Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments
Abstract
:1. Introduction
2. Related Work
- Our method contributes to this evidence by using MFrLFMs. It is known for its stability and invariance to many geometric attacks, which keep robust capability over many attacks such as scaling, rotation, translation, etc.
- In addition, MFrLFMs are not restricted to integer-order values, which give them a high ability to represent the finest details in the image rather than their rival’s orthogonal polynomials of integer order.
- The use of Walsh–Hadamard transform comes under generalized Fourier transforms, known as low-computations compilations. Hadamard transform is a perpendicular function, which is composed of (−1 and +1) values only. Therefore, there is no data redundancy, which makes it widely used in many image processing analyses. FWHT is elastic to low-quality compression compared with other transformations such as traditional DCT and DWT, making it robust to most common image processing attacks.
- The proposed method introduced a new combination method of these multi-channel fractional Legendre–Fourier moments (MFrLFMs) and Hadamard transformation in a holistic way to achieve the main target of the proposed method, which represents robustness to both geometric and image processing attacks.
- The evaluation of our proposed method has been assessed for many common types of attacks and visual imperceptibility measurements.
3. Preliminaries
3.1. Fast Walsh–Hadamard Transformation Technique
3.2. MFrLFM Representation for RGB Color Image
3.3. Geometrical Invariances of MFrLFMs
3.3.1. Rotational Invariance
3.3.2. Scale Invariance
3.3.3. Translation Invariance
3.4. Accurate MFrLFM Computation
4. Proposed Blind Watermarking
4.1. Watermarking Embedding Process
4.2. Blind Watermarking Extraction
5. Experimental Results
5.1. Visual Imperceptibility
5.2. Robustness Evaluation
5.3. Capacity Evaluation
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Quantization Step ∆ | QEMs [60] | QPHTs [61] | QRSCMs [28] | QLFMs [29] | MfrEMs [41] | Proposed Method |
---|---|---|---|---|---|---|
0.2 | 44.20 | 50.03 | 54.03 | 58.25 | 59.27 | 68.84 |
0.4 | 37.78 | 44.12 | 50.67 | 53.21 | 54.24 | 66.42 |
0.6 | 34.31 | 41.08 | 47.46 | 48.86 | 50.21 | 61.03 |
0.8 | 31.51 | 38.25 | 44.67 | 45.05 | 47.05 | 57.32 |
1.0 | 29.81 | 36.78 | 43.97 | 44.91 | 46.41 | 54.21 |
Attacks | BER | NC | Extracted Watermark | |
---|---|---|---|---|
No Attack | 0 | 1 | | |
Rotation Attack | 5° | 0 | 1 | |
15° | 0 | 1 | | |
25° | 0 | 1 | | |
65° | 0 | 1 | | |
Scaling Attack | 0.5 | 0.0023 | 0.9962 | |
0.75 | 0 | 1 | | |
1.25 | 0 | 1 | | |
1.5 | 0 | 1 | | |
2 | 0 | 1 | | |
Translation Attack | (15,2) | 0 | 1 | |
(20,20) | 0 | 1 | | |
(2,15) | 0 | 1 | | |
(0,50) | 0.0001 | 0.9998 | | |
