## 3 Results
### Image Processing of CT Images without Confining Stress
To further check the aperture boundary difference under the RG and ED methods, relative aperture closure CT slices are chosen for comparison. After calculating the fracture aperture and contact area ratio values, the result shows that a large image processing difference occurred on Slice D-E at 0 MPa, as shown in Figure 14. Several aperture boundary positions are identified as the aperture closed under RG. Moreover, the contact area ratio value of RG is revealed to be a bit higher, and the values of Slice D and Slice E are equal to 4% and 3%, respectively. In contrast, the contact area ratio values of Slice D and E are equal to 0% and 0.1%, respectively. It is confirmed that a bit of difference happens. The RG method has a characteristic of assuring the spatial continuity of the same region after the image segmentation, which may lead to the relative low-density areas assimilating into the rock region. Therefore, the aperture boundary is neglected after RG segmentation. Figure 14: Comparative result of the aperture boundary profiles under RG and ED methods (0 MPa Slice D–E). Figure 13: CT image comparison under RG and ED methods at 0 MPa (Slice B–E). The aperture value difference of Slice D-E at 0 MPa is depicted in Figure 15. Figure 15a shows the aperture value difference under the RG and ED methods. The result of Slice D illustrates that the aperture value difference occurred in the \(x\)-direction with the pixel number of 400-600, and the result of Slice E shows that a relatively large aperture value difference occurs in the \(x\)-direction with the pixel number range from 400 to 700. Moreover, the aperture difference distribution of Slice D is more significant in the value of 0-5, as shown in Figure 15b,c. However, the aperture value difference of Slice E is more diverse in the value of 0-10. In general, it can be confirmed that there is a significant difference happening in the aperture value calculation under different image processing methods, and the aperture closed position under each condition should be clarified further. The original CT images and the CT segmentation images of Slice D and Slice E under the RG and ED methods are shown in Figure 11:0 From Figure 16(a1,a2), it is shown that the aperture difference occurs on each CT image slice. The aperture closed position is chosen as an analytical object from each CT image slice. (i.e., the position of Slice D which is located in the pixel number range from 50 to 150 in Figure 16(a1), and Slice E is located in 80-240 in Figure 16(a2) in the \(x\)-direction). A significant difference between RG and ED segmentation images is observed. RG identifies different density of the rock as the same density from the original CT images, and they are recognized as the aperture closure; meanwhile, the ED method can grasp the aperture boundary of the high- or the low-density areas from the original CT images. The image segmentation result indicates that the aperture value difference easily happens on the different density areas of rocks, or on the aperture closed positions. Therefore, the profile line (i.e., line 320 of 0 MPa Slice D, and line 94 of 0 MPa Slice E) are chosen and compared, as shown in Figure 16(b1,b2). From the comparative results, it is shown that the ED method successfully identifies the aperture boundary, and the range of the profile line is quite similar to the original CT image. In contrast, several image misidentifications occur after RG segmentation. From observing 0 MPa Slice D-E, several aperture open positions are misidentified as the aperture closed, and the profile line value is equal to 0, i.e., with the aperture closed, as presented in Figure 16(c1,c2). Those misidentifications may also result in a great difference in the contact area ratio value in Figure 11:1 The contact area ratio value has a big difference in those misidentifications. Figure 11:2 Aperture value difference of Slice D and Slice E at 0 MPa. (**a**) Aperture difference under RG and ED methods. (**b**) Aperture value histogram (RG). (**c**) Aperture value histogram (ED).