## 3 Proposed Method
### Determining the Watermark Inserting Region
The JPEG 2000 image is converted to an RGB color space, and the peak signal-to-noise ratio (PSNR) with the original raw image is calculated and denoted as PSNR\({}_{IP2}\). PSNR is a widely used metric for evaluating image quality in the field of image compression research, as defined in [35]. Figure 4: Structure of the four-level DWT. Figure 5: Example of division using HH1 sub-band (\(Tb=15\), rate control factor \(=10\), \(m=4\)). We select DWT coefficients that have an absolute value greater than the 2\({}^{m}\) value. 3. We change the values of the p-LSB plane of all selected coefficients and save them as JPEG 2000 images (changed JPEG 2000 images). We convert the changed JPEG 2000 image to the RGB color space and calculate the PSNR with the original raw image, defined as \(\text{PSNR}_{F-JP2}\). 4. To compare PSNR reduction, we subtract \(\text{PSNR}_{F-JP2}\) from \(\text{PSNR}_{JP2}\). The above experiment was conducted to observe the visual difference in the change of DWT coefficients to select the optimal location for watermark insertion in the bit plane. The experiment was conducted for each Y, Cb, and Cr component by varying the bit-rate control variables from 5 to 40. A total of 10 sample images, including both indoor and outdoor photos, were selected for the experiment. The sample images are shown in Figure 6.  
Tables A1 and A2 show the average PSNR values (\(\text{PSNR}_{JP2}\)) of the 10 sample images and the corresponding PSNR difference (\(\text{PSNR}_{JP2}-\text{PSNR}_{F-JP2}\)). The Cb and Cr components exhibit similar results, while the Y component differs from the chrominance components. Tables 2 and 3 provide information on the \(m\) values for the \(p\)-th bit plane that guarantee a PSNR difference of 0.1 dB and 0.05 dB or less for all the sample images, respectively. Based on Tables 2 and 3, which set the \(m\) value for the \(p\)-th bit-plane that ensures the minimum PSNR difference, Figure 7 illustrates an example of image division. Figure 7a-d shows an image division example for component Y. When the \(m\) value is less than 4, use the HH bands of levels 1 and 2. When the \(m\) value is 4 or higher, use the HL, LH, and HH bands of level 1. Figure 7e-j shows an example of division for all components in the proposed watermark embedding scheme. Figure 6: Sample images that were used for the experiment. It is not explicitly shown in this paper, but Image 1 (512 \(\times\) 512) used for experimental purposes is the well-known ‘Lena’ image. **(a)** Image 2 (512 \(\times\) 512). **(b)** Image 3 (696 \(\times\) 568) **(c)**. Image 4 (664 \(\times\) 560) **(d)**. Image 5 (512 \(\times\) 472) **(e)**. Image 6 (4312 \(\times\) 1868). **(f)** Image 7 (1000 \(\times\) 640). **(g)** Image 8 (1920 \(\times\) 1080). **(h)** Image 9 (1000 \(\times\) 640). **(i)** Image 10 (4288 \(\times\) 2848). \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{} & \multirow{2}{*}{\(Y\)} & \multicolumn{10}{c|}{\(m\)} \\ \cline{3-10}  & & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \multirow{5}{*}{\(p\)} & 1 & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 2 & & & & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 3 & & & & & & & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 4 & & & & & & & \(\bigcirc\) \\ \cline{2-10}  & 5 & & & & & & & \\ \cline{2-10}  & 6 & & & & & & & \\ \cline{2-10}  & 7 & & & & & & & \\ \hline \multirow{5}{*}{\(CbCr\)} & \multicolumn{10}{c|}{\(m\)} \\ \cline{3-10}  & 1 & 2 & 3 & 4 & 5 & & & \\ \cline{2-10}  & 1 & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 2 & & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 3 & & & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 4 & & & & & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \cline{2-10}  & 5 & & & & & & \(\bigcirc\) \\ \hline \end{tabular}
\end{table}