## 4 Result and Discussion
### Deformation Curve Obtained by Overlapping Difference of Contour Line  
By calibrating each pixel in the image, the size of each pixel can be obtained. The size of each pixel is the theoretical limit of the accuracy in the proposed photogrammetric method. In the steel truss bridge tested, the vertical member is orthogonal to the pixels, as shown in Figure 13. Thus, the calibration of the vertical member is relatively simple. As shown in Table 3, by calibrating 13 visible vertical members, the measurement accuracy of this experiment is 1.12 mm. According to the calibration value, the contour of the pixel in Figure 12 can be transformed into the actual deformation value.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Number of** \\ **Vertical Members** \\ \end{tabular} & \begin{tabular}{c} **Number of Pixels** \\ \end{tabular} & \begin{tabular}{c} **Real Length of** \\ **Members/mm** \\ \end{tabular} & \
\begin{tabular}{c} **Calibration Value** \\ \end{tabular} &
\begin{tabular}{c} **Average Value** \\ \end{tabular} \\ \hline
1 & 344 & 387 & 1.12 \\
2 & 342 & 379 & 1.10 \\
3 & 340 & 380 & 1.11 \\
4 & 345 & 377 & 1.09 \\
5 & 339 & 376 & 1.10 \\
6 & 292 & 332 & 1.12 \\
7 & 346 & 375 & 1.08 & 1.12 mm/px \\
8 & 421 & 473 & 1.12 \\
9 & 330 & 376 & 1.14 \\
10 & 295 & 331 & 1.22 \\
11 & 335 & 377 & 1.12 \\
12 & 351 & 376 & 1.07 \\
13 & 342 & 381 & 1.11 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Pixel size calibration table of vertical members.  
Figure 13: Pixel calibration schematic.  
The edge line shown in Figure 12 is notably discontinuous at the connecting points due to assembly error as analyzed before. However, the discontinuity is not caused by the structural deformation and will not change with the applied load. Therefore, the influence of the discontinuity can be eliminated by the overlapping difference method. Since the bearings contact the reaction frame closely after 100 kN, the edge line of the initial working condition can be overlap differenced by the edge line of the other load grades. Thus, the load-displacement curve of 100-600 kN can be derived, as shown in Figure 14.  
It can be found that the load-displacement curve presents a zigzag feature. The reason for this problem is that the edge of the structure in the image is composed of one or more pixels, as shown in the red pixel of Figure 15. These pixels are arranged side by side to form a bandwidth. The final edge position (shown in deep red in Figure 15) is determined by the gradient change rate of the gray value of all pixels in the bandwidth. Under the influence of illumination conditions, the final edge and the actual edge will have errors, as shown in the dotted line of Figure 15. As a result, the zigzag phenomenon occurs in the load-displacement curve shown in Figure 14. Based on the above analysis, it can be indicated that the deformation extracted from the image will be distributed around the actual deformation of the structure. On this end, the load-deformation curve is polynomial fitted to approximate the actual deformation value of the structure, as shown in Figure 16. The measured comparison of three dial meters is shown in Figure 17.  
Figure 14: Load-displacement curves under various load grades.  
Figure 15: Difference between pixel edge and actual edge.