# Research on Damage Localization of Steel Truss-Concrete Composite Beam Based on Digital Orthoimage
## 3 Static Test of a Steel Truss-Concrete Composite Beam
### Image Data Acquisition  
Using Canon 5 DSR camera to take photos of the experiment specimen, the camera and lens parameters are shown in Table 2, and the camera calibration [24] results are shown in Table 3. The directly acquired specimen images are affected by the natural perspective and show obvious near-large and far-small features (Figure 16), resulting in the images not correctly reflecting the deformation of the structure, so a perspective transformation of the specimen images is required. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Damage** & **Location** & **Loading** & **Load** \\
**Conditions** & **of Damage** & **Situation** & **(KN)** \\ \hline \multirow{3}{*}{No damage} & & O\({}_{1}\) & 0 \\  & & O\({}_{2}\) & 150 \\  & & O\({}_{3}\) & 250 \\ \hline \multirow{3}{*}{Damage to} & & A\({}_{1}\) & 0 \\  & & A\({}_{1}\) & 150 \\  & & A\({}_{1}\) & 250 \\ \hline \multirow{3}{*}{Damage to} & & B\({}_{1}\) & 0 \\  & & B\({}_{1}\) & 150 \\  & & B\({}_{1}\) & 250 \\ \hline \multirow{3}{*}{Damage to} & & C\({}_{1}\) & 0 \\  & & C\({}_{1}\) & 150 \\ \cline{1-1}  & & C\({}_{1}\) & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of damage and load conditions. Figure 16: Test beam image without perspective transformation processing. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number of** **Pixels** & **Sensor Size** & **Image Size** & **Aspect Ratio** & **Pixel Size** & **Lens Models** & **Lens Relative** & **Focal Length** \\ \hline
50.6 million & 36 \(\times\) 24 mm & 8688 \(\times\) 5792 & 3.2 & 4.14 μm & EF 24–70 mm & F2.8–F22 & 24–70 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Camera and lens parameters. Image geometric transformation refers to the geometric transformation of image pixel positions without changing the original image content, mainly including translation, rotation, scaling, reflection, and misalignment. The perspective transformation is a combination of basic geometric transformations. The image of the measured structure will be distorted, when photographed under the condition of non-orthogonal projection [25,26]. If the image is mapped to the plane where the target structure is measured, called the measuring plane, in other words, the camera shoots perpendicular to the measurement plane, the real shape of the target structure can be obtained, and the perspective transformation model is shown in Figure 17.  
Using the projection center of the camera as the origin to establish a three-dimensional Cartesian coordinate system, called the camera 3D coordinate system, let the original imaging plane be the \(xy\) plane, with the focal point at \([0,0,f]^{T}\), (\(f>0\)). A two-dimensional coordinate system is established in the measuring plane, and the origin of this coordinate system is \([x_{0},y_{0},z_{0}]^{T}\) in the camera 3D coordinate system, the unit vector in the \(X\)-axis direction is \([u_{1},u_{2},u_{3}]^{T}\), and the unit vector in the \(Y\)-axis direction is \([v_{1},v_{2},v_{3}]^{T}\). The vectors adhere to the rules as follows:  
\[\left\{ \begin{array}{c}u_{1}v_{1}+u_{2}v_{2}+u_{3}v_{3}=0\\ u_{1}^{2}+u_{2}^{2}+u_{3}^{2}=v_{1}^{2}+v_{2}^{2}+v_{3}^{2}=1\end{array} \right. \tag{8}\]  
Then, the point with coordinates \([u,v]^{T}\) in the target object plane (measuring plane) can be expressed in the camera 3D coordinate system as  
\[u\left[ \begin{array}{c}u_{1}\\ u_{2}\\ u_{3}\end{array} \right]+v\left[ \begin{array}{c}v_{1}\\ v_{2}\\ v_{3}\end{array} \right]+\left[ \begin{array}{c}x_{0}\\ y_{0}\\ z_{0}\end{array} \right] \tag{9}\]  
Assuming that the point in the imaging plane has point coordinates \([x,y,0]^{T}\), then \(\exists k\in R\) must satisfy the following equation. \[u\left[ \begin{array}{c}u_{1}\\ u_{2}\\ u_{3}\end{array} \right]+v\left[ \begin{array}{c}v_{1}\\ v_{2}\\ v_{3}\end{array} \right]+\left[ \begin{array}{c}x_{0}\\ y_{0}\\ z_{0}\end{array} \right]-\left[ \begin{array}{c}0\\ 0\\ f\end{array} \right]=k\left(\left[ \begin{array}{c}0\\ 0\\ f\end{array} \right]-\left[ \begin{array}{c}x\\ y\\ 0\end{array}