## 4 Experiments and Analysis of Results
### Data Embedding Performance
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & **Threshold Value** & **Criteria** & **Best Case** & **Worst Case** & **Average** \\ \hline \multirow{3}{*}{BOSSBase} & (3, 4) & ER (bpp) & 6.9487 & 4.3446 & 5.6934 \\  & (3, 4) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \cline{2-6}  & (6, 6) & ER (bpp) & 7.6495 & 6.7815 & 7.2311 \\  & (6, 6) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \multirow{3}{*}{BOW-2} & (3, 4) & ER (bpp) & 6.8109 & 4.3259 & 5.6361 \\  & (3, 4) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \cline{2-6}  & (6, 6) & ER (bpp) & 7.6035 & 6.7752 & 7.2120 \\  & (6, 6) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \multirow{3}{*}{USID} & (3, 4) & ER (bpp) & 7.3399 & 4.2752 & 5.8142 \\  & (3, 4) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \cline{2-6}  & (6, 6) & ER (bpp) & 7.7799 & 6.7583 & 7.2713 \\ \cline{2-6}  & (6, 6) & PSNR & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The embedding rates and peak signal-to-noise ratio of the algorithm proposed in this paper across various datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Images** & **Total Capacity (bits)** & **Code Length (bits)** & **Extra Bits (bits)** & **Total Load (bits)** & **ERs (bpp)** \\ \hline Jetplane & 1,590,321 & 792,651 & 633 & 797,037 & 5.5202 \\ Man & 5,622,829 & 3,118,402 & 2361 & 2,502,066 & 5.1931 \\ Airplane & 1,663,820 & 683,251 & 633 & 979,936 & 5.8690 \\ Tiffany & 1,537,779 & 785,567 & 633 & 751,579 & 5.4335 \\ Baboon & 1,085,666 & 796,502 & 633 & 288,531 & 4.5503 \\ Lena & 1,477,960 & 792,862 & 633 & 684,465 & 5.3055 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Embedding rates and correlation statistics of different images. In order to demonstrate the superior embedding rate capabilities of our algorithm, we conducted experiments using six widely recognized images: Airplane, Baboon, Lena, Jetplane, Man, and Tiffany. The results, depicted in Figure 9, compare the highest embedding rate achieved by our algorithm with those of existing algorithms. [PERSON] et al. [5]'s algorithm utilized LSB matching for embedding, achieving a modest embedding rate of 2 bpp. [PERSON] et al. [14]'s algorithm attained an average embedding rate of 0.90 bpp, primarily due to less advanced compression technologies. [PERSON] et al. [21]'s algorithm encoded pixels into multiple Hamming code words and leveraged error correction capabilities, reaching embedding rates of up to 3 bpp. In the experiments, our algorithm excelled with a maximum embedding rate of 7.11 bpp, doubling the rate of [PERSON] et al. [21]'s approach. While algorithms in references [22; 23] both utilized image correlation embedding post secret sharing, their embedding rates are constrained by coding techniques. [PERSON] et al. [24] improved upon this by employing a hybrid coding technique, achieving an average embedding rate of up to 3.20 bpp with a (3, 4) threshold. Our algorithm, using the same threshold  
Figure 8: Performance of the algorithm’s ERs Across different databases. (**a**) ERs on the BOSSBase database. (**b**) ERs on the BOWS-2 database. (**c**) ERs on the UCID database.