# Identification of AI-Generated Rock Thin-Section Images by Feature Analysis Under Data Scarcity
## 3 Results and Discussion
It distinguished real from synthetic images across multiple geological groups, likely due to the higher regularity and symmetry characteristic of generated images. As the radius increases, more low- and mid-frequency components are included in the central region, reducing the share of peripheral energy. \[C/E(r)=\frac{E_{center}(r)}{E_{edge}(r)+\epsilon} \tag{1}\]  
\[E_{edge}(r)=E_{total}-E_{center}(r) \tag{2}\]  
This parameter was calculated within a fixed analysis window, defined as a circle with a radius of 80 pixels (Figure 5). This setup enabled a direct comparison of energy between the center and the periphery of the Fourier spectrum within the same image. Although features such as skewness and total spectral energy remained relatively similar between the two classes, the contrast between central and peripheral spectral energy (i.e., low vs. high frequencies) proved to be significant. Figure 6 also illustrates example images in the frequency domain, with white circular masks marking the central energy region for radii of 100 and 399 pixels. A higher concentration of high-frequency components is observed within the same masked area for generated images compared to real ones. With an increasing radius, the edge energy difference diminishes (Figure 7a), while the ratio of central-to-edge energy (Figure 7b) increases. The overall trend is similar for both real and generated images; however, the energy values are consistently higher for the generated images, making the differences distinguishable. Figure 5: Example of frequency spectrum images with a fixed circular mask (white dashed circle, r = 80 px) for a real (**a**) and a generated (**b**) image, using a Dolomite sample. Both parameters can support feature engineering and may be incorporated into a heuristic indicator. For example, a clear relationship was observed in which the product of the C/E coefficient and the skewness of eccentricity effectively separated the analyzed image set. On average, this combined metric showed negative values for real images and positive values for generated ones (Figure 8). This suggests the possibility of defining a relatively dimensionless heuristic coefficient to separate not only by image type but also by rocks type. A heuristic coefficient of this kind could prove particularly useful in practice, as it offers a dimensionless, easily computable indicator for rapid preliminary detection, potentially reducing the need for complex, data-specific models such as deep learning  
Figure 6: Example of frequency spectrum images with a fixed circular mask (white dashed circle, r = 100, 399) for a real (**a**,**c**) and a generated (**b**,**d**) image, using a Dolomite sample. Figure 7: Dependence of edge energy (**a**) and C/E (**b**) on radius of central mask. architectures. While the metric should be further developed, evaluated, and validated, for instance, by exploring the universality of segmentation methods used to extract eccentricity parameters, its practical value as a lightweight screening tool (e.g., in automated image analysis pipelines, particularly in scenarios where computational resources or annotated data are limited) seems to be already apparent. There are additional features that can help distinguish between real and generated images. In the authors' opinion, although these features may not demonstrate as dimensionless a separation as the dependence of edge energy on the radius of the central mask in the frequency domain (DCT), they still represent a valuable source of information. They can be used to develop custom classifiers. Box plots of selected features normalized values are shown in Figure 9 (texture) and Figure 10 (objects). Figure 8: The product of the C/E coefficient and the skewness of eccentricity of generated and real images. Another interesting case involves using a disproportionality coefficient based on Benford's Law (Figure 9b, Equations (3) and (4)), which describes the probability distribution of the first digits in numerical data.