# Identification of Underwater Structural Bridge Damage and BIM-Based Bridge Damage Management
## 2 Commissioning the Camera
### Camera Underwater Calibration Experiments  
When the camera acquires underwater damage images, light will refract through three media, water, lens, and air, and the focal length of the camera changes due to refraction, resulting in large errors in the parameters obtained by the camera, which affects the accuracy of the later measurement results, so the camera must be calibrated underwater to correct the camera parameters. The camera calibration method proposed by [PERSON] et al. is simpler and less expensive than the traditional method [50]. Therefore, this paper adopts [PERSON]'s calibration method for underwater camera calibration experiments. The calibration experiments were carried out in a 1.5 m cube water tank. To ensure the accuracy of the calibration, an aluminium high-precision diffuse reflection calibration plate was used in this paper, on which the calibration plate was divided into squares, all of which were 20 mm \(\times\) 20 mm in size. Figure 1a is the experimental water tank and calibration plate. The experimental procedure is as follows:  
1. A total of 15 images of the underwater calibration plate were acquired by simultaneously photographing the calibration plate from different angles and distances with the left and right infrared lenses of the binocular camera in the water tank. The spatial position of the camera in relation to the calibration plate at the time of acquisition as shown in Figure 2. The above steps were repeated using the colour lens alone and a further 15 images of the plate were acquired. Figure 1: Calibration plate design and results in experimental use of calibration plates: (**a**) calibration late; (**b**) before the picture was corrected, the calibration plate was recessed inward in a curved shape all around; (**c**) after picture correction, the calibration plate is straight all around. The corner points are extracted from the acquired image and the parameters are solved. The corner points are extracted as shown below Figure 3. The centre of the green circle is the extracted corner point, the yellow square is the origin of the corner point coordinate system, and X and Y indicate the coordinate axes. The intrinsic matrix for the left camera is obtained as follows:  
\[M_{L}= \begin{bmatrix}513.6847&0&326.1383\\ 0&513.9499&247.5797\\ 0&0&1\end{bmatrix}  \tag{1}\]  
The matrix of the distortion coefficient is:  
\[(k_{1},k_{2},k_{3},p_{1},p_{2})= \begin{bmatrix}0.4002\\ 0.2833\\ -0.1084\\ 0.0102\\ 0.0029\end{bmatrix}  \tag{2}\]  
The intrinsic matrix for the left camera is:  
\[M_{R}= \begin{bmatrix}513.2454&0&324.5766\\ 0&513.6073&247.4670\\ 0&0&1\end{bmatrix} \text{a}=1, \tag{3}\]  
Figure 3: Corner Point Extraction of Calibration Board. Figure 2: Spatial Distribution of Calibration Plate. The matrix of the distortion coefficient is:  
\[(k_{1},k_{2},k_{3},p_{1},p_{2})= \begin{bmatrix}0.3890\\ 0.3749\\ -0.4866\\ 0.0106\\ 7.5427e-04\end{bmatrix} \text{a}=1, \tag{4}\]  
The rotation matrix of the camera is:  
\[R= \begin{bmatrix}1&4.2220e-5&0.0034\\ -4.0376e-05&1&-0.0011\\ -0.0034&0.0011&1\end{bmatrix} \text{a}=1, \tag{5}\]  
The translation matrix of the camera is:  
\[T= \begin{bmatrix}-62.6907&-0.0370&-0.2397\end{bmatrix} \text{a}=1, \tag{6}\]  
The colour camera is calibrated separately according to the above steps. The intrinsic matrix of the colour camera are as follows  
\[M_{R}= \begin{bmatrix}1377.56&0&946.56\\ 0&1377.42&532.41\\ 0&0&1\end{bmatrix} \text{a}=1, \tag{7}\]  
The matrix of the distortion coefficient is:  
\[(k_{1},k_{2},k_{3},p_{1},p_{2})= \begin{bmatrix}0.1089\\ -0.1374\\ -0.086\\ -7.5427e-04\\ -0.3241\end{bmatrix} \text{a}=1, \tag{8}\]
3. The re-projection error is the position difference between the actual projection point and the theoretical projection point. To ensure the accuracy of image measurement in the later period, the re-projection error should be limited to a certain range. In this paper, the image with large error is eliminated, and the re-projection error is less than 0.5 as the ideal range.