CN111242831B - Zernike moment-based geometric attack resistant reversible robust watermarking method - Google Patents

Zernike moment-based geometric attack resistant reversible robust watermarking method Download PDF

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CN111242831B
CN111242831B CN202010066301.XA CN202010066301A CN111242831B CN 111242831 B CN111242831 B CN 111242831B CN 202010066301 A CN202010066301 A CN 202010066301A CN 111242831 B CN111242831 B CN 111242831B
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zernike
watermark
image
distortion
watermark information
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CN111242831A (en
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项世军
胡润文
李敬轩
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Jinan University
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    • G06T1/00—General purpose image data processing
    • G06T1/0021—Image watermarking
    • G06T1/005—Robust watermarking, e.g. average attack or collusion attack resistant
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Abstract

The invention discloses a Zernike moment anti-geometric attack reversible robust watermarking method, which comprises the following steps: calculating Zernike moments of an original image, embedding the watermark by adopting a quantitative watermarking method, processing distortion information existing in the positive and negative conversion processes of the Zernike, and judging whether the image is attacked or not; when the image is judged not to be attacked, distortion information is extracted by adopting a reversible watermarking method, and a quantization watermark is extracted by utilizing the Zernike moment of the image and the original image is recovered; and when the image is judged to be attacked, calculating the Zernike moment of the image with the watermark information after the image is attacked, and performing quantitative watermark extraction to obtain the watermark information. The invention solves the problem that reversible robust watermarking can not be realized due to a large amount of accumulated errors in the Zernike moment conversion process, can extract the watermark and restore the original image when not attacked, can effectively extract the watermark when attacked, and has stronger robustness on geometric attack and conventional signal processing.

