## 3 Monitoring Methods
### Calculation of Slope Displacement  
First, the proportional coefficient \(\rho\) is calculated according to the object-image relationship. \(\rho\) denotes the ratio of the actual distance to the corresponding pixel distance, whose unit is mm/pixel. This value is mainly related to the parameters of the digital camera and the distance from the camera to the simulated slope. The acquisition method is described as follows:  
1. The distance between the landmarks is obtained to calculate the proportional coefficient \(\rho\). The landmarks are placed separately at the top, bottom, and middle of the simulated slope, amounting to a total of nine landmarks. The actual distance between the landmarks is measured using a tape measure, and the digital camera is fixed 20 m in front of the simulated slope. The sub-pixel algorithm is used to calculate the center coordinates of the ring mark, and the pixel distance between adjacent landmarks is calculated according to their coordinates. The proportional coefficient is calculated according to the coordinates of the landmarks and is expressed as follows:  
\[\rho=\frac{L_{a}}{l_{a}} \tag{15}\]  
where \(L_{a}\) is the actual average distance of all landmarks, with units in \(mm\) and \(l_{a}\) is the pixel average distance between the two landmarks, whose unit is pixels. 2. The distance from the digital camera to the landmarks is calculated:  
When the resolution of the camera parameters, CMOS size, \(fov\), focal length, and other parameters, along with the proportional coefficient \(\rho\), are known, the distance from the digital camera to the landmark can be calculated with these parameters. The formula is as follows:  
\[d=\frac{\rho\times f\times p}{q} \tag{16}\]  
where \(d\) is the distance from the digital camera to the landmark, with units in mm; \(q\) is the size of digital camera CCD, with units in mm; \(f\) is the focal length of the digital camera, with units in mm; and \(p\) is the resolution of the digital camera, with units in pixels. As shown in Figure 6, the initial position of the digital camera is at point \(A\), and point \(B\) is the initial position of the landmark. The corresponding coordinate system is established. The \(X\) axis marks the horizontal direction, the \(Y\) axis marks the direction of the digital camera, and the \(Z\) axis marks the vertical direction, forming the right-handed coordinate system. At the initial time \(t_{0}\), the digital camera located at point \(A\) captures images of the landmarks located at point \(B\). At time \(t_{1}\), due to the influence of other disturbance factors, the position of the digital camera moves from point \(A\) to point \(A^{\prime}\), and the position of the landmark moves from point \(B\) to point \(B^{\prime}\). The digital camera located at point \(A^{\prime}\) takespictures of the landmarks located at point \(B^{\prime}\). The displacement components of landmark \(B\) on the \(X,Y,\) and \(Z\) axes are \(\Delta x_{1},\Delta y_{1},\) and \(\Delta z_{1}\), respectively. \[\Delta S=\sqrt{\Delta{x_{1}}^{2}+\Delta{y_{1}}^{2}+\Delta{z_{1}}^{2}} \tag{17}\]  
where \(\Delta S\) is the displacement of landmark \(B\). 3. Calculating \(\Delta x_{1}\) and \(\Delta z_{1}\)  
As shown in Figure 7, at time \(t_{0}\), the digital camera is located at point \(O\), the vertical range of the image captured is \(MN\), the horizontal range is \(PQ\), and the location of the monitoring landmark is \(E\). At time \(t_{1}\), the digital camera moves to point \(O^{\prime}\), the vertical range of the photograph is \(M^{\prime}N^{\prime}\), the horizontal range is \(P^{\prime}Q^{\prime}\), and the monitoring point \(E\) moves to \(E^{\prime}\). At time \(t_{0}\), for the image captured from point \(O\), the sub-pixel ring algorithm is used to calculate the vertical coordinates \(ME\) of monitoring point \(E\), in units of pixels. After the displacement of the digital camera and the simulated slope at time \(t_{1}\) are known, the  
Figure 6: Schematic diagram of the experimental principle.