## 2 Monitoring Method of Bridge Dynamic Deformation
### Digital Photography Deformation Monitoring Technology Based on an Iso-Metric Virtual Plane  
The displacement parallax method is based on the isometric virtual plane developed from the time baseline parallax method. The time baseline parallax method is often used to solve data processing problems in close-range photogrammetry deformation monitoring. It is used to arrange a control point around the monitored body, so that the photographic scale of the reference plane is consistent with the deformation monitoring point's photographic scale, and the monitoring accuracy can reach a millimeter level within the monitoring distance range of 10 m. Later, the photographic scale change-time baseline parallax method  
Figure 1: Geometric relationship between visual displacement and vertical deformation. is proposed to solve the problem that the photographic axis of the complex monitoring site is not perpendicular to the surface of the monitored body. The reference point is arranged near the photographic equipment to form a reference surface. The photographic scale is transformed by the pinhole imaging principle and correlative mathematical theory. When this method is used for remote monitoring, the reference plane will easily block the monitored body, and the measurement experiment cannot be carried out. To solve the scenario in which control points cannot be set up during remote monitoring, or the control points severely occlude the monitored target, the isometric virtual plane method is proposed, and its basic principle is depicted in Figure 2. A CCD digital camera is utilized to monitor and shoot the monitored body. The actual reference plane at photography distances H3 and H6, and H2 and H5, are the distances between the optical origin and the front end of the CCD; D1 denotes the actual length of the picture on the reference plane when the depth of field is H3, and D2 denotes the actual length of the picture on the object plane when the depth of field is H4. H1 and H4 denote the focal lengths of the digital cameras, whereas N1 and N2 denote the maximum pixel values in the horizontal direction of the image plane, respectively, which are fixed and exhibit no relationship with the change in photography distance. Figure 2 shows the relationship between pixel value and photographic distance depicted in Formula (10):  
\[\frac{H_{1}+H_{2}}{H_{3}}=\frac{N_{1}}{D_{1}} \tag{10}\]  
\[\frac{H_{1}+H_{5}}{H_{6}}=\frac{N_{2}}{D_{2}}\]  
As can be observed from Figure 2, digital photography deformation monitoring technology based on an isometric virtual plane must meet the following conditions:  
\[\left. \begin{array}{l}N_{1}=N_{2},D_{1}=D_{2}\\ H_{1}=H_{4},H_{2}=H_{5},H_{3}=H_{6}\end{array} \right\} \tag{11}\]  
Formula (11) can be obtained as follows:  
\[\frac{H_{1}+H_{2}}{H_{6}}=\frac{N_{1}}{D_{2}} \tag{12}\]  
Displacement Parallax Method Based on the Isometric Virtual Plane  
According to geometric progression pertaining to the depth of field, it can be considered that the photography scale of the isometric virtual plane and monitored target surface's (object plane) photography scale are equal. The displacement of the deformation monitoring point in the isometric virtual plane is transformed into the real displacement of  
Figure 2: Schematic diagram of the equidistant replacement principle. the deformation point using the mathematical relation. The specific derivation process is as follows:  
In Figure 2, the \(\Delta x_{IVP}^{df}\) and \(\Delta z_{IVP}^{df}\) of the deformation points on the isometric virtual plane can be expressed as follows:  
\[ \begin{array}{c}\Delta x_{IVP}^{df}=\frac{QA}{Qa}\Delta p_{x}^{df}=Q\cdot \Delta p_{x}^{df}\\ \Delta z_{IVP}^{df}=\frac{QA}{Qa}\Delta p_{z}^{df}=Q\cdot\Delta p_{z}^{df}\\ \end{array}  \tag{13}\]  
where \(Q\) denotes the photographic scale of the isometric virtual plane, and \(\Delta x_{IVP}^{df}\) and \(\Delta z_{IVP}^{df}\) denote the horizontal and vertical displacements of the deformation points from the object plane, respectively.