## 3 Results  
### Image Processing of CT Images without Confining Stress  
Figure 10a shows the comparative results of the profile line of aperture boundaries. (i.e., upper and lower fracture surfaces) under the RG and ED method. The black profile represents the fracture surface measured from the region growing method, and the red profile is from the edge detection method. Figure 10b,c represent the fracture apertures and contact area ratios under these two methods. Although the profile line and calculation results are almost the same, the mean aperture value of RG and ED has 0.61 px difference. The values of them are 18 px and 18.61 px, respectively. Meanwhile, the contact area ratio value has 0.1% difference. A slight image identification difference between RG and ED is illustrated in the blue rectangle in Figure 10a. Results show that there is no obvious image identification difference under different image processing methods at 0 MPa. However, a slight calculation difference is generated under these two methods. Figure 9: Comparison of different CT images. (**a**) Original CT image, (**b**) region growing method (RG) result, (**c**) edge detection method (ED) result. From Figure 11, it is noted that an image processing difference may easily generate on the aperture boundary, and an aperture value difference under the RG and ED methods are compared at each pixel number in the \(x\)-direction, as shown in Figure 11a. It is obvious that several aperture differences existed, as depicted at the pixel number positions of 300, 450, 550, and 750. The aperture value has a 1.52-pixel size difference after calculation. The aperture differences histogram under the RG and ED methods are illustrated in Figure 11b,c. The result shows that the aperture value has an apparent difference from 0 to 20. It can be guessed that the aperture closure position may result in this slight difference. The RG result shows that the aperture value of 0-5 is larger than the value under the ED method. Although the RG method has an advantage in identifying the aperture closure position, the ED method has a dominant position in grasping the low density of a rock region in the CT image. The low density of a rock region is estimated as the continuous voxel of the rock region under the RG method. Therefore, the aperture value of 0-5 under the ED method is relatively lower than the RG result. In order to verify the image processing difference, a relatively large aperture value difference (i.e., at the pixel number positions of 300, 450, 550, and 750) is further analyzed. Those pixel positions can be directly identified from the original CT image and the segmentation CT images. Therefore, the intercepted CT images are picked up and magnified, as illustrated in the red rectangular frame in Figure 12a. It clearly shows that the image processing difference existed in these positions. The difference between the original CT image and the CT segmentation images under RG and ED can be ensured. In order to further certify the image processing difference, a profile line is portrayed at the same position (i.e., a position located on the pixel number of 459-461 in \(x\)-direction in different  
Figure 11: Aperture value difference at 0 MPa. (**a**) Aperture value difference of Slice A under RG and ED methods. (**b**) Aperture value histogram (RG). (**c**) Aperture value histogram (ED). Figure 10: Aperture boundary profiles and calculation results under RG and ED methods. (**a**) Comparison of aperture boundary profiles; blue frame shows the aperture boundary profile difference under RG and ED methods. (**b**) Aperture and contact area ratio results (RG). (**c**) Aperture and contact area ratio results (ED). CT images, as shown in Figure 12b). Moreover, a yellow profile line comparative result with the number of 514 is depicted. In addition, a value comparison of profile line 514 is shown in three colors, namely, blue-, black-, and red-color dot lines that represent the value of 514 in CT original, RG, and ED segmentation images in Figure 12c.