## 4 Experiments and Analysis
### Sensitivity to Tampering Experiments and Analysis  
Sensitivity to tampering means that the algorithm can effectively detect the tampering of the HRRS images. In this study, if the HRRS image has been tampered, the perceptual hash values of the original image \(I_{o}\) and the processed one \(I_{p}\) should satisfy:  
\[Dis(PH(I_{o}),PH(I_{p}))>T \tag{5}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Manipulation** & **Format Conversion (TIFF to BMP)** & **Digital Watermarking (LSB)** \\ \hline Image A & 100\% & 100\% \\ Image B & 100\% & 100\% \\ Image C & 100\% & 100\% \\ Image D & 100\% & 100\% \\ Image E & 100\% & 100\% \\ Image F & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of the robustness test1 (\(T_{h}\) is set to 0). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Manipulation**} & \multicolumn{2}{c}{**JPEG Compression (99\%)**} & \multicolumn{2}{c}{**JPEG Compression (95\%)**} & \multicolumn{2}{c}{**Lossless Compression**} \\ \cline{2-5}  & **Algorithm** & **This** & **Algorithm** & **This** & **Algorithm** & **This** \\  & **in [10]** & **Algorithm** & **in [10]** & **Algorithm** & **in [10]** & **Algorithm** \\ \hline Image A & 78.6\% & 89.5\% & 72.4\% & 83.1\% & 100\% & 100\% \\ Image B & 80.3\% & 89.1\% & 75.3\% & 82.6\% & 100\% & 100\% \\ Image C & 79.6\% & 90.8\% & 74.9\% & 82.2\% & 100\% & 100\% \\ Image D & 81.3\To test the sensitivity to tampering, we take several kinds of tampering operations, including changing object, appending object, removing object and optional local subtle tampering, to test the sensitivity to tampering. For each kind of tampering operation, we construct a dataset with 50 tampering instances. Some examples of each kind of tampered HRRS images are shown in Figures 11-14. The more popular image perceptual hash algorithm mainly includes the methods based on discrete cosine transform (DCT) [4; 51; 52; 53], the method based on discrete wavelet transform (DWT) [9; 54; 55] and the method based on singular value decomposition (SVD) [5; 56]. In the related research specifically for HRRS images, the algorithms in [10] are the best algorithms currently published. We compare the above algorithm with our proposed algorithm, and the comparison results are shown in Table 3. Here, we take the percentage of successfully detected tampering instances to describe the sensitivity to tampering. The threshold of the normalized Hamming distance for the method based on wavelet transform is set to 0.02, the threshold for the method based on DCT is set to 0.02, the threshold for the method based on SVD is set to 0.01, and the threshold for the algorithms in [10] and our proposed algorithm are set to 0.10. Figure 11: Tampering examples of changing object: (**a**) Original HRRS images, (**b**) corresponding tampered images. Figure 12: Tampering examples of appending object: (**a**) Original HRRS images, (**b**) corresponding tampered images. It can be seen from Table 3 that our algorithm has similar tampering sensitivity to the algorithm in [10] and is capable of detecting subtle tampering of HRRS images, meeting the high-accuracy requirements of HRRS images. In contrast, the tampering sensitivity of traditional algorithms is far from achieving the integrity authentication requirements of HRRS images. In practical applications, if a higher tamper sensitivity is required, a smaller threshold \(T\) can be set so that more subtle tampering can be detected, which may affect the robustness of the algorithm. Figure 14: Examples of local subtle tampering: (**a**) Original images, (**b**) corresponding tampered images.