## 5 Conclusions  
In this paper, we proposed a digital image watermarking method using CNN that does not limit the resolution of the host image and WM information. This method adjusts the complementary relationship between invisibility and robustness using the strength factor. The pre-processing network for watermark increases the WM's resolution to that of the host image for the invisibility of the WM. The embedding network processes using CNNs that maintain the resolution to output the watermarked image. The extraction network also consists of CNNs to output the WM information by reducing the resolution. We performed attack simulations on the same distribution in each mini-batch to verify the robustness of the WM. This network is composed of a simple CNN and does not use \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Attack** & **Strength** & **ReDMark** & **Proposed** \\ \hline PSNR & & 40.24 [dB] & 40.58 [dB] \\ No attack & - & - & 0.7015 \\ \hline \multirow{3}{*}{Gaussian filtering} & Radius = 1 & 8.6 & 7.1429 \\  & Radius = 1.6 & 39 & 9.7258 \\  & Radius = 2 & - & 12.7232 \\ \hline \multirow{2}{*}{Median filtering} & \(3\times 3\) & 13.4 & 8.4184 \\  & \(5\times 5\) & - & 10.5548 \\ \hline \multirow{2}{*}{Salt and pepper noise addition} & 0.02 & 2.9 & 1.0204 \\  & 0.6 & 4.5 & 1.5306 \\  & 0.1 & 9.1 & 3.1888 \\ \hline \multirow{3}{*}{Gaussian noise addition} & 5\% & 2.4 & 5.9949 \\  & 15\% & 14.5 & 27 \\  & 25\% & 25.6 & 38.1696 \\ \hline \multirow{3}{*}{Sharpening} & Radius = 1 & 0.9 & 0.9885 \\  & Radius = 5 & 2.4 & 1.7217 \\  & Radius = 10 & 3.2 & 2.0089 \\ \hline \multirow{3}{*}{JPEG} & 90 & 1.6 & 0.9566 \\  & 70 & 4.2 & 4.24 \\  & 50 & 11.8 & 8.0676 \\ \hline \multirow{3}{*}{Cropout} & 0.1 & 7.7 & 2.1365 \\  & 0.2 & 13.1 & 5.3253 \\ \cline{1-1}  & 0.3 & 18.8 & 8.6735 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the proposed method with ReDMark [11]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Attack** & **Strength** & **[10]** & **[11]** & **[15]** &
\begin{tabular}{c} **Proposed** \\ **(s = 2.75)** \\ \end{tabular} \\ \hline Training dataset & - & COCO & Cifar-10, Pascal VOC & COCO & BOSS \\ Training dataset & - & BOSS & Standard dataset & COCO & Standard dataset \\ PSNR & - & - & 33.5 & 33.5 \\ JPEG & 50 & 37 & 25.4 & 23.8 & 0.6696 \\ Cropout & 0.3 & 6 & 7.5 & 2.7 & 5.8355 \\ Dropout & 0.3 & 7 & 8 & 2.6 & 4.7194 \\ Crop & 0.035 & 12 & 0 & 11 & 44.1327 \\ Gaussian filtering & \(\sigma=2\) & 4 & 50 & 1.4 & 4.3048 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the proposed method with recent studies. any resolution-dependent layer, such as the FC layer. It is, therefore, adaptive to the resolution of the input image. It is also independent of the WM information because it uses the newly and randomly generated WM information for each mini-batch in training. Invisibility and robustness were measured for various pixel value change attacks and geometric attacks, for various WM information and host image resolutions. The results showed excellent performance and showed better performance for meaningful attacks in comparison with the state-of-the-art works. Therefore, our scheme has been proven to be very practical and universal. Besides, by adjusting the strength factor, we confirmed that our scheme could effectively control the complementary relationship between invisibility and robustness. Therefore, we think the proposed method would be a beneficial watermarking scheme for a digital image because it enables the embedding and extraction of WMs without restrictions on the host image and WM information, that is, and without any additional training. The usefulness can be further improved by adequately controlling the invisibility and the robustness to obtain proper performance, as per the user requirements. Conceptualization, J.-E.L. and D.-W.K. ; methodology, J.-E.L.; software, J.-E.L.; validation, J.-E.L., Y.-H.S. and D.-W.K. ; formal analysis, J.-E.L., Y.-H.S. and D.-W.K.