# Screen-Cam Robust Image Watermarking with Feature-Based Synchronization
## 3 Proposed Watermarking Scheme
### Watermark Embedding
#### 3.2.2 Message Embedding  
Figure 7 illustrates the embedding process. Each selected LSFR is treated as an independent communication channel, and the same watermark message will be embedded in every LSFR. Compared with the DCT-based method in [33], which embeds the message in the sub-blocks of feature regions, the proposed DFT-based method takes each LSFR as a whole, it has better robustness against cropping attacks. To avoid the LSFR from being further distorted during the rotation process of orientation normalization, we designed a non-rotating embedding method based on the properties of the DFT  
Figure 6: Detailed variations of discrete Fourier transform (DFT) coefficient magnitudes during screen-cam process. (**a**): Original image spectrum in the log domain. (**b,c**): Difference in log DFT magnitudes of original image and captured image at a vertical distance of 30 and 50 cm. coefficients. Furthermore, to improve extraction accuracy, a preprocessing method of DFT magnitude coefficients is proposed. Specific steps are as follows. First, the minimum square regions that contain the LSFRs to be embedded are extracted in order. The luminance band of this area is converted to the DFT domain. Second, for the watermark information, the pseudorandom sequence \(W=\{w(i)\big{|}w(i)\in\{-1,1\},t=0,\ldots,l-1\}\) is generated by the secret key, where \(l\) is the size of the sequence. In order to achieve blind detection that can cope with the situation where the original size is unknown, the embedding radius \(R\) of \(W\) is set to a fixed value. Correspondingly, the embedding radius \(R_{1}\) of \(W_{\text{RS}}\) is defined as:  
\[R_{1}=\text{round}\bigg{(}\frac{L_{1}}{L_{0}}\cdot R\bigg{)} \tag{12}\]  
where \(R_{1}\) is the embedded radius of the square region and \(L_{1}\) is the side length of the square region. According to the characteristics of the DFT coefficients, which is centrosymmetric, we can have 180 degrees as embedding region. The coordinates \(W_{\text{RS}}(x_{i},y_{i})\) of the message embedding position in the square region are defined as:  
\[ \begin{array}{l}x_{i}=\frac{L_{0}+1}{2}+\text{floor}\bigg{[}R_{1}\cdot\cos \Big{(}\frac{j}{l}\cdot\pi+\theta_{d}\Big{)}\bigg{]}\\ y_{i}=\frac{L_{0}+1}{2}+\text{floor}\bigg{[}R_{1}\cdot\sin\Big{(}\frac{j}{l} \cdot\pi+\theta_{d}\Big{)}\bigg{]}\end{array}  \tag{13}\]  
where \(j\) is the j-th element of \(W\). Therefore, the elements of the message \(W(x_{i},y_{i})\) are equally spaced around the center of the embedding region. \(\theta_{d}\) defines the angle between the feature orientation of the LSFR and the normalized orientation. Third, to obtain a better detection rate, the magnitudes \(M\) need to be preprocessed before the signal embedding. In theory, the more obvious the difference between the magnitudes, where the watermark embedded information is \"1\" and \"\(-1\)\", the better the message extraction results. Considering the various rules of the magnitudes during the screen-cam process, we need to avoid high magnitude values at the positions that represent the watermark information \"\(-1\)\". Therefore, some extreme high magnitude values of these positions and their neighborhoods need to be reduced. For a normal  
Figure 7: Framework of watermark embedding process. distribution, nearly 84% of the values are less than the sum of the mean and one standard deviation. Hence, the preprocess is defined as follows:  
\[m_{p}(x,y)=\left\{ \begin{array}{ll}\overline{m}_{p}+\sigma_{p}&\quad if\ m_{p}(x,y)> \overline{m}_{p}+\sigma_{p}\\ no\ change&\quad otherwise\end{array} \right. \tag{14}\]  
where \(m_{p}(x,y)\) defines all magnitudes of the positions that represent the watermark information \"\(-1\)\" and their eight neighbor magnitudes, and \(\overline{m}_{p}\) and \(\sigma_{p}\) define the mean value and the standard deviation of these magnitudes, respectively. The watermark signal is embedded in preprocessed magnitudes \(M_{\text{P}}\) using the following equation:  
\[M_{w}(x,y)=\left\{