# Real-Time Tunnel Deformation Monitoring Technology Based on Laser and Machine Vision
## 2 Methodology  
The tunnel collapse process is the deformation of the construction fracture surface in the tunnel, which takes a fixed point of the earth as a reference. At present, the new Austrian tunneling method [25], which includes designing an initial support and secondary lining to the construction fracture surface [26], is mostly adopted in tunnel construction. The secondary lining is constructed on the basis of the initial support when the deformation of the initial support becomes stable [27]. Therefore, the deformation of the secondary lining surface can be ignored; however, the deformation of the excavation surface and the edge part of the initial support is significant. The proposed system takes a fixed point of the earth as monitoring reference and measures the deformation of excavation surface. Given the good directivity and energy concentration of a laser, as well as the dusty and dark tunneling environment in low visibility, a laser beam is used to transmit the monitoring reference from the fixed point to the measured point through the dust and darkness, thereby forming an optical projection of the fixed point on the intersecting surface near the measured point, which is the optical equivalent reference, to monitor the tunnel deformation in the system. A sketch map of the system is shown in Figure 1.  
A laser transmitter module, whose laser beam points to the intersecting surface near the measured points and forms an optical projection of the fixed point as a laser spot, is firmly fixed on the earth. To obtain the position relationship between the measured point and the fixed point, an image acquisition module mounted on the measured point and located perpendicularly to the laser beam is used to acquire the laser spot image of the laser beam. This module monitors the laser spot position in the image coordinate system with machine vision technology. The image acquisition mode is shown in Figure 2. The image sensor acquires the laser spot image through a laser receiving screen placed in front of the sensor. Figure 1: System principle. The image acquisition module is fixed on the measured points. When the excavation surface sinks during the deformation, the image acquisition module will sink along with it, thereby changing the laser spot position in the image coordinate system. The change of the laser spot position in the image coordinate system reflects the deformation of the excavation surface, including accumulative deformation and instantaneous deformation velocity [28]. The mathematical model of this principle is shown in Figure 3. The geometric center of the laser is the coordinate origin, the tunnel driving direction is the \(z\)-axis, the horizontal direction is the \(x\)-axis, and the vertical axis is the \(y\)-axis. Therefore, a three-dimensional world coordinate system \(o\)-xyz is established. The laser beam points to the laser receiving screen and forms a laser spot \(P\) on the screen. Considering the horizontal and vertical position information, the coordinates of the spot \(P\) in the world coordinate system \(o\)-_xyz_ are \((x,y)\). To examine the position information of laser spot \(P\) in the image coordinate system, an image coordinate system on the laser receiving screen is established, as shown in Figure 3. The \(o^{\prime}x^{\prime}\) axis is parallel to the \(ox\) axis, and the \(o^{\prime}y^{\prime}\) axis is parallel to the \(oy\) axis; the coordinates of laser spot \(P\) in the image coordinate system are \((x^{\prime},y^{\prime})\). The coordinate transformation of spot \(P\) in the two coordinate systems is shown in Equation (1). The constants \(c_{0}\) and \(c_{1}\) are coordinate conversion parameters, which are related to the relative position of the two coordinate systems:  
\[\left\{ \begin{array}{l}x^{\prime}=x+c_{0}\\ y^{\prime}=y+c_{1}\end{array}