# Robust Image Watermarking in Spatial Domain Utilizing Features Equivalent to SVD Transform
## 4 Experimental Results Discussion
### Robustness Analysis against Attacks  
This section analyzes the robustness of the proposed watermarking scheme, utilizing image distortion attacks to distort the watermarked image shown in Table 1 and the extraction procedure described in Section 3.3. The normalized correlation coefficient (_NCC_) and bits error ratio (_BER_), which are defined in Equations (25) and (26), were employed for this task. A higher _NCC_ value means higher robustness, while a smaller _BER_ value means higher robustness. Therefore, _BER_ and _NCC_ values approaching zero and one, respectively, indicate that the embedded and extracted watermarks are almost the same. The _NCC_ and _BER_ values of the extracted watermarks corresponding to inserted watermarks _W1_ to _W4_ are given in Tables 3-5. To investigate the collective robustness of the proposed scheme, the average NCC and SSIM of all the attacks of the extracted watermarks corresponding to each image are given in Table 3. According to the table, the proposed watermarking scheme was resistant to all distortion attacks with _NCC_ values close to 1 and _BER_ values close to 0. Figures 7 and 8 demonstrate the same phenomenon, representing the average NCC and the average BER, respectively. To investigate the robustness of the proposed scheme against each image manipulation attack, the average NCC and BER values of all extracted watermarks for each image are given in Tables 4 and 5, respectively. The proposed watermarking scheme's ability to retrieve the watermarks exactly as they were inserted is demonstrated by the _NCC_ values of 1 and _BER_ values of 0 in the cases of 90-degree rotation and row and column flipping (_index_2, _index_11, and _index_12). The outcome of the research comes close to fulfilling the objectives of the study. Due to space constraints, the extracted watermarks only from 'image1' are given in Figure 9. The figure demonstrates that the recovered watermarks by the proposed scheme were almost similar to the embedded watermark in every instance. Except in a few cases, the extracted watermark may be recognized with the naked eye. The extracted watermarks in the cases of attack _indices_ 1, 6, 7, 8, 9, and 13 have poor quality in comparison to the other cases. Further improvement of the watermarking scheme is needed considering these cases.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**IMAGE**} & \multicolumn{4}{c}{**PSNR**} & \multicolumn{4}{c}{**SSIM**} \\ \cline{2-9}  & **W1** & **W2** & **W3** & **W4** & **W1** & **W2** & **W3** & **W4** \\ \hline _Image_1 & 49.6187 & 49.1559 & 49.5421 & 49.7881 & 0.9957 & 0.9952 & 0.9965 & 0.9966 \\ _Image_2 & 49.2557 & 49.1345 & 49.8637 & 49.7539 & 0.9950 & 0.9938 & 0.9977 & 0.9969 \\ _Image_3 & 49.0906 & 49.6372 & 49.5223 & 49.5529 & 0.9955 & 0.9967 & 0.9958 & 0.9962 \\ _Image_4 & 48.8722 & 49.1299 & 49.2188 & 48.8660 & 0.9972 & 0.9963 & 0.9971 & 0.9973 \\ _Image_5 & 49.0075 & 48.7838 & 49.3393 & 49.2890 & 0.9964 & 0.9956 & 0.9974 & 0.9965 \\ _Image_6 & 48.6690 & 49.0954 & 49.2958 & 48.9566 & 0.9946 & 0.9956 & 0.9949 & 0.9951 \\ _Image_7 & 48.8956 & 49.2559 & 48.8997 & 49.0164 & 0.9957 & 0.9973 & 0.9954 & 0.9964 \\ _Image_8 & 49.2894 & 49.1746 & 48.8634 & 48.8375 & 0.9841 & 0.9845 & 0.9846 & 0.9857 \\ _Image_9 & 48.8736 & 49.1341 & 49.2494 & 48.8962 & 0.9940 & 0.9923 & 0.9942 & 0.9934 \\ _Image_10 & 49.1469 & 49.0825 & 49.3130 & 48.9508 & 0.9954 & 0.9949 & 0.9963 & 0.9939 \\ \hline \end{tabular}
\end{table}
Table 2: _PSNR_ (dB) and SSIM values of watermarked images.