## 3 The Proposed Method
### Self-Supervised Learning Task  
The objective of our method was to first of all carry out self-supervised training on an appropriate pretext task of correctly classifying authentic images and several kinds of processed images obtained after applying different kinds of manipulation operations on authentic images. This allowed us to learn features/representations that would then be utilized to solve the main task of the discrimination of synthetic CG images created by advanced rendering engines and natural images acquired by digital cameras. We would like to point out that both CG images and NIs involved in the main task remained unseen during the self-supervised learning stage. As mentioned in the previous subsection, in our proposed pretext task we considered eight manipulation operations, which are listed in the first column of Table 1. In the second column we present the specifications concerning their parameters, if any. In practice, for applying manipulations on an image, the random parameters, if any, are drawn uniformly from the ranges/set as given in Table 1. For example, in the color jitter operation, two random scaling factors are drawn, respectively, for the scaling of the color saturation and the color hue, while in the RGB color rescaling operation three factors are drawn randomly and independently and then applied, respectively, on the R, G and B channels. As mentioned in the last subsection, we chose the eight manipulations in Table 1 to introduce a large spectrum of diverse modifications to NIs, in order to simulate, to some extent, the deviations of CG images from NIs. The selection of manipulations is rather empirical but as shown in Section 4 this leads to good forensic performances in different scenarios for the discrimination of CG images and NIs. In general, the selected manipulations are believed to be related to the difference between CG images and NIs. For example, several previous methods extracted color features which proved to be effective for detecting CG images [18; 21]. Therefore, color jitter, color rescaling or even Gamma correction operation would allow us to learn appropriate representations sensitive to color changes and, thus, be discriminative in distinguishing CG images and NIs. Furthermore, in the literature, researchers have found that CG images and NIs differ in terms of edge statistics [16] and local smoothness [6]; accordingly learned features sensitive to Gaussian blurring, noise addition and sharpness enhancement would be useful for the classification of CG images and NIs. In addition, intuitively and perceptually, CG images appear in general less \"colorful\" than NIs, probably due to computational or algorithmic limitations of rendering engines. Hence, the pixel value quantization might also be helpful for the considered CG forensic problem. Finally, including other manipulations not that closely related to deviations of CG images (one possible example might be the histogram equalization) would still be helpful to learn representations sensitive to more changes from NIs in general, which would later be more easily adapted to the main task of CG forensics. One may design the pretext task as a binary classification problem between authentic images and modified ones generated by any of the eight manipulations. However, in practice, this binary-classification pretext task leads to limited performance for the main task of CG forensics, probably due to the somewhat over-simple nature of such a binary