## 6 Experimental Results
\begin{table}
\begin{tabular}{|c|c|c|} \hline \multicolumn{2}{|c|}{**Attack**} & \multicolumn{2}{c|}{**Factor**} & \multicolumn{2}{c|}{**Average of the**} \\ \cline{3-4} \multicolumn{2}{|c|}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{**output statistic \(q\)**} \\ \hline \multirow{4}{*}{Sampling} & Down & 0.7 & 10.14 \\ \cline{3-4}  & & 0.8 & 14.56 \\ \cline{2-4}  & Up & 1.3 & 20.16 \\ \cline{2-4}  & \multirow{2}{*}{Up} & 1.75 & 18.78 \\ \hline \multirow{4}{*}{JPEG Compression} & QF = 90 & 15.75 \\ \cline{2-4}  & QF = 80 & 11.17 \\ \cline{2-4}  & QF = 70 & 7.94 \\ \cline{2-4}  & QF = 60 & 5.83 \\ \cline{2-4}  & \multirow{2}{*}{1\%} & 17.69 \\ \cline{2-4}  & & 2\% & 12.87 \\ \cline{2-4}  & Noise & 3\% & 10.59 \\ \hline \multirow{4}{*}{Salt \& Pepper Noise} & Density = 0.001 & 12.81 \\ \cline{2-4}  & Density = 0.003 & 9.55 \\ \cline{2-4}  & Density = 0.005 & 7.11 \\ \hline \multirow{4}{*}{Row-Column Copying} & 5-11 & 18.63 \\ \cline{2-4}  & 35-78 & 19.08 \\ \cline{1-1} \cline{2-4}  & 67-437 & 18.03 \\ \cline{1-1} \cline{2-4}  & 3-16, 43-72 & 17.88 \\ \cline{1-1} \cline{2-4}  & 139-126, 123-211 & 18.21 \\ \cline{1-1} \cline{2-4}  & 333-164, 431-142 & 17.50 \\ \cline{1-1} \cline{2-4}  & 14-26, 169-99, 119-192 & 17.27 \\ \cline{1-1} \cline{2-4}  & 139-126, 123-211,43-72 & 16.80 \\ \cline{1-1} \cline{2-4}  & 5-11, 35-78, 67-437 & 17.01 \\ \hline \end{tabular}
\end{table} 
Table 2: Robustness of the proposed scheme against common attacks (acceptance threshold \(T\) = 5). Regarding the JPEG compression attack, the watermarked images were compressed with different quality factors QF, ranging between 100 (no compression - best quality) and 0 (maximum compression lowest quality). As can be seen in Table 2, the average of the output statistic \(q\) decreases with the quality factor QF. The watermark can be still detected, with high confidence, if the watermarked images are compressed with a QF = 60 (the average of the value of \(q\) is 5.83). Moreover, the average of the output response \(q\) for images with complex regions (edges, textures) is much higher, thus we can detect the watermark even if they are attacked with a higher compression factor. From our tests, we verified that the robustness against JPEG compression can be improved by:  
* increasing the strength factor \(\beta\);
* decreasing the multiplicative factor \(\delta\);
* increasing the size of the blocks of the original images used in the embedding process. However, we believe that the previously suggested values for \(\beta\), \(\delta\) and the block size can already guarantee a good compromise between robustness and visual quality of the watermarked images. Watermarked images were also attacked by adding white Gaussian noise (AWGN) of different intensities. The effect is a uniformly distributed noise across the image [19]. This noise is visible in all frequencies (i.e., high, middle and low frequencies) and textured regions. The average of the output statistic \(q\) is equal to 10.59 when 3% of additive white Gaussian noise is added to the watermarked images. Another attack applied to watermarked images was the addition of salt and pepper noise with densities within the interval [0.001, 0.005]. The watermark sequence can still be detected even if the average of the output \(q\) is lower compared to other attacks. During the simulation tests, we observed