# A Novel Hybrid Edge Detection and LBP Code-Based Robust Image Steganography Method
## 4 Results and Discussion
### Statistical Analysis  
The novel approach was statistically analyzed using various parameters such as correlation coefficient, entropy, cosine similarities, and pixel difference histogram to check its robustness against various attacks. First, the correlation coefficients \(\rho_{s}C\) were measured between the cover and stego image. \(\rho_{s}C=0\) stands for no relationship between two images. \(\rho_{s}C>0\) means a positive correlation between the cover and stego image and lies at a perfect relationship when it reaches 1. Similarly, a negative value of \(\rho_{s}C\) indicates a negative relationship. Results of \(\rho_{s}C\) are depicted in Table 1. Though the proposed method shows a higher correlation value, its difference from others is insignificant. Rather, as with others, it represents a higher correlation between the cover and the stego image. The entropy values \(H\) were also computed in both cover and stego images. Next, their difference was calculated. That difference value is zero for two identical images. Results are plotted in Figure 10. The figure shows that none of the results are greater than 0.06, i.e., these are very small and close to zero. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Image Name**} & \multicolumn{6}{c}{**Correlation Coefficient Values**} \\ \cline{2-6}  & **Proposed** & **[PERSON] [24]** & **[PERSON] [44]** & **[PERSON] [25]** & **[PERSON] [27]** \\ \hline F16.jpg & 0.9999 & 0.9998 & 0.9993 & 0.9973 & 0.9998 \\ babon.jpg & 0.9999 & 0.9997 & 0.9990 & 0.9960 & 0.9997 \\ basket.jpg & 0.9999 & 0.9999 & 0.9998 & 0.9991 & 0.9997 \\ boat.jpg & 0.9999 & 0.9998 & 0.9993 & 0.9967 & 0.9999 \\ bbrz.jpg & 0.9999 & 0.9999 & 0.9997 & 0.9988 & 0.9990 \\ lena.jpg & 0.9999 & 0.9998 & 0.9994 & 0.9971 & 0.9999 \\ livingroom.jpg & 0.9999 & 0.9998 & 0.9993 & 0.9970 & 0.9998 \\ pepper.jpg & 0.9999 & 0.9998 & 0.9995 & 0.9976 & 0.9998 \\ walkbridge.jpg & 0.9999 & 0.9999 & 0.9995 & 0.9980 & 0.9984 \\ wheel.jpg & 0.9999 & 0.9998 & 0.9996 & 0.9982 & 0.9996 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation coefficient values of various schemes. Figure 9: Comparing SSIM values of BOSS image dataset in different schemes. The figure states that the proposed scheme has the highest SSIM value. To verify further with similar statistics, cosine similarities are measured between the cover and stego images. That value is 1 for two identical images and 0 for two fully mismatched images. The results are demonstrated in Table 2. That table illustrates that our proposed method shows higher values than the other competing schemes. Aggregated result of big data set (BOSS dataset) is shown in Table 3. This table shows that our proposed scheme demonstrates strong resistance to attack from intruders. To detect the stego image, the pixel difference histogram (PDH), another statistical method is also used. Figures 11 and 12 show the PDH of the original images and associated \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Image Name**} & \multicolumn{5}{c}{**Cosine Similarity Values**} \\ \cline{2-6}  & **Proposed** & **[PERSON]**[24] & **[PERSON]**[44] & **[PERSON]**[25] & **[PERSON]**[27] \\ \hline F16.jpg & 0.99999 & 0.99999 & 0.99996 & 0.99984 & 0.99999 \\ babon.jpg & 0.99985 & 0.99985 & 0.99980 & 0.99960 & 0.99986 \\ basket.jpg & 0.99999 & 0.99991 & 0.99995 & 0.99981 & 0.99997 \\ boat.jpg & 0.99999 & 0.99998 & 0.99993 & 0.99966 & 0.99999 \\ brbra.jpg & 0.99999 & 0.99998 & 0.99994 & 0.99977 & 0.99990 \\ lena.jpg & 0.99937 & 0.99939 & 0.99934 & 0.99939 & 0.99939 \\ livingroom.jpg & 0.99999 & 0.99998 & 0.99992 & 0.99963 & 0.99998 \\ pepper.jpg & 0.99999 & 0.99998 & 0.99992 & 0.9996 & 0.99999 \\ walkbridge.jpg & 0.99999 & 0.99998 & 0.99992 & 0.99963 & 0.99984 \\ wheel.jpg & 0.99999 & 0.99998 & 0.99992 & 0.99966 & 0.99996 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cosine Similarity values of various schemes. Figure 10: Performance comparison of the proposed scheme with the competing scheme in terms of entropy values.