A Robust Color Image Watermarking Algorithm Based on APDCBT and SSVD
Abstract
:1. Introduction
2. Preliminary Concepts
2.1. APDCBT
2.2. SSVD
2.3. Fibonacci Transform
2.4. QR Code
3. Proposed Color Image Watermarking Algorithm
3.1. Watermark Preprocessing
Algorithm 1.Watermark Preprocessing Algorithm | |
Variable Declaration: | |
SDUW: color watermark image | |
W: read the watermark image | |
RW, GW, and BW: three components of the color watermark image | |
Rs, Gs, and Bs: three scrambled components using Fibonacci transform | |
URs, VRs, UGs, VGs, UBs, and VBs: orthogonal matrices for Rs, Gs, and Bs | |
SRs, SGs, and SBs: singular value matrices for Rs, Gs, and Bs | |
WR, WG, and WB: three watermark components for embedding | |
Watermark Preprocessing Procedure: | |
Start Procedure: | |
1: | Read the color watermark image |
W ← SDUW.png (color watermark image of size 64 × 64); | |
RW ← W (:, :, 1); GW ← W (:, :, 2); BW ← W (:, :, 3); | |
2: | Scramble the three color components of the watermark image |
Rs ← Fibonacci transform (RW); Gs ← Fibonacci transform (GW); Bs ← Fibonacci transform (BW); | |
3: | Perform SVD on each scrambled color components |
[URs, SRs, VRs] ← SVD (Rs); [UGs, SGs, VGs] ← SVD (Gs); [UBs, SBs, VBs] ← SVD (Bs); | |
4: | Obtain watermark for embedding |
WR = URs × SRs; WG = UGs × SGs; WB = UBs × SBs; | |
End Procedure |
3.2. Watermark Embedding
Algorithm 2.Watermark Embedding Algorithm | |
Variable Declaration: | |
Lena: color host image | |
I: read the color host image | |
R, G, and B: three color components of the host image | |
MC: three DC coefficient matrices obtained by APDCBT, where C = {R, G, B} | |
UC and VC: orthogonal matrices for MC | |
SC: singular value matrices for MC | |
WC: three preprocessed color components of the watermark image, where C = {R, G, B} | |
α: scaling factor | |
SCW: three singular value matrices with the embedded watermark | |
UCW and VCW: the orthogonal matrices for SCW | |
SCW1: the singular value matrices for SCW | |
: watermarked DC coefficient matrices | |
: three watermarked color components, including , , and | |
: watermarked image | |
Watermark Embedding Procedure: | |
Start Procedure: | |
1: | Read the color host image |
I ← Lena.ppm (color host image of size 512 × 512); | |
R ← I (:, :, 1); G ← I (:, :, 2); B ← I (:, :, 3); | |
2: | Perform 8 × 8 APDCBT to three color components |
MC ← APDCBT (C) //C = {R, G, B} | |
3: | Perform SVD on MC |
[UC, SC, VC] ← SVD (MC) | |
4: | Watermark Embedding |
SCW = SC + α × WC | |
[UCW, SCW1, VCW] ← SVD (MC) | |
← | |
5: | Perform the inverse APDCBT |
← inverse APDCBT () // | |
← cat (3, ) | |
End Procedure |
3.3. Watermark Extraction
