## 6 Experimental Results and Discussion
### Comparison with State-of-the-Art Schemes
Regarding the _Recall_ measure, all the methods presented a value of 1.0 for both alteration schemes, including the novel SR-HTR method using the hierarchical authentication method. To perform a visual comparison, the image Kodak-15 was employed. Its modifications can be observed in Figure 13. This comparison is illustrated in Tables 9 and 10, where Table 9 presents the results for the alteration rates between 20% and 50%, and Table 10 shows the results for alteration rates between 60% and 90%. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** \\ \hline SR-HTR & 0.9157 & 0.9585 & 0.9718 & 0.9799 & 0.9885 & 0.9849 & 0.9877 & 0.9892 & 0.9910 \\ [PERSON] [36] & 0.9152 & 0.9580 & 0.9716 & 0.9797 & 0.9884 & 0.9848 & 0.9876 & 0.9891 & 0.9909 \\ [PERSON] [23] & 0.8007 & 0.9210 & 0.9144 & 0.9483 & 1.0000 & 0.9601 & 0.9748 & 0.9659 & 0.9762 \\ [PERSON] [2] & 0.9855 & 1.0000 & 1.0000 & 0.9963 & 1.0000 & 0.9975 & 1.0000 & 1.0000 & 0.9983 \\ [PERSON] [24] & 0.9670 & 0.9855 & 0.9903 & 0.9939 & 1.0000 & 0.9943 & 0.9958 & 0.9963 & 0.9972 \\ [PERSON] [10] & 0.9855 & 1.0000 & 1.0000 & 0.9963 & 1.0000 & 0.9975 & 1.0000 & 1.0000 & 0.9983 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of Precision for different alteration rates between 10% and 90%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **SR-HTR** & \begin{tabular}{c} **[PERSON]** \\ [36] \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ [23] \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ [2] \\ \end{tabular} & \
\begin{tabular}{c} **[PERSON]** \\ [24] \\ \end{tabular} &
\begin{tabular}{c} **[PERSON]** \\ [10] \\ \end{tabular} \\ \hline Kodak-4 & 0.9797 & 0.9782 & 0.9451 & 1 & 0.9939 & 1 \\ Kodak-10 & 0.9148 & 0.9060 & 0.7573 & 1 & 0.9776 & 1 \\ Kodak-17 & 0.9784 & 0.9770 & 0.7628 & 1 & 0.9779 & 1 \\ Kodak-18 & 0.9243 & 0.9177 & 0.8951 & 1 & 0.9884 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of _Precision_ for multiple and irregular modification detection. Figure 12: Multiple and irregular alterations, (**a**) Kodak-4 original, (**b**) Kodak-10 original, (**c**) Kodak-17 original, (**d**) Kodak-18 original, (**e**) Kodak-4 modified, (**f**) Kodak-10 modified, (**g**) Kodak-17 modified, (**h**) Kodak-18 modified, (**i**) Kodak-4 ground truth, (**j**) Kodak-10 ground truth, (**k**) Kodak-17 ground truth, (**l**) Kodak-18 ground truth. Figure 13: Altered images for Kodak-15, (**a**) 20%, (**b**) 30%, (**c**) 40%, (**d**) 50%, (**e**) 60%, (**f**) 70%, (**g**) 80%, (**h**) 90%. It can be noticed in Table 9 that the designed SR-HTR method presents a better visual quality for alteration rates between 20% and 50%, followed by the procedure [36] that inserts three versions of the reconstruction watermark, and then by [10] that inserts only two. The methods [2; 23; 24] reconstruct the original content but with a significant loss of quality in the reconstructed image due to the insertion of a single instance of the recovery watermark. The results given in Table 10 show a dramatic fall in quality for the state-of-the-art methods, while SR-HTR maintains an acceptable visual quality proficiency until 90% when the Kodak-15 image is modified. The second-best results belong to [36], which degrades the image quality but still visibly preserves the original content. This decrease in quality for the state-of-the-art methods is due to the low level of redundancy inserted for the reconstruction watermark, which corresponds to the insertion of up to two copies, such as in [10; 23]. However, the framework [23] presents a larger number of contiguous pixels without reconstruction compared with [10] because it uses the SPITH compression algorithm with \(32\times 32\) pixel blocks to generate the reconstruction bits. This method is sensitive to noise applied to the blocks. Therefore, the decompression algorithm will result in wrong values for the whole block with minimal modification of the reconstruction bits.