# Data Hiding and Authentication Scheme for Medical Images Using Double POB
## 4 Analysis of Simulation Result
### Hiding Performance  
#### 4.2.1 Embedding Capacity Analysis  
This part will analyze the embedding capabilities of the scheme in this paper. To intuitively measure the embedding capacity, it is usually expressed by the embedding rate (ER), which is the amount of data that can be embedded in each pixel on average, calculated by Equation (8):  
\[ER=\frac{n(bit)}{M\times N}(bpp) \tag{8}\]  
where \(n\) is the bits of the embedded data and \(M\times N\) is the number of pixels in the embedded image.  
Because the scheme proposed in this paper is based on the POB algorithm for data hiding, two extra pieces of data can be attached to each pixel, so the embedding capacity is very large. In addition, the method of separation of shares is adopted in this paper, and data embedding can be carried out in both ShareA\" and ShareB\". To protect the sensitive areas of medical images, hiding can be given priority in ShareB\". If the secret data are embedded in a share of a 256 \(\times\) 256 image, the embedding rate can reach 2, and the maximum embedding capacity is 2 \(\times\) 65,536 bits. Compared with the previous methods  
Figure 9: The correlation comparison of the original and re-encrypted image. (**a**) Brain 01; (**b**) Brain 02; (**c**) Pulmonary 01; (**d**) Pulmonary 02.  
of using the POB system to hide data in images, the embedding capacity of this paper's method is greatly improved.  
Table 1 shows the maximum embedding capacity and maximum embedding rate of our scheme and the scheme of [19] in four medical images. The embedding in the scheme of [19] is only carried out at the peak and sub-peak points of the image, whereas our scheme has a very high embedding capacity because it can embed secret messages in all pixels of the image.  
In addition, the ER of our scheme in common images is compared with that of several related information-hiding methods. Figure 10 shows that the ER of our scheme is significantly higher than that of other schemes. Meanwhile, the ER of our scheme is a constant value that is not affected by the image distribution. Among these existing methods, the embedding rate of some methods depends on the image distribution. Images with a smooth texture can obtain a higher embedding rate, while those with a complex texture have a lower embedding rate, so the proposed method can avoid this problem.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Our Scheme (Encrypted ShareA)** & \multicolumn{2}{c}{**Scheme of [19]**} \\ \cline{3-5}
**Test Images** & **ROS** & **Maximum** & **Maximum** & **Maximum** & **Maximum** \\  & & **Embedding** & **Embedding** & **Embedding** \\  & & **Capacity (bits)** & **Rate (bpp)** & **Capacity (bits)** & **Rate (bpp)** \\ \hline Brain 01(512 \(\times\) 512) & 352 \(\times\) 352 & 2 \(\times\) 262,144 & 2 & 263,216 & 1.0041 \\ Brain 02 (512 \(\times\) 512) & 464 \(\times\) 464 & 2 \(\times\) 262,144 & 2 & 185,322 & 0.7069 \\ Pulmonary 01 (256 \(\times\) 256) & 176 \(\times\) 176 & 2 \(\times\) 65,536 & 2 & 93,598 & 1.4282 \\ Pulmonary 02 (256 \(\times\) 256) & 176 \(\times\) 176 & 2 \(\times\) 65,536 & 2 & 94,742 & 1.4456 \\ Pancreas (180 \(\times\) 180) & 120 \(\times\) 120 & 2 \(\times\) 32,400 & 2 & 5808 & 0.1793 \\ Chest (256 \(\times\) 256) & 228 \(\times\) 188 & 2 \(\times\) 65,536 & 2 & 47,166 & 0.7197 \\ Knee (300 \(\times\) 162) & 212 \(\times\) 162 & 2 \(\times\) 48,600 & 2 & 29,028 & 0.5973 \\ Hand (64 \(\times\) 64) & 46 \(\times\) 60 & 2 \(\times\) 4096 & 2 & 2058 & 0.5024 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of maximum embedding capacity and maximum embedding rate between our scheme and the scheme of [19] in four test images.  
Figure 10: Comparison of ER between our scheme and related schemes [5; 6; 7; 8; 9] in ordinary images.