# A Novel STDM Watermarking Using Visual Saliency-Based JND Model
## 5 Experimental Results and Analysis
### Experiment of Robustness with VSI = 0.982  
The scheme described in this paper is based on visual saliency JND model. Therefore, based on the general image quality evaluation standard PSNR and SSIM, we adopt VSI fusing the visual \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Attack** & **STDM-RW** & **STDM-AdpWM** & **STDM-RDMWm** & **LSTDM-WM** & **Proposed** \\ \hline Salt-and-peppers noise & & & & & \\
0.015 & 0.2881 & 0.2292 & 0.2393 & 0.2185 & 0.2093 \\ \hline Wiener filtering & & & & & \\
3 \(\times\) 3 & 0.1611 & 0.1264 & 0.1889 & 0.1533 & 0.1189 \\ \hline Median filtering & & & & & \\
3 \(\times\) 3 & 0.1631 & 0.1201 & 0.1194 & 0.1631 & 0.1130 \\ \hline Average & 0.2041 & 0.1585 & 0.1825 & 0.1783 & 0.1471 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The BER comparisons for some common attacks with SSIM = 0.982. Figure 4: BER versus JPEG compression for different watermarking algorithms with SSIM = 0.982. Figure 5: BER versus volumetric scaling factor for different watermarking algorithms with SSIM = 0.982.  
attention characteristic to quality image [16]. In the visual saliency-induced index (VSI), the role of VS is twofold. First, VS is used as a feature when computing the local quality map of the distorted image. Second, when pooling the quality score, VS is employed as a weighting function to reflect the importance of a local region. Calculate the distribution maps of the original image and watermarked image of the significant distribution map through the VS model. Extensive experiments performed on four large-scale benchmark databases demonstrate that the IQA index VSI works better in terms of the prediction accuracy than all state-of-the-art IQA indices. The VSI index is given as  
\[VSI=\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}S_{VS}(i,j)\cdot[S_{G}(i,j)]^{0.4}\cdot \max[VS_{1}(i,j),VS_{2}(i,j)]}{\sum_{i=1}^{M}\sum_{j=1}^{N}max[VS_{1}(i,j),VS_ {2}(i,j)]} \tag{20}\]  
This paper only considers the quality evaluation of gray image, so the color feature of the original text is not taken into account.\(VS_{1}\) and \(VS_{2}\) are the VS map of the carrier and distorted image. \(S_{VS}\) is the similarity between \(VS_{1}\) and \(VS_{2}\). \(S_{G}\) is the similarity of gradient model. \[S_{VS}=\frac{2 VS_{1}\cdot VS_{2}+C_{1}}{VS_{1}^{2}+VS_{2}^{2}+C_{1}}S_{G}= \frac{2G_{1}\cdot G_{2}+C_{2}}{G_{1}^{2}+G_{2}^{2}+C_{2}} \tag{21}\]  
The gradient model \(G\) is calculated as Ref. [16]. \(C_{1}\) and \(C_{2}\) are positive experience values. The test images were watermarked with a uniform fidelity, a fixed VSI of 0.982. The bit error rate (BER) is computed for comparison purposes. The comparisons of the test results of BER under various attacks are given as follows. Figure 6 shows the bit-error-rate (BER) as a function of the additive white Gaussian noise strength. Results form both our STDM watermarking using visual saliency-based JND model and other STDM algorithms are given as follows. Our proposed scheme does not exceed 8% for the Gaussian noise with variance \(1.5\times 10^{-3}\)\(v\) and outperforms other schemes for the Gaussian noise clearly, especially being 6% and 2% lower than the STDM-RDMWm scheme and the LSTDM-WM scheme, respectively. The JPEG compression is implemented to the watermarked images. The experimental results are demonstrated in Figure 7. From the robustness results, the proposed scheme outperforms STDM-RW [7], STDM-AdpWM [12], STDM-RDMWm [13], and LSTDM-WM [34] schemes. Our proposed scheme has average BER values 3% lower than the STDM-RW and STDM-RDMWm schemes. The superior performance of the proposed scheme is achieved by the superior robustness properties of our proposed STDM scheme. Figure 6: BER versus Gaussian noise for different watermarking algorithms with VSI = 0.982. From the robustness results with volumetric scaling in Figure 8, the watermarking scheme based on visual saliency JND model performs better than others. The proposed method has good robustness for volumetric scaling attack.