Chebyshev Chaotic Mapping and DWT-SVD-Based Dual Watermarking Scheme for Copyright and Integrity Authentication of Remote Sensing Images
Abstract
:1. Introduction
- (1)
- Traditional block-based watermarking algorithms make it difficult to resist desynchronization attacks (such as translation, rotation, and scaling). This study employed image moments and affine transformations to normalize remote sensing images, thus enhancing the desynchronization attack resistance of the watermarking algorithm;
- (2)
- The DWT local transformation accurately delineates the tampered and unaffected portions of remote sensing images, ensuring the accurate detection of the semi-fragile watermarking algorithm. To tackle the problem of false alarms often encountered in integrity watermarking, the verification results were optimized through a 3 × 3 window, resulting in a reduction of the false alarm rate caused by Quantization Index Modulation (QIM) extraction errors;
- (3)
- Entropy was utilized to determine the embedding positions of robust watermarks in the DWT transform domain. The singular value matrix of the horizontal and vertical components of the DWT was used as the embedding template, and the robust watermark embedding algorithm was redesigned, which well solves the false-positive problem that often exists in the SVD and ensures the invisibility and robustness of the robust watermark.
2. Related Works
3. Construction of Dual Watermarking
3.1. Remote Sensing Image Normalization
- (1)
- Angle normalization: Firstly, the remote sensing image is rotated according to the center of mass. In (5), the transformation matrix and , resulting in the centrally processed remote sensing image .
- Scaling normalization: Apart from the rotation, scaling transformation also greatly affects the extraction results, so it is necessary to re-determine the scaling scales and for the horizontal and vertical axes based on the dimensional relationship between the original remote sensing images and :
3.2. Semi-Fragile Watermarking Based on DWT and Chebyshev Chaotic Mapping
3.2.1. DWT Decomposition
3.2.2. Validation Coefficient Construction Based on Chebyshev Chaos Mapping
3.2.3. Mapping Semi-Fragile Watermark Embedding Method
3.2.4. False Alarm Optimization Method
3.3. Robust Watermarking Method Based on Entropy and SVD
3.4. Watermark Scrambling
4. Embedding and Extraction Processes of the Proposed Dual Watermarking
4.1. Watermark Embedding Process
4.1.1. Robust Watermark Embedding
4.1.2. Semi-Fragile Watermark Embedding
Algorithm 1 Watermark embedding process |
; quantization step, ∆; remote sensing image; Watermark. |
Output: Watermarked image; |
1: Convert RGB to YCbCr; |
2: Extract Cr and perform a 4 × 4 DWT; // Robust watermark embedding |
3: Obtain LL, HL, LH and HH; |
4: Compute HH’s entropy to determine embedding position; |
5: Gain embedding region ); |
6: Convert the watermark, and perform Arnold scrambling and SVD; |
7: Obtain ; |
8: Perform SVD on ; |
9: Gain and ; |
according to (18); |
11: Embed according to (19); |
; |
and then inverse DWT; |
14: Gain Cr’; |
15: Extract Y and perform DWT; // Semi-fragile watermark embedding |
16: Obtain LL2, HL2, LH2 and HH2; |
17: Extract HL2 and LH2 to calculate the mean value, then process it according to (11); |
18: Obtain the input coefficient ; |
19: is chaotically mapped according to (10). |
20: Gain ; |
21: if > 0 then // Perform binary processing to |
= 1 |
23: else |
= 0 |
25: end if |
26: Extract and embed in it; |
27: Obtain HH2’; |
28: Perform inverse DWT on HH2’, |
29: Obtain ; |
30: Convert Y’CbCr’ to RGB; |
31: Return: Watermarked image; |
4.2. Watermark Extraction Process
4.2.1. Extract Robust Watermark
4.2.2. Extract Semi-Fragile Watermark
Algorithm 2 Watermark extraction process |
; |
Output: Extracted watermark, optimized verification results; |
1: Convert RGB to YCbCr; |
2: Obtain Y’CbCr’; |
3: Extract Cr’ and perform a 4 × 4 DWT; // Copyright verification |
4: Obtain LL, HL, LH and HH’; |
5: Compute HH’s entropy to determine embedding position; |
); |
; |
, ; |
according to (18); |
according to (20); |
; |
, then reverse the scrambling, and convert back to the “0, 1”; |
12: Gain robust watermark; |
13: Extract Y’ and perform DWT; // Integrity authentication |
14: Obtain LL2, HL2, LH2 and HH2’; |
15: Extract HL2 and LH2 to calculate the mean value, then process it according to (11); |
16: Obtain the input coefficient ; |
17: is chaotically mapped according to (10). |
