## 5 Analysis of 1-LSB, 2-LSB and 3-LSB Schemes in Embedding Stage  
A comparison between the different LSB variants of the designed framework was performed. The watermarked images were compared with the original ones, and the results are reported in Table 1, which shows the average values of the objective quality measures PSNR, SSIM and PSNR-HVS-M for each variant. Furthermore, the comparison was also performed using the bit adjustment for 2-LSB and 3-LSB methods. It can be observed that a minimal enhancement is generally achieved using this adjustment. Figure 3: Images employed from Kodak database [40], (**a**) Kodak-1, (**b**) Kodak-3, (**c**) Kodak-11, (**d**) Kodak-14, (**e**) Kodak-4, (**f**) Kodak-10, (**g**) Kodak-17, (**h**) Kodak-18. During the imperceptibility evaluation of the three variants (1-LSB, 2-LSB or 3-LSB) shown in Table 1, we can observe that the 1-LSB and the 3-LSB variants have the best and the worst performance, respectively, in terms of objective quality evaluation. However, a point worth mentioning is that for the worst case (3-LSB), the embedding of nine copies of the watermark does not produce any recognizable visual modification in the watermarked image. To measure the authentication and reconstruction process's performance, experiments changing the tampering rate from 10% to 90% in the image were carried out, adding pseudo-random noise to the image, as can be observed in Figure 4.  
The authentication stage evaluation is reported in Table 2, where it can be observed that the 1-LSB method maintains the best results in _Precision_. In terms of _Recall_, the proposed variants' performance increases when this measure is close to one. The variants 2-LSB and 3-LSB have the same high Recall value, even though the 3-LSB variant embeds more copies. Additionally, the probability that the 1-LSB variant extracts copies incorrectly is higher than the other variants, generating more errors during the authentication process. Another point worth mentioning is that the 2-LSB variant achieves Recall's best performance, avoiding the tampering coincidence problem, embedding only six copies of the recovery watermark. Finally, the average values of the quality measures PSNR, SSIM and PSNR-HVS-M for the reconstructed images compared with the original ones are shown in Table 3. A significant increase in the values with the 2-LSB method can be recognized. Nevertheless, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**No Bit Adjustment**} & \multicolumn{3}{c}{**With Bit Adjustment**} \\ \hline
**Embedding** & **1-LSB** & **2-LSB** & **3-LSB** & **2-LSB** & **3-LSB** \\ \hline PSNR & 51.17 & 43.89 & 37.51 & 44.33 & 37.69 \\ SSIM & 0.9966 & 0.9824 & 0.9314 & 0.9843 & 0.9340 \\ PSNR-HVS & 59.21 & 49.89 & 41.80 & 49.69 & 41.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Least-significant bit (LSB) embedding analysis in terms of the objective quality. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **Embedding** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** \\ \hline \multirow{3}{*}{Recall} & 1-LSB & 0.9033 & 0.9211 & 0.9369 & 0.9345 & 0.9356 & 0.9386 & 0.9404 & 0.9389 & 0.9384 \\  & 2-LSB & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\  & 3-LSB & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.9999 \\ \hline \multirow{3}{*}{Precision} & 1-LSB & 0.9466 & 0.9733 & 0.9831 & 0.988 & 0.9943 & 0.9913 & 0.9922 & 0.9932 & 0.9944 \\  & 2-LSB & 0.9157 & 0.9585 & 0.9718 & 0.9799 & 0.9885 & 0.9849 & 0.9877 & 0.9892 & 0.9910 \\ \cline{1-1}  & 3-LSB & 0.8893 & 0.9448 & 0.9637 & 0.9744 & 0.9843 & 0.9819 & 0.9855 & 0.9874 & 0.9900 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Precision_ and _Recall_ obtained from the authentication process. Figure 4: Tampered images for Kodak-23, (a) 20%, (b) 30%, (c) 40%, (d) 50%, (e) 60%, (f) 70%, (g) 80%, (h) 90%. although the 3-LSB implementation also showed a sharp increment compared with 1-LSB, its results are slightly lower than the 2-LBS method.