# An Authentication Method for AMBTC Compressed Images Using Dual Embedding Strategies
## 4 Experimental Results
### The Performance of the Proposed Method  
In this paper, we use a threshold \(T\) to classify blocks into smooth and complex ones and embed them using different techniques. The PSNR and SSIM are related to the value of \(T\). Table 1 shows the comparisons between PSNR and SSIM for the test images when the threshold \(T\) is set from 0 to 10. As shown in the table, the highest PSNR is achieved when \(T=6\) or \(T=7\). As \(T\) becomes smaller or larger, the PSNR decreases gradually. For example, the Jet image has a PSNR of 43.32 dB for \(T=6\), which is higher than when \(T=5\) and \(T=7\). Besides, the peak values of SSIM are achieved when \(T=6\). Thus \(T=6\) is adopted in the proposed method. This experiment was performed using the Python programming language, and the average time required to embed an image is less than one second when \(T=6\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\mathbf{T}\) & **Metric** & **Lena** & **Jet** & **Baboon** & **Tiffany** & **Sailboat** & **Splash** & **Peppers** & **House** \\ \hline \multirow{2}{*}{\(T=0\)} & PSNR & 41.02 & 41.02 & 41.00 & 41.01 & 41.05 & 41.02 & 41.02 & 41.06 \\ \cline{2-9}  & SSIM & 0.9564 & 0.9505 & 0.9867 & 0.9612 & 0.9723 & 0.9501 & 0.9613 & 0.9654 \\ \hline \multirow{2}{*}{\(T=1\)} & PSNR & 41.08 & 41.14 & 41.01 & 41.09 & 41.07 & 41.11 & 41.06 & 41.12 \\ \cline{2-9}  & SSIM & 0.9574 & 0.9523 & 0.9867 & 0.9622 & 0.9727 & 0.9514 & 0.9618 & 0.9664 \\ \hline \multirow{2}{*}{\(T=2\)} & PSNR & 41.31 & 41.80 & 41.01 & 41.45 & 41.21 & 41.63 & 41.18 & 41.84 \\ \cline{2-9}  & SSIM & 0.9613 & 0.9638 & 0.9867 & 0.9666 & 0.9746 & 0.9580 & 0.9637 & 0.9788 \\ \hline \multirow{2}{*}{\(T=3\)} & PSNR & 41.62 & 42.39 & 41.02 & 41.80 & 41.34 & 42.04 & 41.34 & 42.02 \\ \cline{2-9}  & SSIM & 0.9660 & 0.9727 & 0.9868 & 0.9709 & 0.9764 & 0.9626 & 0.9657 & 0.9810 \\ \hline \multirow{2}{*}{\(T=4\)} & PSNR & 42.03 & 42.94 & 41.03 & 42.32 & 41.49 & 42.61 & 41.57 & 42.22 \\ \cline{2-9}  & SSIM & 0.9710 & 0.9784 & 0.9870 & 0.9756 & 0.9780 & 0.9679 & 0.9683 & 0.9828 \\ \hline \multirow{2}{*}{\(T=5\)} & PSNR & 42.31 & 43.19 & 41.04 & 42.64 & 41.59 & 43.06 & 41.79 & 42.39 \\ \cline{2-9}  & SSIM & 0.9738 & 0.9805 & 0.9870 & 0.9780 & 0.9792 & 0.9714 & 0.9707 & 0.9844 \\ \hline \multirow{2}{*}{\(T=6\)} & PSNR & 42.48 & 43.32 & 41.05 & 42.78 & 41.64 & 43.31 & 41.93 & 42.48 \\ \cline{2-9}  & SSIM & 0.9748 & 0.9808 & 0.9871 & 0.9786 & 0.9797 & 0.9727 & 0.9716 & 0.9849 \\ \hline \multirow{2}{*}{\(T=7\)} & PSNR & 42.49 & 43.31 & 41.04 & 42.77 & 41.63 & 43.33 & 41.94 & 42.47 \\ \cline{2-9}  & SSIM & 0.9741 & 0.9806 & 0.9870 & 0.9783 & 0.9793 & 0.9722 & 0.9711 & 0.9847 \\ \hline \multirow{2}{*}{\(T=8\)} & PSNR & 42.39 & 43.26 & 40.99 & 42.70 & 41.53 & 43.24 & 41.83 & 42.43 \\ \cline{2-9}  & SSIM & 0.97301 & 0.9798 & 0.9865 & 0.9776 & 0.9783 & 0.9711 & 0.9696 & 0.9843 \\ \hline \multirow{2}{*}{\(T=9\)} & PSNR & 42.24 & 43.17 & 40.90 & 42.55 & 41.37 & 43.09 & 41.65 & 42.35 \\ \cline{2-9}  & SSIM & 0.9719 & 0.9793 & 0.9855 & 0.9766 & 0.9765 & 0.9698 & 0.9675 & 0.9837 \\ \hline \multirow{2}{*}{\(T=10\)} & PSNR & 42.06 & 43.02 & 40.78 & 42.33 & 41.13 & 42.93 & 41.41 & 42.22 \\ \cline{2-9}  & SSIM & 0.9705 & 0.9786 & 0.9843 & 0.9753 & 0.9747 & 0.9688 & 0.9654 & 0.9830 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR and SSIM comparisons with various \(T\) value. Figure 3: Eight test images. (**a**) Lena; (**b**) Jet; (**c**) Baboon; (**d**) Tiffany; (**e**) Sailboat; (**f**) Splash; (**g**) Peppers; (**h**) House. Figure 4 shows the plot of threshold \(T\) versus PSNR for various test images. When \(T=0\), the PSNRs of the eight test images are around 41 dB. Among these images at \(T=6\), Jet has the highest PSNR, while Baboon achieves the lowest PSNR, which is about 2 dB lower than that of Jet. This is because image quality is dependent on the ratio of smooth blocks for a given threshold, which is demonstrated in the following experiments. Table 2 shows the ratio of smooth blocks and the PSNR of images when \(T=6\).