## 3 Experiment Results and Analysis
### Performance Analysis  
Table 2 shows the ER in bpp using different predictors on the five test images. From Table 2, we can see that for the five test images, the best ERs are obtained when using the GAP predictor. The average ER for these five test images is more than 3 bits per pixel. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Image** & **Horizontal** & **Entropy** & \(\chi^{2}\) \\  & **Correlation** & **(in bpp)** & **Test** \\ \hline Original Lena image & 0.9710 & 7.2184 & 242,173 \\ Encrypted Lena image & \(-0.0021\) & 7.9994 & 222 \\ Marked and encrypted Lena image & \(-0.0003\) & 7.9995 & 203 \\ Original Jetplane image & 0.9357 & 6.7059 & 715,669 \\ Encrypted Jetplane image & \(-0.0001\) & 7.9993 & 253 \\ Marked and encrypted Jetplane image & \(-0.0005\) & 7.9994 & 211 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Security evaluation of the proposed method. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Image** & **MED** & **MED-IMP1** & **MED-IMP2** & **GAP** \\ \hline Lena & 3.493 & 3.419 & 3.476 & 3.606 \\ Baboon & 1.832 & 1.667 & 1.824 & 1.903 \\ Jetplane & 3.620 & 3.387 & 3.599 & 3.642 \\ Man & 3.002 & 2.817 & 2.989 & 3.058 \\ Tiffany & 2.825 & 2.730 & 2.813 & 2.920 \\ \hline Average & 2.954 & 2.804 & 2.940 & 3.026 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Embedding rates obtained when using different predictors on the five test images. Figure 18: The correlation distributions in the horizontal direction of: (**a**) the original Lena image, (**b**) the encrypted Lena image, (**c**) the marked-encrypted Lena image, (**d**) the original Jetplane image, (**e**) the encrypted Jetplane image, (**f**) and the marked-encrypted Jetplane image. The x-axis represents the pixel intensity value at coordinates (x, y). On the other hand, the y-axis represents the pixel intensity of the horizontally adjacent pixel located at coordinates (x + 1, y). The total embedding capacity, the auxiliary information, and the net payload for the five test images are calculated, and the results using the GAP predictor are shown in Table 3.  
Figure 19 shows the obtained ERs for the five test images when using different methods. It can be seen that our method outperforms the other five methods for the first four images with the highest ER. [PERSON] et al. [12] proposed to embed additional data into one-MSB only, resulting in a very low ER. For instance, the ERs of their method for the five test images were between 0.838 bpp and 0.993 bpp. [PERSON] et al. [19] proposed an improvement of the [PERSON] et al. 's [18] work by dividing the image pixels into two categories according to a parameter binary tree labeling scheme. By dividing the pixels into embeddable and non-embeddable sets, the overall embedding capacity may be affected. The ERs of the five test images are significantly higher than those obtained by the previous methods and range from 0.969 bpp to 2.6726 bpp. In their work, [PERSON] et al. [8] compressed the auxiliary information by using Huffman coding and embedding multi-bits adaptively by multi-MSB substitution. The scheme requires a large amount of auxiliary information leading to a potential impact on the overall embedding capacity. As an example, the auxiliary information required for the Lena image in [PERSON] et al. 's [8] approach is 793,304 bits, which is over six times greater than that needed in our method, as presented in Table 3. In [10], an RDHEI method is proposed based on pixel prediction scheme and multi-MSB planes reordering. The bit planes were divided into several non-overlapping blocks and the best ERs were found in the blocks of size \(4\times 4\). The blocks are classified as uniform or non-uniform, with a binary label map generated for each bit plane to indicate their positions. The data-embedding method used depends on whether the block is uniform or non-uniform. In uniform blocks, one bit is left unchanged to represent the block's value and aid in image recovery.