(50,0) | 0.0001 | 0.9998 | | |
Shearing Attack | (0–1%) | 0.0075 | 0.9932 | |
Magnification | (1.75) | 0 | 1 | |
Cropping, Right | (25%) | 0.0146 | 0.9820 | |
Cropping, Top | (25%) | 0.0068 | 0.9916 | |
Cropping, Middle | (25%) | 0 | 1 | |
Attacks | BER | NC | Extracted Watermark | |
---|---|---|---|---|
JPEG Compression | 30 | 0 | 1 | |
40 | 0 | 1 | | |
50 | 0 | 1 | | |
60 | 0 | 1 | | |
70 | 0 | 1 | | |
90 | 0 | 1 | | |
Motion Blur | (3,3) | 0 | 1 | |
(4,8) | 0 | 1 | | |
Lossy Compression (80) | 0 | 1 | | |
Salt and Pepper (0.03) | 0 | 1 | | |
Gaussian (0.03) | 0 | 1 | | |
Gaussian Low-Pass (3,3) | 0 | 1 | | |
Poisson Noise | 0 | 1 | | |
Speckle Noise Attack | 0 | 1 | | |
Median Filter Attack | 0.0002 | 0.9972 | | |
Average Filter Attack (3,3) | 0.0003 | 0.9961 | | |
Sharpen Attack | 0.0001 | 0.9998 | | |
Histogram Equalization | 0 | 1 | |
Attacks | QEMs [60] | QPHTs [61] | QLFMs [29] | QRSCMs [28] | MFrEMs [41] | Proposed Method | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Rotation Angle | | Ber = 0.0703 Nc = 0.9143 | | Ber = 0.1582 Nc = 0.7850 | | Ber = 0.0479 Nc = 0.9409 | | Ber = 0.0479 Nc = 0.9408 | | Ber = 0.0195 Nc = 0.9759 | | Ber = 0.0022 Nc = 0.9989 | |
| Ber = 0.0557 Nc = 0.9316 | | Ber = 0.1533 Nc = 0.7941 | | Ber = 0.0361 Nc = 0.9551 | | Ber = 0.0449 Nc = 0.9445 | | Ber = 0.0176 Nc = 0.9782 | | Ber = 0.0050 Nc = 0.9953 | ||
| Ber = 0.0547 Nc = 0.9322 | | Ber = 0.1514 Nc = 0.7945 | | Ber = 0.0459 Nc = 0.9439 | | Ber = 0.0459 Nc = 0.9434 | | Ber = 0.0195 Nc = 0.9758 | | Ber = 0.0025 Nc = 0.9984 | ||
Scaling Factor | 0.75 | | Ber = 0.0781 Nc = 0.9048 | | Ber = 0.1377 Nc = 0.8146 | | Ber = 0.0469 Nc = 0.9424 | | Ber = 0.0518 Nc = 0.9374 | | Ber = 0.0166 Nc = 0.9794 | | Ber = 0.0084 Nc = 0.9922 |
1.5 | | Ber = 0.0283 Nc = 0.9652 | | Ber = 0.0898 Nc = 0.8825 | | Ber = 0.0098 Nc = 0.9880 | | Ber = 0.0127 Nc = 0.9843 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0035 Nc = 0.9954 | |
2 | | Ber = 0.0322 Nc = 0.9605 | | Ber = 0.0586 Nc = 0.9251 | | Ber = 0.0078 Nc = 0.9904 | | Ber = 0.0205 Nc = 0.9745 | | Ber = 0.0039 Nc = 0.9952 | | Ber = 0.0023 Nc = 0.9968 | |
Translation | (H3,V3) | | Ber = 0.0186 Nc = 0.9770 | | Ber = 0.0625 Nc = 0.9237 | | Ber = 0.0205 Nc = 0.9745 | | Ber = 0.0107 Nc = 0.9867 | | Ber = 0.0039 Nc = 0.9952 | | Ber = 0.0012 Nc = 0.9974 |
(H6,V6) | | Ber = 0.0479 Nc = 0.9412 | | Ber = 0.0635 Nc = 0.9226 | | Ber = 0.0215 Nc = 0.9736 | | Ber = 0.0205 Nc = 0.9747 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0014 Nc = 0.9979 | |
Compression | JPEG(80) | | Ber = 0.0205 Nc = 0.9745 | | Ber = 0.0859 Nc = 0.8839 | | Ber = 0.0127 Nc = 0.9843 | | Ber = 0.0186 Nc = 0.9769 | | Ber = 0.0059 Nc = 0.9928 | | Ber = 0.0025 Nc = 0.9986 |
