## 4 Proposed Scheme for Self-Embedding
### Watermark Extraction and Reconstructing Ambtc
's method [29], when the image damaged area was less than 50%, the quality of the reconstructed image was high (33.6). This was improved through image filtering after image restoration. In conclusion, our proposed method had the best restored image quality, but the quality of marked images was not the best. This is because up to 3 LSB was used for restoration performance. Table 4 shows the PSNR and NCC (Normalized Cross-Correlation) of the watermarked images, and it shows their embedding times (seconds). The PSNRs of the marked images were at levels difficult to discriminate with the human visual system. Therefore, the marked image made by the proposed method was very good in the aspect of the images' quality. In addition, the time performance measured with MATLAB was not bad, but the reason why the performance was not high is due to the performance of MATLAB, and it seems that there will be no problem in terms of time when developing in C language. ## 6 Conclusions

In this paper, we present a productive, fragile, self-embedding watermarking method based on AMPTC. Here, we concealed the recovery bits in LSB2 and LSB3 and the checksum bits in LSB in block units using the OPAP method. In addition, a checksum was introduced for accurate block authentication. In the existing method, binary bits were used for authentication, but there was a lack of precision, so checksum was used. Since the proposed method is a fragile watermarking method, the watermark information may be destroyed by image processing such as compression and filtering. However, in case of a partial cropping attack, it is possible to restore the tampered area to the level of the marked area before the forgery by using the hidden restoration information. The limitation of our proposed method is that if the damaged area of the image is large, the restoration information is also removed, so that an area that cannot be restored may occur. In the future we would like to find a way to solve the problem of corruption of recovery information that occurs when the size of the damaged image area is more than 50%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cover Image** & **PSNR (dB)** & **SSIM** & **NCC** & **Embedding Time (s)** \\ \hline Lena & 40.0076 & 0.9488 & 0.9996 & 1.0396 \\ Pepper & 40.0121 & 0.9516 & 0.9997 & 0.9516 \\ Airplane & 40.0306 & 0.9469 & 0.9996 & 0.8567 \\ Boat & 40.0093 & 0.9549 & 0.9996 & 0.9976 \\ Goldhill & 39.9983 & 0.9662 & 0.9995 & 1.2315 \\ Couple & 40.0196 & 0.9691 & 0.9996 & 1.2363 \\ Baboon & 40.0095 & 0.9841 & 0.9996 & 1.2099 \\ Zelda & 39.9805 & 0.9480 & 0.9994 & 0.8555 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measuring PSNR, SSIM, NCC and time (second) of marked images based on the proposed method. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Methods** & **Marked Images** & **Recovered Images** & **Criteria of Restoration** \\  & **(PSNR)** & **(PSNR)** & **Criteria of Restoration** \\ \hline [PERSON] et al. [19] & 51.1 & 32.2 & Tampered areas must be reserved \\ [PERSON] et al. [23] & 37.9 & 29.9 & \(<\)59\% \\ [PERSON] et al. [24] & 37.9 & 35.0 & \(<\)35\% \\ [PERSON] and [PERSON] [27] & 40.7 & 32.0 & \(<\)50\% \\ [PERSON] et al. [29] & 43.7 & 33.6 & \(<\)50\% \\ The proposed method & 40.0 & 36.6 & \(<\)45\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons of PSNR of marked image and recovered image among different schemes. curation, C.K. ; funding acquisition, C.-N.Y., C.K. All authors have read and agreed to the published version of the manuscript. This work was partially supported by the Ministry of Science and Technology (MOST), under Grant 108-2221-E-259-009-MY2 and 109-2221-E-259-010, and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by (2015R1D1A1A01059253), and it was supported under the framework of international cooperation program managed by NRF (2016K2A9A2A05005255). This work was supported by the faculty research fund of Sejong University in 2020. Not applicable.