## 4 Experiments
### Discriminative Capability  
The discriminative capability of a image hashing means that visually distinct images should have significantly different hashes. In other words, two images that are visually distinct should have a very low probability of generating similar hashes. Here, RTD dataset consisting of 220 different uncompressed color images was adopted to validate the discriminative capability of our proposed multi-attack reference hashing algorithm. We first extracted reference hashing codes for all 220 images in RTD and then calculated the hashing distance for each image with the other 219 images. Thus, we can finally obtained 220 \(\times\) (220\(-\)1)/2 = 24,090 hashing distances. Figure 4 shows the distribution of these 24,090 hashing distances between hashing pairs with varying thresholds, where the abscissa is the hashing distance and the ordinate represents the frequency of hashing distance. It can be seen clearly from the histogram that the proposed method has good discriminative capability. For instance, we set \(\tau\) = 0.12 as the threshold on CASIA dataset when extracting the reference hashing by RPIVD method. The minimum value for hashing distance was 0.1389, which is above the threshold. The results show that the multi-attack reference hashing can replace the original image-based reference hashing with good discrimination.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Manipulation**} & \multicolumn{3}{c}{**ORH**} & \multicolumn{3}{c}{**MRH**} \\ \cline{3-8}  & & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** \\ \hline \multirow{8}{*}{RPIVD} & Gaussian noise & 0.25827 & 0.00864 & 0.03086 & 0.29081 & 0.01115 & 0.03234 \\  & Salt\&Pepper & 0.22855 & 0.01131 & 0.02993 & 0.25789 & 0.01191 & 0.03033 \\  & Gaussian blurring & 0.03560 & 0.00411 & 0.01471 & 0.14023 & 0.00545 & 0.01786 \\  & Circular blurring & 0.06126 & 0.00447 & 0.01713 & 0.13469 & 0.00565 & 0.01924 \\  & Motion blurring & 0.03570 & 0.00362 & 0.01432 & 0.18510 & 0.00473 & 0.01825 \\  & Average filtering & 0.07037 & 0.00543 & 0.02109 & 0.20190 & 0.00591 & 0.02237 \\  & Median filtering & 0.06126 & 0.00512 & 0.02234 & 0.18360 & 0.00625 & 0.02465 \\  & Wiener filtering & 0.07156 & 0.00421 & 0.01803 & 0.20421 & 0.00581 & 0.02041 \\  & Image sharpening & 0.06324 & 0.00609 & 0.02442 & 0.18283 & 0.00706 & 0.02765 \\  & Image scaling & 0.03311 & 0.00275 & 0.01154 & 0.18233 & 0.00381 & 0.01761 \\  & Illumination correction & 0.11616 & 0.00769 & 0.02864 & 0.20944 & 0.01047 & 0.02920 \\  & JPEG compression & 0.07037 & 0.00543 & 0.02109 & 0.06180 & 0.00707 & 0.02155 \\ \hline \multirow{8}{*}{QFT} & Gaussian noise & 6.97151 & 0.13508 & 0.73563 & 6.30302 & 0.11636 & 0.60460 \\  & Salt\&Pepper & 7.63719 & 0.16998 & 0.66200 & 7.50644 & 0.15073 & 0.63441 \\  & Gaussian blurring & 0.26237 & 0.00513 & 0.02519 & 0.10820 & 0.00318 & 0.01449 \\  & Circular blurring & 0.26529 & 0.00712 & 0.03163 & 0.17937 & 0.00460 & 0.02075 \\  & Motion blurring & 0.26408 & 0.00465 & 0.02286 & 0.10729 & 0.00300 & 0.01318 \\  & Average filtering & 0.30154 & 0.00976 & 0.04403 & 0.30719 & 0.00760 & 0.03263 \\  & Median filtering & 0.95120 & 0.03084 & 0.19822 & 0.87149 & 0.02706 & 0.19345 \\  & Wiener filtering & 0.64373 & 0.01746 & 0.08046 & 0.68851 & 0.01551 & 0.07616 \\  & Image sharpening & 6.55606 & 0.05188 & 1.52398 & 6.55596 & 0.05189 & 1.52398 \\  & Image scaling & 0.51083 & 0.04031 & 0.10067 & 0.52404 & 0.02800 & 0.09827 \\  & Illumination correction & 4.37001 & 0.27357 & 0.84280 & 4.36692 & 0.27348 & 0.84170 \\  & JPEG compression & 7.55523 & 0.13752 & 1.29158 & 13.1816 & 0.13585 & 1.46682 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._