deviations, where one filter has a larger standard deviation while the other has a smaller one. The smaller-scale Gaussian filter is employed to preserve the edges and details within the image, while the larger-scale Gaussian filter aids in monitoring. The Gaussian difference image is obtained by subtracting the outputs of the two filtered images by the Gaussian filters.  
When selecting scales, the main considerations include edge size, potential displacement range, and image characteristics. If the edge width is small and fine, such as thin lines, a smaller Gaussian scale is needed. Conversely, if the edge is rougher, a larger scale value is required to capture boundary contours effectively. Smaller-scale Gaussian filters perform better at higher spatial frequencies, covering edge features effectively through different scales of Gaussian differences, thus enhancing edge detection sensitivity and accuracy. Considering that the edges of the experimental beam are approximately seven pixels wide, it is advisable to choose a relatively smaller scale within a reasonable range when selecting a smaller-scale Gaussian filter.  
During the initial processing of Gaussian difference, the blurring effect induced by Gaussian filtering may result in image blur, thereby rendering the resultant difference image ineffective. Therefore, it is necessary to perform image binarization to enhance the image information. In addition, during the Difference of Gaussians (DoG) process, two different scales of Gaussian kernels need to be applied.  
For the selection of a smaller scale, given the relatively diminutive edges in this study, an initial decision is made with a smaller scale of 0.5 and a larger scale of 8. The binarization threshold is established at 10. The Gaussian kernel size is 3 \(\times\) 3, and the Gaussian kernels for the two scales are as follows (Figure 18):  
Under the Gaussian kernel scales of 0.5 and 8, with a binary threshold of 10, the resulting edge structure is shown in Figure 19:  
Observations reveal that the Gaussian difference algorithm proposed in this paper adeptly extracts the edge features of the structure in comparison to alternative algorithms. It has a higher efficiency in suppressing noise and achieves a more complete extraction of edge line shapes.  
Figure 18: Gaussian difference method, Gaussian kernel (**(a)** Description of a smaller Gaussian kernel; **(b)** Description of a bigger Gaussian kernel).