# A Hybrid Domain Color Image Watermarking Scheme Based on Hyperchaotic Mapping
## 3 The Proposed Watermarking Scheme
### Watermark Extraction  
In the watermark extraction process, the watermarked image is first converted to the YCbCr color space, and then the Y component is subjected to discrete wavelet decomposition. The LL sub-band is selected for discrete cosine transform and singular value decomposition. Then, the singular value matrix of the watermark is extracted by inverse Alpha mixing. Finally, the encrypted watermark image is obtained by inverse singular value decomposition, and then the watermark image is restored by the decryption process. The steps of watermark extraction are shown in Figure 5.  
The specific steps of watermark extraction are as follows:  
Figure 5: Watermark extraction process.  
Step 1: Read the watermarked color image and convert it to the \(YCbCr\) color space:  
\[[WM_{Y},WM_{Cb},WM_{Cr}=RGB2 YCbCr(WM_{RGB})] \tag{22}\]  
Step 2: Select the Y component and perform first-order Haar wavelet decomposition on it:  
\[[LL_{WM},HL_{WM},LH_{WM},HH_{WM}]=DWT(WM_{Y}) \tag{23}\]  
Step 3: Discrete wavelet transform is performed on the \(LL_{WM}\) sub-band to obtain \(D_{LL}\):  
\[D_{LL}=DCT(LL_{WM}) \tag{24}\]  
Step 4: Perform the singular value decomposition of \(D_{LL}\), which is decomposed into three matrices \(U_{WM}\), \(S_{WM}\) and \(V_{WM}\):  
\[[U_{WM},S_{WM},V_{WM}]=SVD(D_{LL}) \tag{25}\]  
Step 5: The singular value matrix of the encrypted watermark can be obtained by embedding the factor \(\alpha\) and the singular value matrix \(S_{H}\):  
\[S^{\prime}_{W}=\frac{S_{WM}-(1-\alpha)\times S_{H}}{\alpha} \tag{26}\]  
Step 6: Recover the encrypted watermark by performing inverse singular value decomposition on the matrices \(U_{W}\), \(S^{\prime}_{W}\) and \(V_{W}\):  
\[W^{\prime}_{E}=U_{W}\times S^{\prime}_{W}\times V^{T}_{W} \tag{27}\]  
Step 7: Use Lorenz hyperchaotic map to decrypt the image and finally obtain the watermark image.  
**4. Experimental Results and Analysis**  
In this section, six color cover images with a resolution of \(512\times 512\) and a gray watermark with a resolution of \(256\times 256\) are used to verify the performance of the proposed scheme. Figure 6 shows the cover image and watermark image used in this paper. All the image data used in this paper are from USC-SIPI: Signal and Image Processing Institute, University of Southern California ([[https://sipi.usc.edu/database/](https://sipi.usc.edu/database/)]([https://sipi.usc.edu/database/](https://sipi.usc.edu/database/))) (accessed on 1 June 2024). The experiment is carried out in MATLAB (R2020b) environment on Intel (R) Core (TM) i5-12400F CPU 2.50 GHz, 16.0 GB RAM computer. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are used to measure the imperceptibility of the proposed scheme, while the normalized correlation coefficient (NCC) and bit error rate (BER) are used to measure the robustness of the proposed scheme. The embedding factor is calculated by using Equation (10). In this paper, the value of \(\lambda\) is 0.1. Table 1 shows the embedding factor of each cover image.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Images** & \(\alpha\) & **Images** & \(\alpha\) \\ \hline Airplane & 0.0214 & Baboon & 0.0307 \\ Goldhill & 0.0381 & House & 0.0245 \\ Lake & 0.0398 & Peppers & 0.02368 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Embedding factors of cover image and watermark image.