18: Gain ; |
19: if > 0 then // Perform binary processing to |
= 1 |
21: else |
= 0 |
23: end if |
; |
; |
26: |
27: Obtain verification results; |
28: Fale alarm optimization; |
29: Obtain optimized verification results |
30: Return: Extracted watermark, optimized verification results; |
5. Experimental Results and Analysis
5.1. Evaluation Methods
5.2. Experimental Data Sets
5.3. Invisibility Analysis
5.4. Efficiency Analysis
5.5. False Positive Test
5.6. Robustness Analysis
5.6.1. Noise Attacks
5.6.2. Geometric Attacks
5.6.3. Cropping Attacks
5.6.4. Filtering Attacks
5.6.5. Compression
5.6.6. Affine Transformation
5.7. Integrity Authentication
5.7.1. Local Tampering
5.7.2. Combined Attacks
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Data Set | Data Type | Precision | Bit Depth | Bands |
---|---|---|---|---|
Anhui | Landset8 | 30m | 16 Bit | 7 |
Xinjiang | Worldview2 | 0.5m | 16 Bit | 8 |
Suzhou | GF2 | 0.8m | 16 Bit | 4 |
Jilin | Landset5 | 30m | 8 Bit | 6 |
Nanning | Landset3 | 60m | 8 Bit | 4 |
Huaian | Landset7 | 30m | 8 Bit | 6 |
Index | Datasets | Proposed | Ref. [35] | Ref. [36] | Ref. [15] |
---|---|---|---|---|---|
PSNR | Anhui | 84.094 | 70.538 | 77.211 | 76.594 |
Xinjiang | 87.724 | 79.937 | 77.562 | 63.187 | |
Suzhou | 84.689 | 79.677 | 77.205 | 61.378 | |
Jilin | 46.427 | 42.020 | 45.420 | 51.043 | |
Nanning | 45.262 | 40.998 | 43.211 | 50.828 | |
Huaian | 47.661 | 51.361 | 45.420 | 47.513 | |
SSIM | Anhui | 1.000 | 0.999 | 1.000 | 1.000 |
Xinjiang | 1.000 | 1.000 | 0.999 | 1.000 | |
Suzhou | 1.000 | 1.000 | 0.999 | 1.000 | |
Jilin | 0.999 | 0.988 | 0.998 | 0.999 | |
Nanning | 0.997 | 0.991 | 0.998 | 0.999 | |
Huaian | 0.996 | 0.986 | 0.998 | 0.997 |
Datasets | Original Image | Watermarked Image | False Positive Problem |
---|---|---|---|
Anhui | NC = 0.000 | NC = 0.999 | No |
Xinjiang | NC = 0.000 | NC = 0.999 | No |
Suzhou | NC = 0.000 | NC = 1.000 | No |
Jilin | NC = 0.000 | NC = 0.999 | No |
Nanning | NC = 0.000 | NC = 0.999 | No |
Haian | NC = 0.000 | NC = 0.999 | No |
Attack Mode | Proposed | Ref. [35] | Ref. [36] | Ref. [15] |
---|---|---|---|---|
NC = 0.999 | NC = 0.941 | NC = 0.945 | NC = 0.916 | |
NC = 0.999 | NC = 0.895 | NC = 1.000 | NC = 0.942 | |
NC = 0.999 | NC = 0.893 | NC = 1.000 | NC = 0.936 | |
NC = 0.999 | NC = 0.761 | NC = 1.000 | NC = 0.955 | |
NC = 0.999 | NC = 0.783 | NC = 0.897 | NC = 0.940 |
Transformation Matrix | Proposed | Ref. [35] | Ref. [36] | Ref. [15] |
---|---|---|---|---|
NC = 0.999 | NC = 0.961 | NC = 0.966 | NC = 0.922 | |
NC = 0.998 | NC = 0.565 | NC = 0.997 | NC = 0.915 | |
NC = 0.995 | NC = 0.501 | NC = 1.000 | NC = 0.904 | |
NC = 0.995 | NC = 0.481 | NC = 1.000 | NC = 0.905 |
Watermarked Image | Modified Image | Authentication Results | Watermarked Image | Modified Image | Authentication Results |
---|---|---|---|---|---|
Local replacement | Add ground elements | ||||
Crop | Paste | ||||
Watermarked Image | Modified Image | Authentication Results | Watermarked Image | Modified Image | Authentication Results |
---|---|---|---|---|---|
0.00001 speckle + 0.1 Gaussian filtering + paste | 0.0001 salt and pepper + [1 1] mean filtering +add scenery | ||||
[1 1] mean filtering + 0.1 Gaussian filtering + crop | 90JPEG compression + [1 1] median filtering + paste | ||||
90JPEG + 0.2 Gaussian filtering + add scenery | 0.0001 salt and pepper noise + [1 1] median filtering + local replacement | ||||
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Zhang, J.; Du, J.; Xi, X.; Yang, Z. Chebyshev Chaotic Mapping and DWT-SVD-Based Dual Watermarking Scheme for Copyright and Integrity Authentication of Remote Sensing Images. Symmetry 2024, 16, 969. https://doi.org/10.3390/sym16080969
Zhang J, Du J, Xi X, Yang Z. Chebyshev Chaotic Mapping and DWT-SVD-Based Dual Watermarking Scheme for Copyright and Integrity Authentication of Remote Sensing Images. Symmetry. 2024; 16(8):969. https://doi.org/10.3390/sym16080969
Chicago/Turabian StyleZhang, Jie, Jinglong Du, Xu Xi, and Zihao Yang. 2024. "Chebyshev Chaotic Mapping and DWT-SVD-Based Dual Watermarking Scheme for Copyright and Integrity Authentication of Remote Sensing Images" Symmetry 16, no. 8: 969. https://doi.org/10.3390/sym16080969
APA StyleZhang, J., Du, J., Xi, X., & Yang, Z. (2024). Chebyshev Chaotic Mapping and DWT-SVD-Based Dual Watermarking Scheme for Copyright and Integrity Authentication of Remote Sensing Images. Symmetry, 16(8), 969. https://doi.org/10.3390/sym16080969