## 4 Result and Discussion
### Edge Contour Extraction of Structures  
Several types of operators can be employed for the edge detection, including the Sobel [28] operator, Prewitt operator [29], [PERSON] operator [30], and log operator [31], in which different methods are used to solve the gradient extremum. In this paper, all the five operators have been applied to detect the edge of the specimen using the image after perspective transformation, as shown in Figure 9. Compared with the Log operator, the edge detection results of the other four operators are not satisfactory due to the lack of edge information, which in turn has a negative impact on the accuracy. The advantage of the Log operator over the other methods is that the Gauss spatial filter is employed to smooth the original image, which minimizes the influence of noise on edge detection. The Log operator is a second-order edge detection operator [32], as shown in Equations (19) and (20):  
\[\
abla^{2}f=\frac{\partial^{2}f}{\partial x^{2}}+\frac{\partial^{2}f}{\partial y ^{2}} \tag{19}\]  
\[\left\{ \begin{array}{l}\frac{\partial^{2}f}{\partial x^{2}}=f(i,j+1)-2f(i,j) +f(i,j-1)\\ \frac{\partial^{2}f}{\partial y^{2}}=f(i+1,j)-2f(i,j)+f(i-1,j)\end{array} \right.. \tag{20}\]  
Based on the second-order differential of the image, the extreme points can be generated at the abrupt position of the gray value. According to these extreme points, the edge of the structure can be determined. Figure 9: The applied five kinds of edge detection operators; (**a**) [PERSON] operator edge detection; (**b**) [PERSON] operator edge detection; (**c**) [PERSON] operator edge detection; (**d**) log operator edge detection. As shown in Figure 9, the distribution of the light intensity respecting the specimen is inconsistent, and the gray value of some edges does not change significantly, resulting in discontinuity in the detection of some edges. The discontinuous edges like Figure 9 are very normal in actual structure images. On the other hand, the distribution of edge pixels obtained by various edge algorithms is also different. The distribution density of edge pixels in this paper is shown in Figure 10.  
As shown in Figure 10, the edge features obtained by the above five operators are entirely different. For instance, the edge distributions in some operators are three pixels wide, while in some operators, e.g., the Log operator, the edges are just concentrated in one pixel. Because of the large scatter in the pixel distribution, it is difficult to determine the exact edge position of the structure. Naturally, an efficient edge detection operator should have the centralized pixel distribution and good pixel continuity. After comparison, it is found that the Log operator can extract the edges of the structure relatively intact and maintain a relatively centralized distribution of edge pixels. Thus, the log operator has been selected in extracting the edge of the structure. The phenomenon of discontinuous edges and scattered edge distribution of the above-mentioned is similar to the detection issue in real structures, which is induced by the environment of measurement. In dealing with such kind of problem, the data processing and analysis process have been employed, as illustrated in the following. As an important part of the deformation, the edge of the structure is the key content of this paper. For the specimens in this paper, the upper and lower edges of the bridge deck and the lower edges of the specimens can be used as characteristic contours to analyze the overall deformation of the structure. From Figure 2, we can see that the noise caused by the environment will make the edge location confused. Points with continuous gradient change are very rare in the actual  
Figure 10: Distribution density of edge pixels by various edge detection operators; (**a**) edge width distribution degree of [PERSON] operator; (**b**) edge width distribution degree of [PERSON] operator; (**c**) edge width distribution degree of [PERSON] operator; (**d**) edge width distribution degree of log operator. structure image.