JPEG(90) | | Ber = 0.0107 Nc = 0.9867 | | Ber = 0.0693 Nc = 0.9107 | | Ber = 0.0029 Nc = 0.9964 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0039 Nc = 0.9952 | | Ber = 0.0005 Nc = 0.9998 | |
Magnification (1.5) + (JPEG, 90%) | | Ber = 0.0889 Nc = 0.8880 | | Ber = 0.0293 Nc = 0.9643 | | Ber = 0.0107 Nc = 0.9867 | | Ber = 0.0127 Nc = 0.9843 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0025 Nc = 0.9984 | |
Magnification(1.75) + Rotation (25o) | | Ber = 0.1699 Nc = 0.7677 | | Ber = 0.0342 Nc = 0.9582 | | Ber = 0.0215 Nc = 0.9737 | | Ber = 0.0244 Nc = 0.9697 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0028 Nc = 0.9956 | |
Reduction(0.75) + JPEG (90%) | | Ber = 0.1064 Nc = 0.8591 | | Ber = 0.0557 Nc = 0.9319 | | Ber = 0.0205 Nc = 0.9745 | | Ber = 0.0215 Nc = 0.9736 | | Ber = 0.0107 Nc = 0.9867 | | Ber = 0.0072 Nc = 0.9972 | |
Noise Salt and Pepper (0.03) | | Ber = 0.084 Nc = 0.8907 | | Ber = 0.0166 Nc = 0.9794 | | Ber = 0.0146 Nc = 0.9820 | | Ber = 0.0156 Nc = 0.9806 | | Ber = 0.0068 Nc = 0.9916 | | Ber = 0.0036 Nc = 0.9989 | |
Gaussian Noise (0.03) | | Ber = 0.0723 Nc = 0.9067 | | Ber = 0.0293 Nc = 0.9643 | | Ber = 0.0107 Nc = 0.9867 | | Ber = 0.0186 Nc = 0.9769 | | Ber = 0.0039 Nc = 0.9952 | | Ber = 0.0036 Nc = 0.9989 | |
Gaussian Filter (3 × 3) | | Ber = 0.1006 Nc = 0.8674 | | Ber = 0.0166 Nc = 0.9794 | | Ber = 0.0127 Nc = 0.9843 | | Ber = 0.0146 Nc = 0.9820 | | Ber = 0.0049 Nc = 0.9940 | | Ber = 0.0027 Nc = 0.9992 | |
Median Filter (3 × 3) | | Ber = 0.0859 Nc = 0.8953 | | Ber = 0.0342 Nc = 0.9582 | | Ber = 0.0137 Nc = 0.9831 | | Ber = 0.0283 Nc = 0.9650 | | Ber = 0.0068 Nc = 0.9916 | | Ber = 0.0039 Nc = 0.9984 |
Method | Prabha and Sam [6] | Rahman et al. [9] | Fares et al. [16] | Yuan et al. [18] | Huynh-The et al. [33] | Proposed Method |
---|---|---|---|---|---|---|
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 |
Method | Watermark Image (Bits) | Cover Image (Pixels) | Bits/Pixels |
---|---|---|---|
Method [8] | 32 × 32 | 512 × 512 × 3 | 0.00130208 |
Method [24] | 64 × 64 | 512 × 512 × 3 | 0.00520833 |
Method [25] | 64 × 64 | 512 × 512 × 3 | 0.00520833 |
QEMs [60] | 16 × 16 | 256 × 256 × 3 | 0.00130208 |
QPHTs [61] | 32 × 32 | 512 × 512 × 3 | 0.00130208 |
Proposed | 32 × 32 | 256 × 256 × 3 | 0.00520833 |
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Abdel-Aziz, M.M.; Hosny, K.M.; Lashin, N.A.; Fouda, M.M. Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments. Sensors 2021, 21, 7845. https://doi.org/10.3390/s21237845
Abdel-Aziz MM, Hosny KM, Lashin NA, Fouda MM. Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments. Sensors. 2021; 21(23):7845. https://doi.org/10.3390/s21237845
Chicago/Turabian StyleAbdel-Aziz, Mostafa M., Khalid M. Hosny, Nabil A. Lashin, and Mostafa M. Fouda. 2021. "Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments" Sensors 21, no. 23: 7845. https://doi.org/10.3390/s21237845