Algorithm 3. Watermark Extraction Algorithm | |
Variable Declaration: | |
: the suspicious color image | |
, , and : three color components of | |
: three DC coefficient matrices obtained by APDCBT, where | |
and : orthogonal matrices for | |
: singular value matrices for | |
SC: saved singular value matrices for MC of host image | |
UCW and VCW: saved orthogonal matrices for SCW in watermark embedding process | |
: watermarked singular value matrices | |
α: scaling factor | |
: extracted watermark | |
: three reconstructed color components of watermark image | |
: three inverse scrambled color components of watermark image | |
: reconstructed watermark image | |
Watermark Embedding Procedure: | |
Start Procedure: | |
1: | Read the suspicious color image |
← Suspicious image.ppm | |
← (:, :, 1); ← (:, :, 2); ← (:, :, 3); | |
2: | Perform 8 × 8 APDCBT to three color components |
← APDCBT (C) // | |
3: | Perform SVD on |
[, , ] ← SVD () | |
4: | Watermark Extraction |
← // | |
← | |
← | |
5: | Apply inverse Fibonacci transform on |
← inverse Fibonacci transform () // | |
6: | Reconstruct the final watermark image |
← cat (3, ) | |
End Procedure |
4. Experimental Results and Analysis
4.1. Evaluation Indexes
4.2. Imperceptibility
4.3. Robustness
4.4. Real-Time Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Size of Image | 4 × 4 | 8 × 8 | 16 × 16 | 32 × 32 | 64 × 64 | 128 × 128 | 256 × 256 |
Period | 6 | 12 | 24 | 48 | 96 | 192 | 384 |
Host Images | Logo | SDUW | QR Code | |||||||
---|---|---|---|---|---|---|---|---|---|---|
PSNR (dB) | SSIM | NCC | PSNR (dB) | SSIM | NCC | PSNR (dB) | SSIM | NCC | ||
Baboon | 1 | 55.90 | 1.0000 | 0.9992 | 55.49 | 1.0000 | 0.9993 | 56.88 | 1.0000 | 0.9980 |
3 | 47.88 | 0.9998 | 1.0000 | 48.25 | 0.9998 | 1.0000 | 49.20 | 0.9998 | 1.0000 | |
5 | 44.84 | 0.9992 | 1.0000 | 46.53 | 0.9995 | 1.0000 | 46.78 | 0.9995 | 1.0000 | |
7 | 42.91 | 0.9982 | 1.0000 | 45.97 | 0.9988 | 1.0000 | 45.80 | 0.9989 | 1.0000 | |
Airplane | 1 | 55.69 | 0.9997 | 0.9979 | 55.20 | 0.9998 | 0.9986 | 56.63 | 0.9998 | 0.9965 |
3 | 47.17 | 0.9979 | 1.0000 | 47.15 | 0.9984 | 1.0000 | 48.32 | 0.9984 | 1.0000 | |
5 | 43.63 | 0.9942 | 1.0000 | 44.34 | 0.9955 | 1.0000 | 45.15 | 0.9960 | 1.0000 | |
7 | 41.43 | 0.9877 | 1.0000 | 43.11 | 0.9914 | 1.0000 | 43.40 | 0.9922 | 1.0000 | |
Sailboat | 1 | 55.98 | 0.9999 | 0.9995 | 55.46 | 0.9999 | 0.9998 | 56.85 | 0.9999 | 0.9992 |
3 | 48.09 | 0.9993 | 1.0000 | 48.18 | 0.9994 | 1.0000 | 49.09 | 0.9995 | 1.0000 | |
5 | 45.43 | 0.9979 | 1.0000 | 46.52 | 0.9986 | 1.0000 | 46.62 | 0.9985 | 1.0000 | |
7 | 44.10 | 0.9960 | 1.0000 | 46.56 | 0.9973 | 1.0000 | 45.78 | 0.9970 | 1.0000 | |
House | 1 | 55.78 | 0.9997 | 0.9991 | 55.29 | 0.9998 | 0.9995 | 56.71 | 0.9998 | 0.9975 |
