## 5 Discussion
### Comparison with State-of-the-Art Approaches  
In this section, we compare the capabilities of the proposed schemes with those of state-of-the-art approaches. We list seven parts of each scheme to assist in the evaluation. The criteria are illustrated as follows:  
1. Type of images: In other schemes, the experimental images are all black-and-white or halftone images. There is only 1 bit used per pixel in each image. In our scheme, we use grayscale and color images, and the bits per pixel are 8 and 24, respectively.
2. Pixel expansion: This refers to whether the scheme suffers from the pixel expansion problem. Pixel expansion increases the transmission time and decreases bandwidth utilization. There is no pixel expansion in our scheme.
3. Number of cover image: This refers to how many covers can be imported. The higher the cover number, the more situations can be used.
4. The number of share images: In our scheme, the amount of covers we import denotes how many shares we can generate. From Table 8, we can obviously see that our scheme is the same as the others.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cases** & **Theoretical MSE** & **Theoretical PSNR** & **Experimental PSNR** \\ \hline \((3,3)\) & 2427.1851 & 14.2797 & 16.4814 \\ \((4,4)\) & 1820.3888 & 15.5291 & 18.1383 \\ \((5,5)\) & 1456.3110 & 16.4982 & 19.4192 \\ \((6,6)\) & 1213.5925 & 17.2900 & 20.3865 \\ \((7,7)\) & 1040.2221 & 17.7959 & 21.1766 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The theoretical MSE, PSNR, and experimental PSNR for \(n=3\) to 7 of Algorithm 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cases** & **Theoretical MSE** & **Theoretical PSNR** & **Experimental PSNR** \\ \hline \((3,3)\) & 2427.1851 & 14.2797 & 16.2671 \\ \((4,4)\) & 1820.3888 & 15.5291 & 18.0392 \\ \((5,5)\) & 1456.3110 & 16.4982 & 19.2421 \\ \((6,6)\) & 1213.5925 & 17.2900 & 20.3442 \\ \((7,7)\) & 1040.2221 & 17.7959 & 21.4743 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The theoretical MSE, PSNR, and experimental PSNR for \(n=3\) to 7 of Algorithm 6.  
* Meaningful share: This refers to whether the scheme can generate a meaningful share. Meaningful shares are more desirable than meaningless shares, because they look more natural and other people will not be attracted by them.
* Decryption operation: There are two operations for any VCS, OR, and XOR operation. The secret image can be completely reconstructed using the XOR operation, while at most one-half of the image can be reconstructed by the OR operation.
* Contrast: As defined in [3; 16; 17; 18], this decides how human eyes recognize the reconstructed image. It ranges from 0 to 1. The higher the value, the more easily the restored image can be identified.  
Table 8 shows a comparisons between the capabilities of our schemes and those of [1; 16; 17; 18]. Compared to our schemes, that in [1] has the problem of pixel expansion. Moreover, the scheme in [1] cannot generate meaningful shares, and the contrast of the restored secret is only one-half. It can be easily observed that the number of cover images of the schemes in [1; 16; 18] are 0, 1, and \(n/2\), respectively. The main difference between our schemes and that in [17] is that our schemes work on grayscale and color images. We can apply our schemes to a wider variety of situations.