# An Authentication Method for AMBTC Compressed Images Using Dual Embedding Strategies
## 4 Experimental Results
### Detectability Comparisons with Prior Works  
This section shows the detectability comparisons of [25; 26; 27] and the proposed method. In this experiment, the marked compressed codes of Sailboat are tampered with by adding a bird. Figure 7a,b show the tampered image and the region of tamper, while Figure 7c-f present the detection results of [25; 26; 27] and the proposed method. The results show all methods can achieve a satisfactory detection result. Different metrics are used to measure the detection results of Figure 7, as shown in Table 4. The number of tampered pixels (NTB) in Figure 7a is 19,712, and the tampering rate is \(19712/(512\times 512)=7.52\%\), where. True positive (TP) represents the number of tampered pixels detected as tampered ones, while false negative (FN) is the number of tampered pixels incorrectly detected as untampered ones. The refined detection rate is calculated by \(\text{TP}/(\text{NTB})\). In all methods, the length of authentication codes embedded in each block is 6. Therefore, the collision probability is \(1/2^{6}=1.56\%\), i.e., the coarse detection rate is as high as \(100\%-1.56\%=98.44\%\). The table shows that the refined detection rates of [25; 26; 27] and the proposed method are up to 99%, which are better than the coarse detection rates and meet the theoretical values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & [25] & [26] & [27] & **Proposed** \\ \hline Number of tampered blocks (NTB) & & & 19,712 & \\ \hline Tampering rate & & & 7.52\% & \\ \hline True positive (TP) & 19,680 & 19,696 & 19,696 & 19,712 \\ \hline False negative (FN) & 32 & 16 & 16 & 0 \\ \hline The refined detection rate & 99.83\% & 99.91\% & 99.91\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Detectability comparisons using different metrics. Figure 6: Comparisons between PSNR and the number of smooth blocks for 200 images. A good detection method should be able to detect any kind of tampering. The following experiments are performed with some special tampering to further compare the detectability of [25; 26; 27] and the proposed method. The special tampering consisted of the marked codes of Peppers by adding bananas, orange and watermelon, and Figure 8a,b present the tampered image and regions. Let \(\{\hat{a}_{i},\ \hat{b}_{i},\hat{B}_{i}\}_{i=0}^{N-1}\) be the marked codes of Peppers. Suppose \(\{a_{i}^{\text{B}},\ b_{i}^{\text{B}},B_{i}^{\text{B}}\}_{i=0}^{N^{\text{B}- 1}}\), \(\{a_{i}^{\text{O}},\ b_{i}^{\text{O}},B_{i}^{\text{O}}\}_{i=0}^{N^{\text{O}- 1}}\) and \(\{a_{i}^{\text{W}},\ b_{i}^{\text{W}},B_{i}^{\text{W}}\}_{i=0}^{N^{\text{W}- 1}}\) are the codes of the bananas, orange and watermelon, and \(N^{\text{B}}\), \(N^{\text{O}}\) and \(N^{\text{W}}\) represent the number of blocks of these images, respectively. For tampering with bananas, codes \(\{a_{i}^{\text{B}},\ b_{i}^{\text{B}},B_{i}^{\text{B}}\}_{i=0}^{N^{\text{B}- 1}}\) are used to replace \(\{\hat{a}_{i},\ \hat{b}_{i},\hat{B}_{i}\}_{i=0}^{N^{\text{B}- 1}}\). Then, from \(\{\hat{a}_{i},\ \hat{b}_{i},\hat{B}_{i}\}_{i=0}^{N^{\text{B}- 1}}\), find the codes \(\{\hat{a}_{i}^{\text{B}},\ \hat{b}_{i}^{\text{B}},\hat{B}_{i}^{\text{B}}\}_{i=0}^{N^{\text{B}- 1}}\) which are the closest to \(\{a_{i}^{\text{B}},\ b_{i}^{\text{B}},B_{i}^{\text{B}}\}_{i=0}^{N^{\text{B}- 1}}\), and the found codes are used to replace \(\{a_{i}^{\text{B}},\ b_{i}^{\text{B}},B_{i}^{\text{B}}\}_{i=0}^{N^{\text{B}- 1}}\). For orange's tampering, the codes \(\{a_{i}^{\text{O}},\ b_{i}^{\text{O}},B_{i}^{\text{O}}\}_{i=0}^{N^{\text{O}- 1}}\) are used to replace \(\{\hat{a}_{i},\ \hat{b}_{i},\hat{B}_{i}\}_{i=0}^{N^{\text{O}- 1}}\). Then, the pixel pair \((a_{i}^{\text{O}},\ \hat{b}_{i}^{\text{O}})\) that satisfy \((14\times\hat{a}_{i}^{\text{O}}+\hat{b}_{i}^{\text{O}})\) mod \(64\) and has the minimum distance to \((a_{i}^{\text{O}},\ b_{i}^{\text{O}})\) is found. Finally, we use \((a_{i}^{\text{O}},\ \hat{b}_{i}^{\text{O}})\) to replace \((a_{i}^{\text{O}},\ b_{i}^{\text{O}})\) for \(0\leq i\leq N^{\text{O}}-1\).