## 3 Experimental Results
(**a**) The first maintenance train captured with five photos in seven seconds; (**b**) the second maintenance train captured with five photos in four seconds; (**c**) the third passenger train captured with six photos in 16 s.  
To verify the accuracy of the scale-adjusted parameters, the ground coordinates of the 18 checkpoints were computed by the co-planarity equation using Equation (6). Their 3D coordinates were also rotated and shifted to compare the results with the measurements by the total-station. Figure 6 shows the target locations obtained by ROP--applying rotation and shift--before and after scale adjustment. It clearly reveals that the target locations after scaling ROPs are almost identical to the measured locations compared to before scaling. Table 2 shows that the accuracy after the scale-adjusted ROPs is dramatically improved compared to the value before adjustment. They illustrated sufficiently accurate consistency within 2 mm root means square error and 4 mm absolute maximum error, respectively; it was therefore determined that the scale-adjusted ROPs could be enough to measure the bridge instantaneous displacement. In the next step, the image-matching technique was carried out with the first image as a reference, the image coordinates of 18 targets including a laser reflector point attached at the bridge were determined by applying the target-matching technique for the left and right all frames. Figure 7 shows an example in which the reflector position was accurately obtained in the second and 16 th images (bottom), respectively, from its positions in the first left/right images (top). Then, as a final step, while the trains enter a test span of the bridge, the 3D ground coordinates of all targets and a reflector point are computed by the co-planarity based on Equation (6) using the scale-adjusted ROPs and the image coordinates with the passage of time. Meanwhile, to compare the proposed techniques, 3D displacements of the reflector point on the bridge were simultaneously measured at 0.1-s intervals by a laser tracker, as shown in Figure 8. The laser tracker measures the reflector position with less than 0.5 mm precision in the three axes [40]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\mathbf{X_{0}}\) (mm) & \(\mathbf{Y_{0}}\) (mm) & \(\mathbf{Z_{0}}\) (mm) & \(\mathbf{\omega}\) (Degree) & \(\mathbf{\varphi}\) (Degree) & \(\mathbf{\kappa}\) (Degree) \\ \hline Left & 894.1 & 8940.6 & 1788.1 & 0.000 & 0.000 & \(-\)0.000 \\ \hline Right & 3451.1 & 8983.0 & 2454.0 & \(-\)0.586 & 14.594 & 1.921 \\ \hline \(\sigma_{ROP}\) & - & 0.201 & 0.201 & 0.001 & 0.004 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scale-adjusted ROPs of the cameras in two cases. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scale Adjustment**} & \multicolumn{2}{c}{\(\mathbf{X}\)} & \multicolumn{2}{c}{\(\mathbf{Y}\)} & \multicolumn{2}{c}{\(\mathbf{Z}\)} \\ \cline{2-7}  & **RMSE** & **Abs. Max. Error** & **RMSE** & **Abs. Max. Error** & **RMSE** & **Abs. Max. Error** \\ \hline Before & 100.6 & 188.5 & 39.6 & 71.6 & 35.3 & 98.3 \\ \hline After & 1.0 & 2.1 & 0.5 & 1.1 & 1.4 & 2.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Location error of the checkpoints by the determined ROPs (mm). Figure 6: Eighteen target checkpoint locations before and after scale adjustment of the relative orientation parameter. (**a**) Before scale adjustment; (**b**) after scale adjustment. Figure 8: _Cont_. Figure 7: Target matching results using the correlation-coefficient and the least-squares techniques. (**a**) Matched points of the second images from the first images; (**b**) matched points of the 16 th images from the first images. Figure 8 compares the displacement of the reflector point caused by the cyclic load from the first train to the third train measured by the proposed method and a laser tracker.