## 3 The Proposed Method
### Motivation
Similar to the fact that pretext tasks for image understanding (such as playing the jigsaw puzzles [41] or predicting image rotation [38]) are sub-optimal for downstream computer vision tasks (as reflected by a performance gap between self-supervised and supervised methods), we could not guarantee that the simulated deviations in our method could foresee all possible deviations of CG images from NIs. However, as shown later in our experimental studies, in general, the proposed self-supervised method was ableto accurately detect CG images produced by four advanced rendering engines which remained _unseen_ during the self-supervised training. This could be considered evidence of the appropriateness of our designed pretext task, although, of course, we were not able to ensure that our method could work well on any unseen CG images created by other untested rendering algorithms. In addition, we show, in the following, that these manipulations indeed introduced diverse deviations in terms of the simple yet intuitive first- and second-order image statistics. In Figure 2 we show a natural image from the ImageNet dataset and five modified versions of this NI. We can observe that visually the modified images are quite different from each other, which illustrates the good diversity of introduced modifications. In order to demonstrate that the various modified versions can indeed represent different deviations from the real distributions of NIs, we show in Figure 3 the empirical marginal distribution of pixel values (i.e., embodied by the conventional image pixel histogram) and in Figure 4 an empirical joint-distribution of pixel values (here embodied by the co-occurrences of two horizontally neighboring pixels). The results in these two figures are for the green channel of images and we have similar observations for other channels. It can be seen from Figure 3 that different manipulations tend to introduce different types of distortions, in terms of the pixel value histogram. For example, the quantization operation results in a comb-like histogram, and the Gamma correction operation (here with a factor smaller than 1) stretches the histogram towards big values with the appearance of gaps and peaks in the histogram after manipulation. Similarly, differences in distribution modifications can be observed for the pixel co-occurrences in Figure 4. For instance, Gaussian blurring makes the distribution less dispersed with a thinner concentration band around the diagonal direction. Noise addition has, somewhat, the inverse effect, which, to some extent, expands the band near the diagonal. The diversity of the considered manipulations, as demonstrated in Figures 3 and 4, would be helpful to learn appropriate representations of neural networks for the main task of differentiating between CG images and NIs. Figure 4: Normalized co-occurrences (shown as heatmaps) of two horizontally neighboring pixels in the green channel of the six images in Figure 2. In each sub-figure, the horizontal and vertical axes represent two pixels’ values (between 0 and 255). The color map used to represent normalized co-occurrence values in the six sub-figures is given at the rightmost of the figure. Zoom-in is recommended to well observe the red dots in the sub-figure of the pixel quantization operation. Figure 3: Normalized histogram of pixel values of the green channel of the six images in Figure 2. In each sub-figure, the horizontal axis represents the pixel value (between 0 and 255) and the vertical axis represents normalized occurrence. Please notice that the range of the vertical axis is not always the same for the six sub-figures.