# Reversible Data Hiding in Encrypted Image Based on Multi-MSB Embedding Strategy
## 4 Experimental Results and Analysis
### Comparisons with Related Methods and Analysis
Ideally, nearly 3/4 of the pixels of the whole image can be used to embed data, and each pixel can be embedded into 5 bits of data. Thus, the highest embedding rate of an image is close to 3.75 bpp. As can be seen from Table 4, the highest embedding rate of the proposed method reaches 3.7140 bpp. But for those complex images, the embedding rate is not ideal, the worst case is only 0.1863 bpp. To better compare the embedding rate of different images, we randomly selected 500 images from the 10,000 images, and the embedding rate of these images were obtained. The experimental results are shown in Figure 9. Compared with the methods proposed by [PERSON] et al. EPE [38] and [PERSON] et al. [39], respectively, the proposed method had a significant improvement on most images in terms of embedding rate. For these 500 tested images, the embedding rates of 495 images in the proposed method were higher than those of [PERSON] et al. EPE [38], and the embedding rates of 475 images were higher than that of [PERSON] et al. [39]. For the proposed method, the embedding rates of most tested images were between 1.6 bpp and 2.7 bpp, which are satisfying. For [PERSON] et al. 's method [39], the embedding rates were between 1.2 bpp and 1.7 bpp for most images, which are obviously lower than the proposed method. In [PERSON] et al. EPE [38], the maximum embedding rates of most images were between 0.8 bpp and 1 bpp. We used three straight lines to indicate the average embedding rate of the 500 tested images for three methods. For the proposed method, the average embedding rate of 500 images was 2.0061 bpp. Correspondingly, the average embedding rates of [38; 39] were 0.9736 bpp and 1.4531 bpp, respectively. For these 500 tested images, the proposed method was higher than Puteaux et al. EPE [38] and [PERSON] et al. [39] by 1.0325 bpp and 0.5530 bpp, respectively. Overall, the experimental results demonstrate that the embedding rate of the proposed method is approximately 1.8 and 1.3 times those of the methods [38] and [39], respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Image** & **Lena** & **Airplane** & **Man** & **Crowd** & **Baboon** & **Hill** & **Peppers** & **Lake** & **Average** \\ \hline [PERSON] et al. CPE [38] & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) \\ [PERSON] et al. EPE [38] & \(0.9779\) & \(0.9817\) & \(0.9698\) & \(0.9830\) & \(0.8499\) & \(0.9919\) & \(0.9705\) & \(0.9722\) & \(0.9621\) \\ [PERSON] et al. [39] & \(1.1408\) & \(1.2498\) & \(1.0111\) & \(1.0030\) & \(0.4093\) & \(1.0404\) & \(1.1131\) & \(0.8973\) & \(0.9831\) \\ Proposed & \(1.7964\) & \(1.8318\) & \(1.3256\) & \(1.5081\) & \(0.4838\) & \(1.3410\) & \(1.8443\) & \(1.2834\) & \(1.4268\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum embedding rate comparison between the proposed method with methods [38; 39] (bpp). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Best Case** & **Worst Case** & **Average** \\ \hline [PERSON] et al. CPE [38] & \(1\) & \(1\) & \(1\) \\ [PERSON] et al. EPE [38] & \(1\) & \(0.3805\) & \(0.9681\) \\ [PERSON] et al. [39] & \(1.992\) & \(0.115\) & \(1.3512\) \\ Proposed & \(3.7140\) & \(0.1863\) & \(1.7215\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum embedding rate comparison between the proposed method and methods [38; 39] on the BOW-2 database (bpp, 10,000 images). For RDH in the encrypted domain, the visual quality of the reconstructed image with only knowledge of the encryption key is an important evaluating index. Our method was compared with other relevant methods [31; 35; 36; 38; 39]. To do this, the well-known images of Lena, Airplane, and Man were used. Figure 10 shows the rate-distortion curves generated from the three tested images. For all tested images, since the approach of [PERSON] et al. EPE [38] and the method of [PERSON] et al. [39] do not need to use overhead, the reconstructed images are lossless (i.e., PSNR\(->+\infty\)).