# Multi-Point Displacement Synchronous Monitoring Method for Bridges Based on Computer Vision
## 2 Multi-Point Displacement Synchronous Monitoring Method  
We used the Scale-invariant Feature Transform (SIFT) [19; 20; 21; 22; 23; 24] algorithm to generate structural feature points. The SIFT algorithm decomposes the image into scale space and calculates extreme points in the scale space. These extreme points are detected after down-sampling and have obvious image features called feature points. Further, we calculate the gradient direction of each feature point and assign direction values to the feature points. Even if the object in the image undergoes displacement, the detected feature points can be matched through directional values. Therefore, the feature points extracted by the SIFT algorithm are invariant to scale, direction, and rotation. In addition, SIFT feature points are also stable to brightness change, affine transformation, and noise. The SIFT algorithm process is shown in Figure 1.  
The structural surface has natural texture features, which can be extracted and matched using the SIFT algorithm before and after deformation. The extracted feature points can be used as measurement points for displacement monitoring. We placed the calibration board  
Figure 1: SIFT algorithm process.  
in two different positions and took photos. The extracted calibration board feature points are shown in Figure 2a, and the matching results of feature points are shown in Figure 2b. There are 2131 extracted feature points, and Figure 2a,b only presents the matching results of the first 9 feature points. The green line in Figure 2b is the matching line of feature points on the calibration board.  
As shown in Figure 2b, the feature points on the calibration board at different positions can be matched using the SIFT algorithm. The structural surface has natural features, and the SIFT algorithm can extract these feature points. We used these feature points as monitoring points to achieve structural full-field displacement monitoring. As shown in Figure 3, we fixed the camera in front of the structure and captured two images, \(I_{1}(x,y)\) and \(I_{2}(x,y)\), before and after deformation. Due to the fixed camera, the same image coordinate system _Oxy_ can be established before and after deformation. The coordinates of feature point \(A_{1}\) (Figure 3 red dot) extracted before deformation are \(A_{1}(x_{1},y_{1})\), and the coordinates of its matching point after deformation are \(A^{\prime}{}_{1}(x^{\prime}{}_{1},y^{\prime}{}_{1})\). The vector formed by the feature points \(A_{1}(x_{1},y_{1})\) and \(A^{\prime}{}_{1}(x^{\prime}{}_{1},y^{\prime}{}_{1})\) is the displacement \(D_{1}\). \(D_{1}\) has two parameters, length \(L_{1}\) and angle \(\theta_{1}\). The calculation method for vector \(D_{1}\) is as follows:  
\[L_{1}=\sqrt{\left(x^{\prime}{}_{1}-x_{1}\right)^{2}+\left(y^{\prime}{}_{1}-y_{ 1}\right)^{2}} \tag{1}\]  
\[\theta_{1}=\arctan\frac{\left|x^{\prime}{}_{1}-x_{1}\right|}{\left|y^{\prime}{ }_{1}-y_{1}\right|} \tag{2}\]  
Figure 2: Feature points extraction and matching results based on the SIFT algorithm. (**a**) Feature points on the calibration board. (**b**) Matching of feature points on calibration board at different positions.  
\(D_{1}\) is the displacement of one point on the structural surface, and the displacement of all feature points on the structural surface is the set:  
\[D=\{D_{i}:i=1,2,\ldots,n\} \tag{3}\]  
Set \(D\) comprises all \(D_{i}\), which is the initial calculation result of the structural multi-point displacement. Figure 4 shows the multi-point displacement calculation flowchart.  
Figure 4: Calculation flowchart of structural multi-point displacement.  
Figure 3: Calculation method for structural multi-point displacement.