# Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments
## 6 Conclusions  
In this paper, a robust and efficient blind watermark method was proposed by utilizing FWHT and MfrLFMs on color images. The input binary watermark was scrambled using Arnold transformation to add more security and reliability to the proposed method. The accurate magnitude of MfrLFMs was selected to attain the goal of the watermarking  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Watermark Image (Bits)** & **Cover Image (Pixels)** & **Bits/Pixels** \\ \hline Method [8] & 32 \(\times\) 32 & 512 \(\times\) 512 \(\times\) 3 & 0.00130208 \\ Method [24] & 64 \(\times\) 64 & 512 \(\times\) 512 \(\times\) 3 & 0.00520833 \\ Method [25] & 64 \(\times\) 64 & 512 \(\times\) 512 \(\times\) 3 & 0.00520833 \\ QEMs [60] & 16 \(\times\) 16 & 256 \(\times\) 256 \(\times\) 3 & 0.00130208 \\ QPHTs [61] & 32 \(\times\) 32 & 512 \(\times\) 512 \(\times\) 3 & 0.00130208 \\ Proposed & 32 \(\times\) 32 & 256 \(\times\) 256 \(\times\) 3 & 0.00520833 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Capacity analysis for different methods.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **[PERSON] and [PERSON] [6]** & **[PERSON] et al.** & **[PERSON] et al.** & **[PERSON] et al.** & **[PERSON]** & **Proposed** \\  & **[PERSON] [6]** & **[9]** & **[16]** & **[18]** & **et al. [33]** & **Method** \\ \hline Max PSNR (dB) & 64.3830 & 35.0406 & 42.42 & 44.4994 & 50.175 & 68.84 \\ Rotation attack & 0.8560 & 0.3567 & 0.9873 & — & 0.8534 & 0.9984 \\ Scaling attack & 0.9014 & 0.1928 & 0.96131 & — & 0.999 & 0.9968 \\ JPEG 2000 attack & 0.8577 & 0.9509 & 0.97639 & 0.9944 & 0.852 & 1 \\ JPEG compression & — & 0.9976 & 0.9998 & 0.9943 & — & 0.9998 \\ Salt and peppers & 0.9971 & 0.2569 & 0.8739 & 0.9849 & 0.996 & 0.9989 \\ Gaussian & — & 0.2186 & 0.94325 & — & 0.915 & 0.9989 \\ Median filter & 0.8370 & 0.9233 & 0.9011 & 0.9460 & 0.924 & 0.9984 \\ Average filtering & — & 0.8428 & — & — & 0.938 & 0.9961 \\ Gaussian low-pass & 0.9075 & — & — & — & — & 1 \\ Gaussian filtering & — & 0.9845 & 0.92237 & — & 0.997 & 0.9992 \\ Blurring attack & 0.9965 & 0.98814 & — & 0.965 & 1 \\ Histogram Equalization & — & 0.9449 & 0.96082 & — & 0.755 & 1 \\ Zooming attack & — & 0.9640 & — & 0.9995 & — & 1 \\ Sharpen attack & 0.9123 & 0.9179 & 0.98521 & — & — & 0.9998 \\ Poisson noise & — & 0.7168 & — & — & — & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Robustness evaluation of the proposed method and other exiting watermarking methods under common attacks.  
system, which resulted in improved robustness and visual imperceptibility. The watermark bits were embedded in the modified magnitudes of the MFrLFMs based on the quantization step with optimum selected values. The proposed method successfully countered common geometric attacks, processing attacks, and combination complex attacks. The numerical results clearly show that our method surpassed existing similar methods with higher watermark invisibility, efficiency, and security, and it was suitable for medical images applications. In future work, we are looking to extend improvement to apply this method in a complete color image watermarking system to conceal color watermark logo images into color host cover images in a holistic way.  
Conceptualization, K.M.H. and M.M.A.-A.; methodology, K.M.H. and M.M.A.-A.; software, K.M.H. and M.M.A.-A.; validation, M.M.A.-A., K.M.H., N.A.L. and M.M.F.; formal analysis, K.M.H. and N.A.L.; investigation, K.M.H. and M.M.A.-A.; resources, K.M.H. and M.M.A.-A.; data curation, M.M.A.-A.; writing--original draft preparation, M.M.A.-A. and M.M.F.; writing--review and editing, K.M.H., N.A.L., M.M.A.-A. and M.M.F.; visualization, M.M.A.-A. and K.M.H.; supervision, K.M.H. and N.A.L.; project administration, K.M.H.; funding acquisition, M.M.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.