## 3 Main Scheme
### Algorithm III. Meaningful Shares Scheme
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\gamma\) & **Scheme** & \(\mathbf{\alpha_{shares}}\) & \(\mathbf{\alpha_{R_{0}}}\) & \(\mathbf{\alpha_{R_{1}}}\) \\ \hline \multirow{4}{*}{1} & Method 1 & 0.73112 & 0.41256 & 0.41242 \\ \cline{2-5}  & Method 2 & 0.73121 & 0.00456 & 0.00370 \\ \cline{2-5}  & Method 3 & 0.73105 & 1.00000 & 0.01860 \\ \cline{2-5}  & Method 4 & 0.52898 & 0.00000 & 0.00000 \\ \hline \multirow{4}{*}{0.7} & Method 1 & 0.46104 & 0.55675 & 0.55639 \\ \cline{2-5}  & Method 2 & 0.46080 & 0.26068 & 0.25982 \\ \cline{2-5}  & Method 3 & 0.46111 & 0.99480 & 0.23623 \\ \cline{2-5}  & Method 4 & 0.33886 & 0.29930 & 0.29939 \\ \hline \multirow{4}{*}{0.5} & Method 1 & 0.30524 & 0.66746 & 0.66728 \\ \cline{2-5}  & Method 2 & 0.30492 & 0.45372 & 0.45297 \\ \cline{2-5}  & Method 3 & 0.30516 & 0.99155 & 0.40721 \\ \cline{2-5}  & Method 4 & 0.23194 & 0.49910 & 0.49963 \\ \hline \multirow{4}{*}{0.3} & Method 1 & 0.17385 & 0.78586 & 0.78570 \\ \cline{2-5}  & Method 2 & 0.17338 & 0.64508 & 0.64515 \\ \cline{2-5}  & Method 3 & 0.17387 & 0.98794 & 0.60569 \\ \cline{2-5}  & Method 4 & 0.12970 & 0.69844 & 0.69816 \\ \hline \multirow{4}{*}{0} & Method 1 & 0.00022 & 0.98313 & 0.98359 \\ \cline{2-5}  & Method 2 & 0.00011 & 0.98335 & 0.98342 \\ \cline{1-1} \cline{2-5}  & Method 3 & 0.00035 & 0.98344 & 0.98328 \\ \cline{1-1} \cline{2-5}  & Method 4 & 0.00012 & 0.98347 & 0.98350 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Contrast analysis of the proposed schemes. ### PSNR Analysis

In this subsection, we introduce the Peak Signal-to-Noise Ratio (PSNR), which is a ratio of the maximum possible power of the signal and destructive noise power affecting its representation accuracy, and PSNR is often expressed in decibel units. In the image, we can use PSNR as a more objective method to calculate the distortion of the image because it has quantitative data. The PSNR is defined simply by the mean-square error (MSE). Given an original image \(I\) of size \(w\times h\) and a reconstructed image \(K\), the PSNR and mean square error (MSE) are defined as:

\[MSE=\frac{1}{w\times h}\sum_{0}^{m-1}\sum_{0}^{n-1}[I(i,j)-K(i,j)]^{2} \tag{3}\]

\[PSNR=10\times\log_{10}\left(\frac{MAX_{I}^{2}}{MSE}\right) \tag{4}\]

\(MAX_{I}\) is the maximum possible value of pixels for an image. If each pixel is represented by 8 bits, then black pixels are 0 and white pixels are 255, so \(MAX_{I}\) in our scheme is always calculated using 255. We perform PSNR analysis of our schemes in Table 3. In this table, we use the corresponding method to encrypt two secret images and five camouflaged images with \(p=45\), \(N=2\), and \(n=5\) in different \(\gamma\) cases for the analysis. The values in this table are the average PSNR for two restored images (except Method 3) and five shares. A total of 7! (= 5040) experimental results were averaged and presented in Table 3. PSNR is generally used for gray-scale image or color image analysis, so the results are for reference only since we use binary data in these schemes. Observing Table 3, we can find that the PSNR value of the shares decreases as \(\gamma\) decreases. The PSNR values of shares in Methods 1-3 are almost the same and better than shares in Method 4. As \(\gamma\) decreases, the PSNR of restored images gets better. With the same value of \(\gamma\) for Method 1, Method 2, and Method 4, the PSNR of the two restored images is almost identical, so we show their average value in this table. In Method 3 with the same value of \(\gamma\), the PSNR for the first restored image is much better than the second restored image; thus, we write them separately. In conclusion, Method 1 gives the best results for the average PSNR in restored images, and Method 3 has the best PSNR for the first restored image.