# A Robust Multi-Watermarking Algorithm for Medical Images Based on DTCWT-DCT and Henon Map
## 3 The Proposed Algorithm
### Feature extraction  
In order to find a visual feature applicable to medical images, a normal human brain image (128 pixels \(\times\) 128 pixels) was randomly selected to carry out the DTCWT-DCT transformation, and this image was subjected to a variety of different types of attacks, as shown in Figure 7. By observing the coefficient data of the low-frequency part of the image after transformation, we found that although its numerical value changed significantly, its symbol remained basically the same. Table 1 lists the low frequency coefficients of the brain image under different attacks. In this paper, we selected 32 bits of low-frequency data for symbol transformation, and directly replaced data greater than or equal to 0 with 1, and all other data with 0. For the sake of explanation, we only list the first 10 data in the table; all data were in 1.0e+003 units. In this way, we obtained a set of DTCWT-DCT low-frequency coefficient symbol sequences of the original image, i.e., '1100010010'. As seen from Table 1, after transformation, the symbol sequences of all attacked images were consistent with the original image, and the NC values were all equal to 1.00. Figure 6: The process of the proposed algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Image Processing** & **PSNR (dB)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** & **O (I,J)** \\ \hline Original image & / & 3.1649 & 0.0688 & \(-\)2.6346 & \(-\)0.6947 & \(-\)0.0089 & 0.4841 & \(-\)1.3026 & \(-\)0.0307 & 0.7381 & \(-\)0.0505 & 1100010010 & 1.00 \\ Gaussian noise (\%) & 12.32 & 3.9336 & 0.0596 & \(-\)2.1852 & \(-\)0.5869 & \(-\)0.0237 & 0.4020 & \(-\)1.0897 & \(-\)0.0284 & 0.6235 & \(-\)0.0657 & 110001010 & 1.00 \\ JPEG compression (\%) & 17.61 & 3.2728 & 0.0950 & \(-\)2.3404 & \(-\)0.5863 & \(-\)0.0078 & 0.3865 & \(-\)1.1486 & \(-\)0.0304 & 0.5989 & \(-\)0.1025 & 110001010 & 1.00 \\ Median filter [3,3] (10 times) & 21.85 & 3.1894 & 0.0603 & \(-\)2.66947 & \(-\)0.7458 & \(-\)0.0015 & 0.5370 & \(-\)1.3083 & \(-\)0.0270 & 0.7627 & \(-\)0.0654 & 110001010 & 1.00 \\ Rotation (clockwise, 20\({}^{\prime}\)) & 12.38 & 3.1646 & 0.3167 & \(-\)2.4485 & \(-\)0.6399 & \(-\)0.4100 & 0.3956 & \(-\)1.4398 & \(-\)0.0410 & 0.8207 & \(-\)0.0261 & 1100010010 & 1.00 \\ Scaling (\(\sim\)0.5) & / & 1.5867 & 0.0325 & \(-\)1.3179 & \(-\)0.3473 & \(-\)0.0045 & 0.4212 & \(-\)0.6513 & \(-\)0.0157 & 0.3664 & \(-\)0.0258 & 110001010 & 1.00 \\ Translation (\%, left) & 11.38 & 3.1649 & 0.7388 & \(-\)2.4519 & \(-\)0.6947 & \(-\)0.1520 & 0.4520 & \(-\)1.3026 & \(-\)0.2903 & 0.6846 & \(-\)0.0505 & 1100010010 & 1.00 \\ Translation (\%, down) & 12.20 & 3.0723 & 0.0611 & \(-\)2.5176 & \(-\)1.2228 & \(-\)0.0188 & 0.8428 & \(-\)1.1085 & \(-\)0.0297 & 0.7524 & \(-\)0.0317 & 110001010 & 1.00 \\ Cropping (\%, Y direction) & / & 3.1502 & 0.0660 & \(-\)2.5637 & \(-\)1.0598 & \(-\)0.0196 & 0.6615 & \(-\)0.9666 & \(-\)0.0226 & 0.6086 & \(-\)0.1695 & 110001010 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Changes of DTCOWT-DCT coefficients under different attacks for the original image. Then, taking this conclusion as a reference, we conducted the same test on a large number of randomly selected medical images, and verified the value of the normalized correlation coefficient between the images using their respective 32-bit symbol vectors. Figure 8 and Table 2 show some of the medical images and the NC values between them. From the data, it can be concluded that the NC values of the different images obtained using the feature vector selected with the above method are all less than 0.5, and their own NC values are 1.00. These results are consistent with human visual features.