## 3 Experimental Results  
An experiment was performed to verify the proposed method for the 3D instantaneous displacement measurement using two cameras. The railway bridge tested in the experiment was installed with a length of 150 m across the Suncheon River, and it is quietly long among the I-plate girder bridges. The distance of the bridge opening is about 9 m for displacement measurement. It is impossible to take a measure of the entire bridge displacement crossing over a river. A bridge span was selected for the experiment such that a camera could be easily installed as shown in Figure 4. Image coordinates of the 26 feature points marked on the side of one span bridge were obtained and used as CPs to compute the ROP. To check the accuracy of the ROPs and measure the three-dimensional displacement, 18 dontu-shaped targets were stuck on the bridge span. The 3-D spatial coordinates of the targets were measured using the total-station, a distance-and-angle measuring instrument used for the 3D terrestrial survey. The field test was conducted on 29 March 2016 from 4:00 PM to 5:00 PM, at which time the temperature was about 18 degrees Celsius and the humidity was 48 percent. Since it was performed at a time of the season when temperature change does not occur dramatically during the day, and the measurement time for each train does not exceed 20 s, it is not expected to have a significant effect on the deformation measurement of the steel rail bridge. The technique uses two identical cameras to take consecutive images, a remote controller, and two receivers for time synchronizing of the stereo frames. The camera is a non-metric NIKON D200 that can take six frames per second (fps); this study does not use sophisticated expensive devices. The resolution was 3872 pixels \(\times\) 2592 pixels (pixel size = 6 \(\upmu\)m \(\times\) 6 \(\upmu\)m). The camera focal length, the baseline, and camera-to-object distances were 55 mm, about 3 m, and 9 m from the bridge, respectively. A 3D laser tracker and a laser reflector were also installed to compare displacement accuracy with the proposed method. Figure 4 shows the installed equipment and the points used in the test area. Using two cameras with a remote controller and two receivers, photographs were taken as three types of trains entered the bridge. At several-second intervals, two maintenance trains were each captured with five photographs, and the passenger train was captured with six photographs. The first maintenance train entered the test area from left to right, and the other trains entered from right to left, as shown in Figure 5. In a previous experience, we analyzed vibration by the photographing moment with a remote control and camera shake due to ground vibration when a train passed over the bridge, but there was almost no influence in the change of the image coordinates. Figure 4: **(a)** Test span of the curviform railway bridge in Suncheon of South Korea, two-camera setup with a remote controller and two receivers, laser tracker; **(b)** layout of 26 feature points and 18 target checkpoints on the test span bridge, N1 and N2 points used to adjust the scale of the ROPs, the zoomed-in view of a laser reflector in the lower left part of the bridge. The first stereo frames were taken before trains entered the test span of the bridge. The ROPs of the two cameras were calculated by the relative orientation method using coplanarity and scale adjustment with 26 feature points and their image coordinates provided in the first stereo frames on the bridge. The scale 0.89 was determined from the ratio between the measured and calculated distances from ROPs on points N1 and N2 in the right in Figure 4. Table 1 shows the results of the scale-adjusted ROPs, and their standard deviations (\(\sigma_{ROP}\)) to check the quality of the determined parameters. The precisions indicate that, overall, the parameters are determined well through the solution of the least-squares method. Figure 5: Train entry on the test span of the bridge.