## 3 Results and Discussion
### Horizontal Displacements  
To investigate the horizontal displacements of the paving blocks, six blocks were horizontally displaced by 5, 7.5, and 10 mm, respectively. As demonstrated in Figure 13, it was possible to detect all the investigated cases, but the horizontal displacement of 5 mm was not clear, compared with the other cases. Overall, the horizontal displacement cases were not clearly visible compared with the vertical displacement. Note that blue indicates no displacement and green indicates displacement. Since the displacement zone is narrow, the number of subset points is approximately 1000, which is only 4% of that of the vertical cases. If the number of detected displaced points is small, the visibility may be poor.  
As shown in Figure 14, the histogram of each case was close to the normal distribution, but the histogram bars were jagged compared with the vertical cases. The mean values of the PCD measurements for the 5, 7.5, and 10 mm displacement cases were 2.260, 3.614, and 6.225 mm, respectively. Clearly, the differences between the actual displacement value and mean were large, and the counts were very small at the actual displacements. Although horizontal displacements can be detected, the measurement errors are significant.  
To determine why the measurement errors in the horizontal displacements were large compared with the vertical cases, further investigation was performed on the horizontal displacement cases. Figure 15 shows the PCD of the reference and investigated cases of a 10 mm horizontal displacement. Note that only a portion was extracted from the PCD for better presentation. The small dent shown in Figure 15a represents the chamfers of two closely adjoining paving blocks. Figure 15b indicates the PCD when one of the two adjacent paving blocks is horizontally separated by 10 mm, and the two PCD are plotted  
Figure 13: PCD analysis results of the horizontal displacement cases of 5 mm, 7.5 mm, and 10 mm.  
together in Figure 15c. In Figure 15d, the color of PCDd is expressed using the calculated distance from PCDr instead of actual color information obtained from the digital image, and the distance scale is shown in the color bar. As previously noted, the algorithm used to compare PCDd with PCDr was C2C, which calculates the distance between two PCD. Since the algorithm simply computes the distance between the nearest neighbor points, the calculated distance does not represent the horizontal displacement; rather, it is closer to the vertical distance. Thus, it only provides scalar information and not vectors. Additionally, it cannot be concluded whether the vertical displacement is a rise or subsidence based on the computation results alone. When a displacement is detected, it is necessary to compare the PCD in the corresponding area.  
Figure 16 shows an enlarged view of the area where the 10 mm horizontal displacement occurred. As can be seen in Figure 16, a 10 mm displacement could be found from the PCDd with the actual color. In addition, it was not easy to determine the difference from Figure 16b. However, it was shown that the green lines parallel to the slit were found to the right of the 10 mm displacement in Figure 16c, and the PCD was expressed using the  
Figure 14: Histogram of investigated horizontal displacement cases: (**a**) 5 mm; (**b**) 7.5 mm; (**c**) 10 mm.  
Figure 15: PCD of the reference and investigated cases for 10 mm horizontal displacement: (**a**) reference; (**b**) 10 mm horizontal displacement; (**c**) reference with 10 mm horizontal displacement; and (**d**) C2C distance.  
calculated distance from PCDr. This is because the paving blocks on the right side of the slit moved to the right when the spacing was 10 mm. When paving blocks are horizontally displaced, this pattern is expected to be found in the field.