# High-Frequency Artifacts-Resistant Image Watermarking Applicable to Image Processing Models
## 3 Experimental Results and Analysis
### Qualitative and Quantitative Results
#### 3.2.2. Frequence Invisibility  
Our primary objective is to achieve imperceptibility of watermarking in the frequency domain by mitigating high-frequency artifacts. To illustrate the good imperceptibility of our novel image watermarking technique in the frequency domain, we examine the DCT heatmaps of the marked images generated by our framework, as displayed in Figure 4. It is evident that the DCT heatmap results of our framework closely mirror those of natural images at the bottom of Figure 1a,e, indicating that our proposed framework produces images that are exceptionally natural and devoid of high-frequency artifacts. In contrast, previous model watermarking methods, as depicted in at the bottom of Figure 1c,d,g,h, exhibit small square high-frequency artifacts, while our method conspicuously eliminates such artifacts.  
In addition, we evaluate the frequency domain invisibility performance (FP).The results are shown in Figure 5. Where \"Wu\" denotes the method [17] and \"Zhang\" represents another method [19]. And \"Original\" represents the benchmark host network that performs specific image processing tasks such as paint transfer [29] and de-raining [28]. We observe  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task** & **Watermark** & **Mean PSNR** & **Mean SSIM** & **PSNRw** & **SR** \\ \hline PT & _Baboon_ & 50.58 dB & 0.998 & 42.88 dB & 100\% \\ DE & _Baboon_ & 53.34 dB & 0.999 & 46.47 dB & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Quality assessment for the marked images and the extracted watermarks. All experimental results shown in this Table are mean values. \"DE\" means “de-raining” and “PT\" means “Paint Transfer”. PSNR measures the quality of the extracted color watermarks.  
Figure 4: DCT heatmap of our method (average results): (**a**) the DCT heatmaps of embedding “Baboon” in paint transfer, (**b**) the DCT heatmaps of embedding “MDPI” in paint transfer, (**c**) the DCT heatmaps of embedding “Baboon” in de-raining, (**d**) the DCT heatmaps of embedding “MDPI” in de-raining.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task** & **Watermark** & **Mean PSNR** & **Mean SSIM** & **BER** & **SR** \\ \hline PT & _MDPI_ & 57.18 dB & 0.999 & 0.0009 & 100\% \\ DE & _MDPI_ & 54.59 dB & 0.999 & 0.0010 & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Quality assessment for the marked images and the extracted watermarks. All experimental results shown in this Table are mean values. “DE” means “de-raining” and “PT” means “Paint Transfer”. BER measures the quality of the extracted binary watermarks.  
good performance across various tasks with our proposed method. For example, in the de-raining task with the \"MDPI\" watermark, our approach outperforms method [17] by 44%, showing a 24.9% improvement in average performance compared to method [17] and a 7.2% improvement over method [19]. These observations reveal that our method produces images with smooth surfaces, avoiding the introduction of high-frequency artifacts, a notable advantage.  
This underscores the superior imperceptibility of our proposed framework in the frequency domain. In summary, based on the collective evidence from these experiments, we can assert that our method effectively reduces high-frequency artifacts, preserving the concealment of the embedded watermark in both the frequency and spatial domains, all while upholding the visual quality of the labeled image.