## 3 Results and Discussion
### Image Generation Results  
This study quantitatively analyzed the image generation results, demonstrating the impact of different training parameters on model performance. Specifically, as shown in Table 2, we set three different total training image counts: 500,000, 1,000,000, and 2,000,000, corresponding to training endpoints after 500,000, 1,000,000, and 2,000,000 image iterations, respectively. Additionally, by adjusting the batch sizes to 4, 8, and 16, we further refined the training process to explore its specific effects on the results. Through nine different training settings, we deeply analyzed and compared the models' performance under various parameter configurations. In the field of image generation, a high Inception Score (IS) does not guarantee that generated images will have visual style consistency and diverse content similar to the real images. To address this issue, we introduced the KID and LPIPS metrics. The KID metric measures the proximity of the generated images to the real images at the feature level; a lower KID value indicates that the generated image distribution  
Figure 6: (**a**) Original 2D CT grayscale image of Fontainebleau sandstone; (**b**) pore segmentation of the same region using the OTSU algorithm. closely approximates the real image distribution, reflecting superior model performance. Conversely, the LPIPS metric assesses the visual similarity between the generated and real images from a human perceptual perspective; a lower LPIPS value signifies a closer visual resemblance. As the total number of training images and batch size increased, the overall performance of the model improved. Under the condition of a total training image count of 500,000 and a batch size of 4, we observed an IS of 1.0120, a KID of 7.4536, and an LPIPS of 0.5521. When the batch size increased from 4 to 8 and then to 16, the IS value significantly improved by 0.5937, the KID value significantly decreased by 2.5479, and the LPIPS value slightly increased by 0.0237. These changes indicate that with an increase in batch size, both the diversity of the generated images and their proximity to real images in the feature space improved, while their visual similarity to real images also increased. Furthermore, when the total number of training images increased to 1,000,000 and the batch size increased from 4 to 16, the IS value further rose by 0.3705, the KID value decreased by 2.3793, and the LPIPS value decreased by 0.0873. The rate of change in these values gradually slowed, indicating that at this stage, the performance improvement of the model began to stabilize, although there was still room for further parameter optimization. Finally, when the total number of training images increased to 2,000,000 and the batch size remained adjusted from 4 to 16, the IS value rose by 0.238, the KID value decreased by 0.9378, and the LPIPS value decreased by 0.0421. Compared to the previous stage, the changes in these indicators were smaller, showing that the model's performance was approaching its optimal state. With a total training image count of 2,000,000 and a batch size of 16, the model not only performed excellently in the diversity of the generated images but also achieved significant improvements in visual quality, attaining dual optimization in visual and statistical characteristics. This indicates that meticulously adjusting training parameters can significantly enhance the performance of the generative model. In previous quantitative analyses, it was determined that increasing the total number of training images to 2,000,000 and adjusting the batch size to 16 significantly enhanced the performance of the generative model. To further evaluate the model's generative capabilities, we conducted a visual analysis of the generated images, as shown in Figure 7a,b. Through detailed comparisons, it is evident that the generated images exhibit a high degree of visual similarity to real images.