## 4 Proposed Scheme for Self-Embedding
### Watermark Extraction and Reconstructing Ambtc
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cover Image**} & \multicolumn{6}{c}{**Tampering Rate**} \\ \cline{2-10}  & **5\%** & **10\%** & **15\%** & **20\%** & **25\%** & **30\%** & **35\%** & **40\%** & **45\%** \\ \hline Lena & 40.0894 & 40.0741 & 39.8066 & 39.2411 & 38.7654 & 38.2036 & 37.6783 & 36.754 & 36.6321 \\ Pepper & 39.1559 & 38.8223 & 38.258 & 37.8034 & 37.4989 & 37.0547 & 36.7648 & 36.1718 & 36.0495 \\ Airplane & 39.9916 & 40.0421 & 39.8804 & 39.0067 & 39.087 & 38.9265 & 39.1673 & 35.7464 & 35.7072 \\ Boat & 40.1693 & 39.9564 & 39.6507 & 38.9742 & 38.4153 & 37.7102 & 37.5841 & 35.8619 & 35.7968 \\ Goldhill & 39.7814 & 39.6703 & 39.95971 & 38.0752 & 37.8333 & 37.5566 & 37.4104 & 36.2497 & 35.8103 \\ Couple & 38.6335 & 37.9082 & 36.0183 & 34.9058 & 33.5838 & 33.1666 & 32.4731 & 32.1509 & 31.7149 \\ Baboon & 34.9313 & 33.6695 & 32.1257 & 31.5393 & 31.0723 & 30.4577 & 29.6961 & 29.551 & 28.6731 \\ Zelda & 40.0645 & 39.7914 & 39.0381 & 38.847 & 38.4935 & 37.7322 & 38.0708 & 36.3148 & 37.4341 \\ Barbara & 37.8367 & 37.0637 & 35.9489 & 35.8704 & 35.4713 & 34.1328 & 33.2672 & 31.9851 & 31.4458 \\ Average & 38.96151 & 38.55533 & 37.81376 & 37.14034 & 36.6912 & 36.10454 & 35.79023 & 34.53173 & 34.36264 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR comparisons between original images and recovered images according to tampered rates. Figure 5: Cropping attack according to various ratios on Lena images and reconstructed Lena images applying the method we proposed. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cover Image**} & \multicolumn{6}{c}{**Tampering Rate**} \\ \cline{2-10}  & **5\%** & **10\%** & **15\%** & **20\%** & **25\%** & **30\%** & **35\%** & **40\%** & **45\%** \\ \hline Lena & 0.9508 & 0.9517 & 0.9534 & 0.9506 & 0.951 & 0.9516 & 0.9521 & 0.9495 & 0.9507 \\ Pepper & 0.9504 & 0.9505 & 0.9504 & 0.9495 & 0.9497 & 0.9484 & 0.948 & 0.9458 & 0.9463 \\ Airplane & 0.9477 & 0.9492 & 0.9509 & 0.953 & 0.955 & 0.9573 & 0.9599 & 0.9546 & 0.9571 \\ Boat & 0.9582 & 0.9601 & 0.9625 & 0.9638 & 0.9644 & 0.9647 & 0.9668 & 0.9608 & 0.9632 \\ Goldhill & 0.9665 & 0.9668 & 0.9674 & 0.9604 & 0.9593 & 0.958 & 0.9572 & 0.9502 & 0.9502 \\ Couple & 0.9664 & 0.9658 & 0.9604 & 0.9609 & 0.9552 & 0.9513 & 0.9465 & 0.9441 & 0.94 \\ Baboon & 0.9776 & 0.9732 & 0.9655 & 0.9615 & 0.9572 & 0.9516 & 0.9454 & 0.9421 & 0.9359 \\ Zelda & 0.9494 & 0.9486 & 0.947 & 0.9462 & 0.9446 & 0.943 & 0.9443 & 0.9398 & 0.9421 \\ Barbara & 0.969 & 0.9686 & 0.967 & 0.9689 & 0.9682 & 0.9644 & 0.9618 & 0.9585 & 0.9565 \\ Average & 0.959556 & 0.959389 & 0.958278 & 0.9572 & 0.956067 & 0.954478 & 0.953556 & 0.949489 & 0.949111 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SSIM comparisons between original images and recovered images according to tampered rates. decreased, showing a downward trend. However, the line was relatively smooth. In the case of the Lena image, the maximum performance was 40 dB or more at 5% and 36 dB or more at 45%. In the case of the Pepper image, it showed about 39 dB at 5% and more than 36 dB at 45%, showing the lowest performance. The texture of the Pepper image has a smoother characteristic than that of the Lena image, and the surface of the cover image is very bright. Such features seem to degrade the quality of the recovered image during the reconstruction process using AMBTC. That can be a minor weakness of the method we have proposed. Since the recovered image using the proposed method used AMBTC derived from the BTC, this staircase effect could be reduced to some extent. The staircase effect may tend to appear larger in the brighter parts of the image. As a result, as the tampering rate increased, the staircase effect on the nose of [PERSON]'s image was slightly revealed. Overall, the quality of the image restored with the method we proposed was excellent. Figure 7 compares the performance of the existing self-embedding methods (i.e., [PERSON] et al. [17], [PERSON] et al. [25], [PERSON] [27], [PERSON] [30]) with our proposed method.