3 | 47.49 | 0.9972 | 1.0000 | 47.57 | 0.9984 | 1.0000 | 48.60 | 0.9985 | 1.0000 | |
5 | 44.25 | 0.9934 | 1.0000 | 45.22 | 0.9963 | 1.0000 | 45.73 | 0.9965 | 1.0000 | |
7 | 42.33 | 0.9879 | 1.0000 | 44.45 | 0.9932 | 1.0000 | 44.36 | 0.9936 | 1.0000 | |
Peppers | 1 | 56.13 | 0.9826 | 0.9984 | 55.79 | 0.9844 | 0.9990 | 57.16 | 0.9843 | 0.9977 |
3 | 48.80 | 0.9729 | 1.0000 | 49.70 | 0.9793 | 1.0000 | 50.36 | 0.9775 | 1.0000 | |
5 | 46.34 | 0.9685 | 1.0000 | 48.89 | 0.9808 | 1.0000 | 49.07 | 0.9777 | 1.0000 | |
7 | 44.13 | 0.9662 | 1.0000 | 46.06 | 0.9824 | 1.0000 | 46.21 | 0.9806 | 1.0000 |
Watermarks | Logo | SDUW | QR Code |
---|---|---|---|
Watermarked images (PSNR (dB)/SSIM) | 45.24/0.9982 | 47.66/0.9986 | 47.70/0.9982 |
Extracted watermarks (NCC) | 1.0000 | 1.0000 | 1.0000 |
Watermarked images (PSNR (dB)/SSIM) | 44.84/0.9992 | 46.53/0.9995 | 46.78/0.9995 |
Extracted watermarks (NCC) | 1.0000 | 1.0000 | 1.0000 |
Algorithms | Patvardhan et al. [18] | Su et al. [31] | Jia et al. [34] | Proposed |
---|---|---|---|---|
Host images | 512 × 512 × 3 | 512 × 512 × 3 | 512 × 512 × 3 | 512 × 512 × 3 |
Watermark images | gray | color | color | color |
PSNR (dB) | 52.13 | 46.07 | 41.45 | 49.03 |
SSIM | 0.9975 | 0.9913 | 0.9842 | 0.9992 |
NCC | 0.9962 | 0.9999 | 1.0000 | 1.0000 |
Capacity | 128 × 128 | 64 × 64 × 3 | 32 × 32 × 3 | 64 × 64 × 3 |
Attacks | Parameter | Lena | Baboon | Sailboat |
---|---|---|---|---|
JPEG | QF = 30 | 0.9999 | 0.9999 | 0.9998 |
QF = 60 | 1.0000 | 1.0000 | 1.0000 | |
Gaussian noise | 0.01 | 0.9997 | 0.9998 | 0.9997 |
0.02 | 0.9986 | 0.9994 | 0.9990 | |
Salt and Pepper noise | 0.01 | 0.9998 | 0.9999 | 0.9999 |
0.02 | 0.9995 | 0.9998 | 0.9997 | |
Average filter | 5 × 5 | 0.9991 | 0.9988 | 0.9984 |
Median filter | 5 × 5 | 0.9999 | 0.9988 | 0.9995 |
Gaussian filter | 5 × 5 | 1.0000 | 1.0000 | 1.0000 |
Sharpening | 0.2 | 0.9977 | 0.9971 | 0.9974 |
Rotation | 0.9922 | 0.9905 | 0.9941 | |
Scaling | 0.5 | 1.0000 | 1.0000 | 1.0000 |
Attacks | Parameter | Lena | Baboon | Sailboat |
---|---|---|---|---|
JPEG | QF = 30 | 0.9997 | 0.9998 | 0.9996 |
QF = 60 | 0.9999 | 0.9999 | 0.9999 | |
Gaussian noise | 0.01 | 0.9991 | 0.9994 | 0.9994 |
0.02 | 0.9966 | 0.9979 | 0.9978 | |
Salt and Pepper noise | 0.01 | 0.9996 | 0.9998 | 0.9999 |
0.02 | 0.9986 | 0.9993 | 0.9991 | |
Average filter | 5 × 5 | 0.9978 | 0.9971 | 0.9963 |
Median filter | 5 × 5 | 0.9996 | 0.9972 | 0.9988 |
Gaussian filter | 5 × 5 | 1.0000 | 0.9999 | 0.9999 |
Sharpening | 0.2 | 0.9955 | 0.9932 | 0.9941 |
Rotation | 0.9886 | 0.9855 | 0.9900 | |
Scaling | 0.5 | 1.0000 | 1.0000 | 1.0000 |
Attacks | Patvardhan et al. [18] | Su et al. [31] | Jia et al. [34] | Proposed |
