# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 5 Verification Results of Field Tests
### Discussion of Displacement Measurement of Bridge B (Concrete Bridge)  
Figure 23 shows the measurement position on the side of the girder using the compact digital camera for non-marker image measurement B. Here, the effect of the contrast at a subset position on the image measurement is discussed using three locations with significantly different contrasts as an example. The subset point I in the figure is the target area for evaluating the influence of the contrast, and exhibits a clear high contrast in black and white. The subset point II is the location used for image processing of non-marker image measurement B of bridge B, and is the boundary between the side surface and the bottom surface of the girder. Subset III is the concrete surface on the side of the girder, having an unclear black and white and low contrast.  
Figure 24 shows the displacement responses of bridge B during the train passage, which were calculated for each location. It can be confirmed that the error increases with a decrease in contrast. To investigate the increase and decrease in the error due to the high and low contrast, the standard deviations were calculated for the section where the original displacement was 0, except when the train passed, and the magnitude of the errors was arranged by the 2\(\sigma\) values. Table 10 shows the 2\(\sigma\) values for each subset. The 2\(\sigma\) value of subset II is about 0.5 mm, whereas, in the low contrast area III, the noise more than doubles to 1.16 mm. The 2\(\sigma\) value of the high contrast point I is halved to 0.23 mm.  
Figure 23: Example of differences in contrast at the measurement subset position (bridge B).  
Figure 22: Comparison of maximum displacements of bridge B: (**a**) four up-train passages, (**b**) four down-train passages.  
If the noise included in the result of the non-marker image measurement is random, a certain degree of error can be minimized by smoothing the moving average. However, because smoothing may round the maximum and minimum values, it is suggested that it is used within a maximum of about 0.1 s. When smoothing in a range higher than this, or when the span is short and the high frequency is predominant, it is necessary to focus on the length for calculating the moving average.  
Figure 25 shows the result of smoothing with a 0.1 s moving average filter. Table 10 shows the 2\(\sigma\) values calculated in the section where the original displacement is 0, except when the train passes. When the contrast of subsets such as II and I is high, the noise reduction effect tends to be high. However, at subset III, an error in the 2\(\sigma\) value of about 0.8 mm remains, even after smoothing. From the above, it can be observed that the capacity to improve the accuracy by smoothing is limited.  
As mentioned above, the improvement of the measurement surface contrast significantly contributes to the improvement of the image measurement accuracy. Therefore, if high accuracy is required for measurement, it is desirable to have a marker with clear contrast and structural feature points, even during non-marker image measurement. In particular, for concrete bridges it is useful to embed a marker-like color scheme on the side of the girder during construction, such as using a spacer of a different color from the base when placing the concrete.  
Figure 24: Effect of contrast in the measurement subset on image processing (bridge B).  
Figure 25: The effect of smoothing on the non-marker image measurement error (bridge B).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subset Position** & **I** & **II (Reference)** & **III** \\ \hline Contrasts & high & - & low \\ 2\(\sigma\) values & 0.23 mm & 0.46 mm & 1.16 mm \\ Variations to the reference II & 49\% & 100\% & 252\% Smoothing (0.1 s moving average) & 0.18 mm & 0.27 mm & 0.79 mm \\ \hline \hline \end{tabular}
\end{table}
Table 10: Errors (2\(\sigma\) value) of each measurement subset position with different contrasts.