# Enhanced Dual Reversible Data Hiding Using Combined Approaches
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Images** & **Message (bits)** & \(R_{M}\) & \(R_{-M}\) & \(S_{M}\) & \(S_{-M}\) & **RS Value** \\ \hline \multirow{2}{*}{Boat} & 20,000 & 19,152 & 24,271 & 9748 & 4629 & 0.3253 \\  & 50,000 & 19,143 & 24,264 & 9757 & 4636 & 0.3247 \\ \hline \multirow{2}{*}{Barbara} & 20,000 & 19,978 & 26,131 & 8922 & 2769 & 0.3825 \\  & 50,000 & 19,974 & 26,132 & 8926 & 2768 & 0.3822 \\ \hline \multirow{2}{*}{Tiffany} & 20,000 & 18,899 & 23,851 & 10,001 & 5049 & 0.3078 \\  & 50,000 & 18,897 & 23,849 & 10,003 & 5051 & 0.3077 \\ \hline \multirow{2}{*}{Pepper} & 20,000 & 19,232 & 24,559 & 9668 & 4341 & 0.3309 \\  & 50,000 & 19,232 & 24,556 & 9668 & 4344 & 0.3309 \\ \hline \multirow{2}{*}{Goldhill} & 20,000 & 19,242 & 24,762 & 9658 & 4138 & 0.3316 \\  & 50,000 & 19,242 & 24,767 & 9658 & 4133 & 0.3316 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of RS analysis for different marked image \(I_{2}^{\prime}\) with varying message lengths. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Images** & **Message (bits)** & \(R_{M}\) & \(R_{-M}\) & \(S_{M}\) & \(S_{-M}\) & **RS Value** \\ \hline \multirow{2}{*}{Boat} & 20,000 & 19,147 & 24,274 & 9753 & 4626 & 0.3250 \\  & 50,000 & 19,140 & 24,272 & 9760 & 4628 & 0.3245 \\ \hline \multirow{2}{*}{Barbara} & 20,000 & 19,976 & 26,129 & 8924 & 2771 & 0.3824 \\  & 50,000 & 19,973 & 26,128 & 8927 & 2772 & 0.3822 \\ \hline \multirow{2}{*}{Tiffany} & 20,000 & 18,899 & 23,848 & 10,001 & 5052 & 0.3078 \\  & 50,000 & 18,899 & 23,842 & 10,001 & 5058 & 0.3078 \\ \hline \multirow{2}{*}{Pepper} & 20,000 & 19,231 & 24,555 & 9669 & 4345 & 0.3308 \\  & 50,000 & 19,227 & 24,550 & 9673 & 4350 & 0.3305 \\ \hline \multirow{2}{*}{Goldhill} & 20,000 & 19,244 & 24,559 & 9668 & 4341 & 0.3309 \\  & 50,000 & 19,244 & 24,765 & 9656 & 4135 & 0.3317 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of RS analysis for different marked image \(I_{1}^{\prime}\) with varying message lengths. In the Pepper image, the RS values for both \(I_{1}^{\prime}\) and \(I_{2}^{\prime}\) are similarly observed at 0.3308 (or 0.3309) for 20,000 bits and 0.3305 (or 0.3309) for 50,000 bits. This suggests that the two hiding methods exhibit almost identical statistical characteristics in the Pepper image. As the message length increases, the RS values show a slight decreasing trend, which consistently appears in both images, indicating that data hiding has minimal impact on the statistical properties of the image. For the Goldhill image, the RS values show highly consistent results in both experiments. For a 20,000-bit message, the value is measured at 0.3309 (or 0.3316), and for a 50,000-bit message, the value remains nearly the same at 0.3317. The Goldhill image contains natural scenes with complex textures, which helps to reveal the effects of data hiding more clearly. Overall, the two experiments yielded very similar RS values for the same image, suggesting that the two proposed data hiding methods have a consistent impact on the statistical properties of the image. The consistency of RS values for each image indicates that the data hiding methods can effectively conceal data without significantly compromising the statistical integrity of the image. Additionally, the minimal variation in RS values as the message length increases implies that the proposed methods maintain stable performance across various message lengths. Tables 3 and 4 summarize the results under specific experimental conditions. Instead of including all nine test images, representative images were selected to effectively illustrate the key trends observed in the experiments. The selection includes images with different texture characteristics to ensure a balanced evaluation. However, all nine images were tested, and the complete results remain consistent with the trends presented in these tables. Figure 4 shows the results of analyzing the pixel value difference (PVD) histogram to evaluate data hiding performance.