---|---|---|---|---|
Gaussian noise (0.02) | 0.8104 | 0.8300 | 0.8848 | 0.9966 |
Salt and Pepper noise (0.02) | 0.9335 | 0.9024 | 0.9676 | 0.9986 |
Average filter (3 × 3) | 0.9910 | 0.8662 | 0.9485 | 0.9996 |
Median filter (3 × 3) | 0.9958 | 0.8697 | 0.9622 | 0.9999 |
Gaussian filter (3 × 3) | 0.9960 | 0.9449 | 0.9602 | 1.0000 |
JPEG (30) | 0.9953 | 0.8437 | 0.8831 | 0.9997 |
Sharpening (0.2) | 0.7964 | 0.8406 | 0.8943 | 0.9955 |
Rotation () | 0.9940 | 0.9666 | 0.8709 | 0.9886 |
Scaling (2) | 0.9961 | 0.9901 | 0.9997 | 1.0000 |
Gaussian noise (0.02) + Average filter (3 × 3) | 0.9951 | 0.8406 | 0.8724 | 0.9964 |
Salt and Pepper noise (0.05) + Median filter (5 × 5) | 0.9937 | 0.8453 | 0.9202 | 0.9995 |
Gaussian noise (0.02) + JPEG (30) | 0.8157 | 0.8394 | 0.8785 | 0.9963 |
Salt and Pepper noise (0.05) + JPEG (50) | 0.8402 | 0.8432 | 0.8923 | 0.9934 |
Average filter (3 × 3) + JPEG (30) | 0.9910 | 0.8413 | 0.8801 | 0.9995 |
Median filter (3 × 3) + JPEG (70) | 0.9950 | 0.8405 | 0.9062 | 0.9999 |
Gaussian noise (0.02) + Scaling (0.5) | 0.9907 | 0.8389 | 0.8821 | 0.9967 |
Salt and Pepper noise (0.05) + Scaling (2) | 0.9639 | 0.8580 | 0.9668 | 0.9938 |
Average filter (5 × 5) + Scaling (0.5) | 0.9883 | 0.8366 | 0.9002 | 0.9977 |
Median filter (5 × 5) + Scaling (2) | 0.9917 | 0.8826 | 0.9260 | 0.9996 |
JPEG (30) + Scaling (0.5) | 0.9895 | 0.8424 | 0.8822 | 0.9998 |
JPEG (50) + Sharpening (0.2) | 0.9394 | 0.8462 | 0.8801 | 0.9969 |
JPEG (70) + Rotation () | 0.9964 | 0.8326 | 0.8677 | 0.9885 |
Scaling (2) + Sharpening (0.2) | 0.9275 | 0.8306 | 0.9000 | 0.9959 |
Gaussian noise (0.02) + Median filter (3 × 3) + Sharpening (0.2) | 0.8190 | 0.8320 | 0.8777 | 0.9925 |
Salt and Pepper noise (0.05) + Average filter (3 × 3) + Scaling (0.5) | 0.9889 | 0.8306 | 0.8849 | 0.9936 |
Average filter (5 × 5) + Scaling (0.5) + JPEG (30) | 0.9883 | 0.8402 | 0.8771 | 0.9980 |
Scaling (2) + Rotation () + Gaussian filter (3 × 3) | 0.9957 | 0.8339 | 0.9496 | 0.9960 |
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Yu, X.; Wang, C.; Zhou, X. A Robust Color Image Watermarking Algorithm Based on APDCBT and SSVD. Symmetry 2019, 11, 1227. https://doi.org/10.3390/sym11101227
Yu X, Wang C, Zhou X. A Robust Color Image Watermarking Algorithm Based on APDCBT and SSVD. Symmetry. 2019; 11(10):1227. https://doi.org/10.3390/sym11101227
Chicago/Turabian StyleYu, Xiaoyan, Chengyou Wang, and Xiao Zhou. 2019. "A Robust Color Image Watermarking Algorithm Based on APDCBT and SSVD" Symmetry 11, no. 10: 1227. https://doi.org/10.3390/sym11101227
APA StyleYu, X., Wang, C., & Zhou, X. (2019). A Robust Color Image Watermarking Algorithm Based on APDCBT and SSVD. Symmetry, 11(10), 1227. https://doi.org/10.3390/sym11101227