# Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks
## 3 Results and Discussion  
A final check was performed before continuing with the experiments. It is known that long image acquisition times can imply image distortions due to slight movements of the camera or supporting systems, or sensor deformation due to heat. Therefore, we implemented a \"dry\" experiment: i.e., the probe was filmed and measured without adding water. From the ROI location for each time, strains were obtained by (1). As the system is supposed to be static, all the obtained shifts may be assigned to experimental errors. Figure 8 represents the absolute displacement of each ROI from initial position, where we can see a clear drift in the setup, mainly in the vertical direction, which can be up to 15 \(\upmu\)m. This behavior was repeated in all the experiments similarly, so this was probably an effect of camera heating, which caused the support to loosen and made the camera move down due to objective weight. Notice also that the results present small instabilities of the order of 0.25 \(\upmu\)m or, equivalently, 0.1 px, which is approximately twice the error obtained with the synthetic sequence in the movement direction (see Figure 6). These errors may be due to Gaussian noise in the image and fitting errors in the subpixel calculation algorithms. These fluctuations can be cancelled out by applying smoothing filters in the signal, but since they do not distort the main trend of the result, we preferred to show the data as obtained. According to these data, our method is not advisable for absolute measurements. However, according to Equation (1), as we were interested in relative positions and strains, it was possible that overall drifting did not affect our results. Figure 9 represents the horizontal and vertical strains obtained for each pair of corresponding ROIs from the images obtained in this dry experiment. Note that in the vertical case, in the same color, we show the strains obtained for each pair of ROIs that are located at the same height, but on different sides of the samples. Figure 7: Flow chart for the image processing used in this work. Despite experimental instabilities, the method's accuracy was acceptable with error peak values below \(1\times 10^{-3}\). Mean errors and their standard deviations are presented in Tables 1 and 2. From them, we take the worst obtained case as the error of this method, which was (0.56 \(\pm\) 0.16) \(\times\) 10\({}^{-3}\). \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Horizontal Strain Error (\(\times\)10\({}^{-3}\))**} \\ \hline
**ROIs** & **MEAN** & **STD** \\ \hline
1–4 & \(-\)0.1110 & 0.0411 \\
2–5 & \(-\)0.2163 & 0.0560 \\
3–6 & \(-\)0.4175 & 0.1013 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Horizontal strain error for a long-term still sequence of the recorded images. Figure 8: The measured horizontal (left) and vertical (right) shifts for a static dry experiment for each ROI. The results are shown for sample 1, but similar graphs were obtained for all the measured samples. Figure 9: Measured horizontal (left) and vertical (right) strains for a static dry experiment for each ROI. The results are shown for sample 1, but similar graphs were obtained for all the measured samples. It is worth noting that errors in the vertical deformations are slightly larger and more disperse than in the horizontal direction. On the one hand, this may be due to the camera moving, but also to the shorter distance between ROIs. In fact, distance between the lateral ROIs was 3-fold longer than the distance between two consecutive vertical ROIs. As the strain was inversely proportional to the initial position of ROIs, according to Equation (1), the expected error was 3-fold bigger. Figure 10 depicts the relative displacement measured for all the ROIs in sample 1 during the experiment. Compared to the error graphs in Figure 8, we can see that the displacement measured in the wet experiment was much larger than in the dry experiment. This means that the influence of the error must be considered to be minimum.