## 4 Experiments
### Qualitative Analysis  
Watermarked DCT coefficients produced by the framework are illustrated in Figure 14. A random 1024-bit (32 \(\times\) 32) watermark is embedded in the DCT domain of the 'Cat', 'Barbara' and 'Baboon' images from the Granada dataset using the proposed framework. The absolute difference between the original and the watermarked images is used to display the watermark distribution. This difference is multiplied by 10, 20, 50, 80 and 100 to improve the visualization. In addition, a small area of the image is enlarged to facilitate the presentation. We revealed that the amplitude of the resulting artifact varies in different regions of the original DCT coefficients in diverse images. The variation in the difference matrix indicates that the watermark symbol is adaptively embedded on the basis of local features of the image.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Images** & **Cat** & **Barbara** & **Baboon** \\ \hline \hline Attacks & & & \\ \hline \hline
**Blurring (1.20)** & 0.015 & 0.020 & 0.016 \\ \hline
**Cropping (0.06)** & 0.026 & 0.020 & 0.021 \\ \hline
**Gaussian noise (8.00)** & 0.000 & 0.002 & 0.001 \\ \hline
**Block noise (0.16)** & 0.011 & 0.019 & 0.000 \\ \hline
**Scaling (2.00)** & 0.0001 & 0.004 & 0.001 \\ \hline
**Rotation (10.00)** & 0.0483 & 0.0513 & 0.0480 \\ \hline
**JPEG (60.00)** & 0.020 & 0.020 & 0.000 \\ \hline
**Sharpening (4.00)** & 0.000 & 0.009 & 0.006 \\ \hline
**Moiree (U-Net)** & 0.0179 & 0.0201 & 0.0103 \\ \hline
**Perspective (\(\theta\) = 5)** & 0.036 & 0.030 & 0.0298 \\ \hline
**Light (0.3, 1.5)** & 0.0015 & 0.0026 & 0.0010 \\ \hline
**Visible watermark (16.00)** & 0.010 & 0.0091 & 0.0099 \\ \hline \hline \end{tabular}
\end{table}
Table 4: For each attack, the attack parameter and the resulting extraction BER are shown for SSDeN.  
Figure 14: The results of images watermark embedding and the residual for original and watermarked images.  
Analysis of the diffusion pattern of the DCT domain and its frequency energy map demonstrated that SSDeN adopts a distributed embedding policy concentrated in the middle- and low-frequency bands. As demonstrated in Figures 15 and 16, Figure 16 presents the 3D plot of frequency energy. The frequency energy is calculated using the absolute values of DCT coefficients of an \(8\times 8\) block of the diffusion watermark. DCT coefficients are arranged on the horizontal axis in zigzag order of the DCT block. For example, we start from the DC coefficient DCT(0, 0) toward the maximum frequency DCT(7, 7). The framework learns to avoid embedding in the DC coefficient due to destructive effects on image quality and PSNR.  
Figure 16: DCT energy 3D plot of the framework.  
Figure 15: The results of the DCT coefficient: (**Row 1**) original images; (**Row 2**) DCT coefficient of original images; (**Row 3**) DCT coefficient of watermarked images; (**Row 4**) the residual for original and watermarked DCT coefficients.  
According to the Table 4, the proposed framework achieves an acceptable trade-off between imperceptibility and robustness. The experimental results showed that the proposed algorithm is superior to existing advanced schemes.