# An Innovative Information Hiding Scheme Based on Block-Wise Pixel Reordering
## 3 Proposed Scheme
### Data Hiding
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Image Name** & **Block Size** & **Group Size** & **EC** & **PSNR** & **UACI** & **MAE** \\ \hline \multirow{4}{*}{Airplane} & \(1\times 8\) & 256 & 197,888 & 51.15 & 49.90 & 0.1957 & 0.4990 \\  & \(1\times 6\) & 64 & 180,048 & 51.15 & 49.89 & 0.1957 & 0.4989 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 49.98 & 0.1960 & 0.4998 \\  & \(1\times 2\) & 4 & 131,072 & 51.14 & 50.06 & 0.1963 & 0.5006 \\ \hline \multirow{4}{*}{Baboon} & \(1\times 8\) & 256 & 197,888 & 51.15 & 49.90 & 0.1957 & 0.4990 \\  & \(1\times 6\) & 64 & 180,048 & 51.12 & 50.22 & 0.1969 & 0.5022 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 50.05 & 0.1963 & 0.5005 \\  & \(1\times 2\) & 4 & 131,072 & 51.14 & 50.01 & 0.1961 & 0.5001 \\ \hline \multirow{4}{*}{Barbara} & \(1\times 8\) & 256 & 197,888 & 51.14 & 50.06 & 0.1963 & 0.5006 \\  & \(1\times 6\) & 64 & 180,048 & 51.15 & 49.95 & 0.1959 & 0.4995 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 49.98 & 0.1960 & 0.4998 \\  & \(1\times 2\) & 4 & 131,072 & 51.14 & 50.02 & 0.1961 & 0.5002 \\ \hline \multirow{4}{*}{Boat} & \(1\times 8\) & 256 & 197,888 & 51.14 & 49.99 & 0.1960 & 0.4999 \\  & \(1\times 6\) & 64 & 180,048 & 51.15 & 49.88 & 0.1956 & 0.4988 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 50.00 & 0.1961 & 0.5000 \\  & \(1\times 2\) & 4 & 131,072 & 51.13 & 50.07 & 0.1964 & 0.5007 \\ \hline \multirow{4}{*}{Couple} & \(1\times 8\) & 256 & 197,888 & 51.14 & 50.01 & 0.1961 & 0.5001 \\  & \(1\times 6\) & 64 & 180,048 & 51.14 & 49.97 & 0.1960 & 0.4997 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 49.99 & 0.1960 & 0.4999 \\  & \(1\times 2\) & 4 & 131,072 & 51.13 & 50.08 & 0.1964 & 0.5008 \\ \hline \multirow{4}{*}{Lena} & \(1\times 8\) & 256 & 197,888 & 51.13 & 50.08 & 0.1964 & 0.5008 \\  & \(1\times 6\) & 64 & 180,048 & 51.14 & 49.98 & 0.1960 & 0.4998 \\  & \(1\times 4\) & 8 & 155,648 & 51.14 & 49.97 & 0.1960 & 0.4997 \\  & \(1\times 2\) & 4 & 131,072 & 51.14 & 49.97 & 0.1960 & 0.4997 \\ \hline \multirow{4}{*}{ Peppers} & \(1\times 8\) & 256 & 197,888 & 51.14 & 50.06 & 0.1963 & 0.5006 \\  & \(1\times 6\) & 64 & 180,048 & 51.14 & 50.04 & 0.1962 & 0.5004 \\ \cline{1-1}  & \(1\times 4\) & 8 & 155,648 & 51.15 & 49.93 & 0.1958 & 0.4993 \\ \cline{1-1}  & \(1\times 2\) & 4 & 131,072 & 51.14 & 50.05 & 0.1963 & 0.5005 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance with different block-group sizes and different pixel-block. table was the same. Simultaneously, we observed that the most efficient partitioning is to have \(2^{n}\) pixel-blocks within a block-group when the size of a pixel-block is n.

In addition to these metrics, we also employed the number of pixels changing rate (NPCR), unified average changed intensity (UACI), and mean absolute error (MAE) to evaluate image distortion between the original and the restored images. The calculation formulas for these metrics are as follows:

\[\text{NPCR}=\frac{\sum_{i,j}D(i,j)}{W\times H}\times 100\%, \tag{13}\]

\[D(i,j)=\left\{ \begin{matrix}1,\ O(i,j)\
eq R(i,j)\\ 0,\ \text{otherwise}\end{matrix} \right., \tag{14}\]

\[\text{UACI}=\frac{\sum\lvert O(i,j)-R(i,j)\rvert}{W\times H\times 255}\times 100\%, \tag{15}\]

\[\text{MAE}=\frac{1}{W\times H}{\sum_{i=1}^{W}\sum_{j=1}^{H}\lvert O(i,j)-R(i, j)\rvert}, \tag{16}\]

where \(W\) and \(H\) represent the width and height of the images, and \(O(i,j)\) and \(R(i,j)\) denote the pixel values at position \((i,j)\) for the cover image and the restored image. NPCR is employed to compute the number of differing pixels between two images, while UACI is utilized to calculate the average change in pixels between two images. Unlike Table 1, Table 2 is a test of the proposed scheme with various codebook table sizes. From Table 2, it can be clearly seen that as the size of the codebook table becomes larger, the EC of the proposed scheme also becomes larger.