## 4 Experimental Studies
In addition, the comb effect, which indicates that there is secret data in the stego images, was not observed. The second method used in security tests is to obtain the distribution of pixel differences as called PDH. In the PDH diagram, the cover image is expected to be according to the zero mean normal distribution. In the stego image PDH, using some data hiding methods, it is possible that the distribution curve is zigzagging, periodically flats (e.g., PVD), multiple peaks (e.g., Histogram Shifting) or deviation from normal distribution. In addition, the similarity of the distributions of two stego images to each other can be a criterion in dual image based reversible data hiding methods. For the proposed data hiding method, PDHs are presented in Figure 11 for \(n=1\)-4 values. It can be seen from Figure 11 that, for all \(n\) values, the PDH graphics of two stego images overlap with each other. It is also seen that cover and stego images PDH analyzes for \(n=1\) to 3 are close. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**References** & **Measurement Metrics** & **[PERSON]** & **Baboon** & **[PERSON]** & **Barbara** & **[PERSON]** & **Average** \\ \hline \multirow{4}{*}{[43]} & PSNR (dB) & 49.20 & 49.21 & 49.19 & 49.22 & 49.23 & 49.21 \\ \cline{2-7}  & PSNR (dB) & 49.21 & 49.20 & 49.21 & 49.20 & 49.18 & 49.20 \\ \cline{2-7}  & PSNR(Average) & 49.21 & 49.21 & 49.20 & 49.21 & 49.21 & 49.21 \\ \cline{2-7}  & EC (bits) & 524,288 & 524,204 & 524,192 & 524,288 & 524,287 & 524,257 \\ \cline{2-7}  & P (bpp) & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ \hline \multirow{4}{*}{[44]} & PSNR (dB) & 47.34 & 47.34 & 47.34 & 47.34 & 47.34 & 47.34 \\ \cline{2-7}  & PSNR (dB) & 47.41 & 47.41 & 47.41 & 47.41 & 47.41 & 47.41 \\ \cline{2-7}  & PSNR(Average) & 47.37 & 47.38 & 47.37 & 47.37 & 47.37 & 47.37 \\ \cline{2-7}  & EC (bits) & 917,504 & 917,504 & 917,504 & 917,504 & 917,504 & 917,504 \\ \cline{2-7}  & P (bpp) & 1.75 & 1.75 & 1.75 & 1.75 & 1.75 & 1.75 \\ \hline \multirow{4}{*}{Proposed (\(n=1\))} & PSNR (dB) & 51.14 & 51.14 & 51.15 & 51.15 & 51.15 & 51.15 \\ \cline{2-7}  & PSNR (dB) & 51.14 & 51.13 & 51.14 & 51.15 & 51.14 & 51.14 \\ \cline{2-7}  & PSNR(Average) & 51.14 & 51.14 & 51.15 & 51.15 & 51.15 & 51.14 \\ \cline{2-7}  & EC (bits) & 524,288 & 524,190 & 524,104 & 524,136 & 524,136 & 524,171 \\ \cline{2-7}  & P (bpp) & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ \hline \multirow{4}{*}{Proposed (\(n=2\))} & PSNR (dB) & 46.12 & 46.23 & 46.16 & 46.07 & 46.11 & 46.14 \\ \cline{2-7}  & PSNR (dB) & 45.92 & 46.14 & 45.94 & 45.77 & 45.93 & 45.94 \\ \cline{2-7}  & PSNR(Average) & 46.02 & 46.19 & 46.05 & 45.92 & 46.02 & 46.04 \\ \cline{2-7}  & EC (bits) & 786,432 & 786,222 & 786,351 & 786,144 & 786,144 & 786,259 \\ \cline{2-7}  & P (bpp) & 1.50 & 1.50 & 1.50 & 1.50 & 1.50 & 1.50 \\ \hline \multirow{4}{*}{Proposed (\(n=3\))} & PSNR (dB) & 40.37 & 40.40 & 40.30 & 40.23 & 40.33 & 40.33 \\ \cline{2-7}  & PSNR (dB) & 40.33 & 40.44 & 40.21 & 40.14 & 40.18 & 40.26 \\ \cline{1-1} \cline{2-7}  & PSNR(Average) & 40.35 & 40.42 & 40.26 & 40.19 & 40.26 & 40.29 \\ \cline{1-1} \cline{2-7}  & EC (bits) & 1048,576 & 1047,832 & 1047,896 & 1048,168 & 1,048,168 & 1,048,128 \\ \cline{1-1} \cline{2-7}  & P (bpp) & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._Figure 8: Comparisons of histogram analysis for \(n=1\) in grayscale Lena image. Figure 9: Comparisons of histogram analysis for \(n=2\) in grayscale Lena image. of the singular pixel group (Sm, S-m) indicates that there is distortion in the image, that is, secret data may be embedded. In other words, that image is normal when the expression \"Sm \(\approx\) S-m \(<\) Rm \(\approx\) R-m\" is provided. When the difference between (Rm, R-m) values and (Sm, S-m) values increase, it is understood that there is secret data in the image. Figure 12 presents RS analysis results for the proposed method.