# A Novel STDM Watermarking Using Visual Saliency-Based JND Model
## 3 Visual Saliency-Based JND Model
### Visual Saliency Effect  
This part describes \(M_{VS}\) in detail, which fuses the prior information for calculating the significant value distribution of the image.  
The proposed visual saliency models are mostly based on a bottom-up framework, but these algorithms have high computational complexity and low calculation efficiency. Here, we use a simple visual saliency model [29], which is driven by low-level visual stimulus in the scene, such as frequency prior and location prior. Watermarking algorithms are for grayscale images mostly. Thus, the color prior in the expression doesn't need to be considered.  
Firstly, we resort to band-pass filtering [30] for saliency detection. With respect to the band-pass filter, we adopt the log-Gabor filter [31].  
The frequency prior \(I_{f}\) is defined as  
\[I_{f}=IFFT(FFT(I)\times G) \tag{13}\]  
where \(I\) is the carrier image \((I=(i,j)\in R^{2})\) and \(G\) is the transfer function of a log-Gabor filter in the frequency domain.  
Several previous studies have demonstrated that objects near the image center are more attractive to people [32]. That implies locations near the center of the image will be more likely to be \"salient\" than the ones far away from the center. This prior can be simply and effectively modeled as a Gaussian map. Suppose \(C\) is the center of the image. Then, the \"location saliency\" at \(X\) under the \"location prior\" can be expressed as a Gaussian map  
\[I_{l}=exp(-\frac{\|X-C\|_{2}^{2}}{\sigma_{D}^{2}}) \tag{14}\]  
As discussed in Ref. [29], \(\sigma_{D}\) is the experience parameter and often set to \(114\). Then we can get the saliency value \(I_{VS}\),  
\[I_{VS}=I_{f}\times I_{l} \tag{15}\]Consequently, the VS value of each block can be shown,  
\[\mu_{VS}=\frac{\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}I_{VS}(i,j)}{N^{2}} \tag{16}\]  
where \(N\) is the DCT block size. \(I_{VS}(i,j)\) is the visual saliency at the position \((i,j)\) of the block, and \(\mu_{VS}\) is the final block-based VS map. The saliency value distribution of the image obtained by the VS model is a gray scale image with a range of [0, 1]. The closer pixel value is to \"1\", the higher degree of saliency is. The closer the pixel value is to the area, the higher the degree of saliency. We set a threshold (set to 0.3) to binarize the VS map into \"saliency\" area and \"non-saliency\" area. HVS is more sensitive to changes in the \"saliency\" area so it is easier to perceive distortion of the image. According to the image area of the \"saliency\" or \"non-saliency\" area, we take different weights to modulate JND model. In the \"saliency\" area of the image, the quantization step size is reduced. However, in the \"non-saliency\" area, the quantization step is increased. By this way, we can reduce the distortion.  
Then the \(M_{VS}\) can be described as:  
\[M_{VS}=\left\{\begin{array}{l}1,\mu_{VS}\geq 0.3\\ 1.15,\mu_{VS}<0.3\end{array}\right. \tag{17}\]  
where \(M_{VS}\) is the parameter of \(JND(n,i,j)\) in Equation (4) and \(\mu_{VS}\) is the final block-based VS map as Equation (16) shown.