# High-Frequency Artifacts-Resistant Image Watermarking Applicable to Image Processing Models
## 2 Preliminaries and Proposed Method  
### Detection of High-Frequency Artifacts  
High-frequency artifacts manifest as unnatural and inconsistent textures, such as box-like patterns, in the frequency domain. In this section, we show the high-frequency artifacts present in the images that marked by the generative model watermarking, thus revealing the flaws in their covertness. We employed a frequency domain detection method [23] to detect high-frequency artifacts. Specifically, we used the Type II Discrete Cosine Transform (2D-DCT) to generate a DCT spectrum, which was then represented as a heatmap. Within this heatmap, the size of each data point indicates the coefficient of the respective spatial frequency, with larger values leading to brighter points. Frequency levels gradually increase from left to right and from top to bottom on the heatmap. The upper left section of the heatmap corresponds to lower frequencies, while the lower right section represents higher frequencies. In our experiments, we used two datasets: the Danbooru2019 dataset [27] and the De-raining dataset [28], to evaluate the previous generative model watermarking methods [17; 19].  
For the spatial domain, the evaluation results for these datasets are depicted in Figure 1. In Figure 1a, randomly selected ground-truth images from the Danbooru2019 dataset are showcased, while in Figure 1b, carrier images generated by the generative network [29] are presented. Figure 1c,d display images marked by [19] and [17], respectively. It is evident that the images in Figure 1a,b exhibit high similarity, indicating that the generative network [29] effectively accomplishes the image task. Simultaneously, the images in Figure 1c,d also closely resemble those in Figure 1a,b, suggesting that the previous generative model watermarking method successfully achieved the watermarking task without compromising the quality of the spatial domain in the original image. Figure 1e-h demonstrates similar results.  
More importantly, our investigation delves into the characteristics and variations of the test images in the frequency domain. Typically, in natural images, low-frequency components depict smoothly varying image intensities and carry the majority of the image information [30; 31]. Conversely, higher-frequency components approximate image edges, representing abrupt pixel transitions. The DCT heatmap for the various methods is presented at the bottom of Figure 1. At the bottom of Figure 1a, the DCT heatmap for the natural image are depicted. In the bottom of Figure 1b, the DCT heatmap for the generated image are shown, presenting box-like high-frequency artifacts. In the bottom of Figure 1c,d, the DCT heatmap for the marked images displays even more pronounced high-frequency artifacts. Similar results are observed at the bottom of Figure 1e-h. Therefore, through the DCT frequency domain analysis, we identify severe high-frequency artifacts in the marked images generated by existing generative model watermarking methods, highlighting a deficiency in frequency domain imperceptibility.  
In summary, prior generative model watermarking methods have focused on the invisible embedding of watermarks in the spatial domain of images, making it difficult for potential attackers to discern the model watermarking within this spatial context. However, the identification of high-frequency artifacts in the frequency domain of the marked images renders generative model watermarking conspicuous within this frequency domain, thereby compromising the overall imperceptibility and security of the generative model watermarking system. Consequently, generative model watermarking becomes susceptible to detection by potential attackers. This situation underscores the imperative need for enhancing frequency-based imperceptibility in generative model watermarking.