Description

Zernike moment-based geometric attack resistant reversible robust watermarking method
Technical Field
The invention relates to the technical field of digital watermarking, in particular to a Zernike matrix geometric attack resistant reversible robust watermarking method.
Background
In recent years, the existence of redundancy is discovered by researching the correlation relationship among image pixels, and by utilizing the redundancy, a reversible watermarking technology is provided, so that an original image can be accurately recovered after a watermark is extracted, however, in an actual application scene, a transmitted image is often attacked (such as noise, geometric attack and the like), and the reversible watermarking technology cannot resist the attack;
on the other hand, the existing Zernike matrix transformation technology has a large amount of accumulated errors in the implementation process and distortion in the processing process, so that the reversible robust watermarking technology cannot be realized through the Zernike matrix transformation.
Disclosure of Invention
In order to overcome the defects and shortcomings of the prior art, the invention provides a reversible robust watermarking method based on Zernike matrix anti-geometric attack, which solves the problem that the reversible robust watermarking can not be realized due to a large amount of accumulated errors in the Zernike matrix transformation process by processing the quantization distortion, the watermark distortion, the overflow distortion and the transformation distortion existing in the watermark embedding process, can extract the watermark and restore the image when not attacked, can effectively extract the watermark when attacked, has an important effect on the integrity authentication of digital media, and can effectively resist various attacks such as JPEG compression, stretching, rotation, gaussian noise, salt and pepper noise and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a Zernike moment anti-geometric attack reversible robust watermarking method, which comprises the following steps:
calculating the Zernike moment of the original image I to obtain the n-order m-fold Zernike moment A nm ；
Watermark embedding is carried out by adopting a quantization watermark method to obtain quantization distortion d q And watermark distortion d w ；
Zernike inverse transformation is carried out to obtain an image I with watermark information w Obtaining an image after a rounding operation
Figure GDA0003738959370000021
Processing the transformation distortion d existing in the positive and negative transformation process of Zernike t ；
For images
Figure GDA0003738959370000022
Performing overflow saturation processing to obtain an image
Figure GDA0003738959370000023
And overflow distortion d o ；
Distortion of quantization d by reversible watermarking q Distortion d of watermark w Distortion of overflow d o And transformation distortion d t Embedding in images
Figure GDA0003738959370000024
In order to obtain an image
Figure GDA0003738959370000025
Generating images
Figure GDA0003738959370000026
The hash value H is processed by a reversible watermarking methodH embedding into images
Figure GDA0003738959370000027
Obtaining an image
Figure GDA0003738959370000028
Using reversible watermarking methods to extract images from images
Figure GDA0003738959370000029
Extracts the hash value H 1 And restoring the image
Figure GDA00037389593700000210
Generating an image
Figure GDA00037389593700000211
Hash value of (H) 2 Judgment of H 1 And H 2 Judging whether the images are equal or not, and judging whether the images are attacked or not;
when the image is judged not to be attacked, a reversible watermarking method is adopted to extract the image
Figure GDA00037389593700000212
To extract the quantization distortion d q Distortion d of watermark w Distortion of overflow d o And transformation distortion d t And restoring the image
Figure GDA00037389593700000213
Based on overflow distortion d o Compensating images
Figure GDA00037389593700000214
Restoring images
Figure GDA00037389593700000215
Computing images
Figure GDA00037389593700000216
The Zernike matrix is obtained to obtain the Zernike matrix containing the watermark information, and the quantitative watermark extraction is carried out to obtain and recover the watermark information wComplex Zernike moments;
performing Zernike inverse transformation to obtain an image I 1 By using transformation distortion d t For image I 1 Compensating and recovering an original image I;
when the image is judged to be attacked, calculating the image I with the watermark information after the image is attacked aw Obtaining the Zernike matrix containing the watermark information after the attack;
performing quantitative watermark extraction to obtain watermark information w a 。
As a preferred technical solution, the calculating Zernike moments of the original image I specifically includes:
determining the order N, taking the center of the original image I with the size of M multiplied by M as the center of a circle, making an inscribed circle, taking the inscribed circle as a unit circle, and solving the Zernike moment of the pixels in the unit circle. Constructing Zernike base V based on the inscribed circle nm (x, y) by the Zernike group V nm (x, y) calculating Zernike moments to obtain n-order m-fold Zernike moment A nm The specific calculation formula is as follows:
Figure GDA0003738959370000031
where Δ x and Δ y represent the step size of the unit circle of the image, f (x) i ,y j ) Representing the pixels within the unit circle.
As a preferred technical solution, the watermark embedding is performed by using a quantization watermark method to obtain quantization distortion d q And watermark distortion d w The method comprises the following specific steps:
selecting the Zernike moment A nm In which the Zernike moment A satisfies the predetermined conditions pq Regularization is carried out to obtain Zernike moment
Figure GDA0003738959370000032
Using quantization watermarking method to align Zernike matrix
Figure GDA0003738959370000033
Absolute value of (2)
Figure GDA0003738959370000034
Embedding watermark to obtain
Figure GDA0003738959370000035
The specific formula is as follows:
Figure GDA0003738959370000036
the quantization distortion d q And watermark distortion d w The specific formula of (A) is as follows:
Figure GDA0003738959370000037
Figure GDA0003738959370000038
where s represents the step size in the quantized watermark and w represents the watermark information.
As a preferred technical solution, the image I with watermark information is obtained by performing inverse Zernike transformation w The method comprises the following specific steps:
calculating the Zernike matrix after embedding the quantization watermark by using the reciprocal of the absolute value ratio of the Zernike matrix before and after embedding the quantization watermark as a scale coefficient
Figure GDA0003738959370000039
The specific formula is as follows:
Figure GDA00037389593700000310
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image with watermark information and the low-frequency reconstructed image without the watermark information
Figure GDA0003738959370000041
The specific formula is as follows:
Figure GDA0003738959370000042
wherein L represents the length of watermark information, and L represents the length of watermark information in space domain
Figure GDA0003738959370000043
Adding the original image I to obtain an image I with watermark information w The concrete formula is as follows:
Figure GDA0003738959370000044
as a preferred technical scheme, the transformation distortion d existing in the process of processing the positive and negative transformation of the Zernike is processed t The method comprises the following specific steps:
computing images with watermark information
Figure GDA0003738959370000045
M-fold Zernike moment of order n
Figure GDA0003738959370000046
Obtain the corresponding Zernike moment
Figure GDA0003738959370000047
Regularization is carried out to obtain
Figure GDA0003738959370000048
Performing quantitative watermark extraction to obtain watermark information w;
using the quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure GDA0003738959370000049
The specific formula is as follows:
Figure GDA00037389593700000410
calculating the restored Zernike moment based on the inverse of the absolute value ratio of the Zernike moments before and after the extraction of the quantized watermark as the scale coefficient
Figure GDA00037389593700000411
The specific formula is as follows:
Figure GDA00037389593700000412
performing Zernike inverse transformation to obtain the difference between the low-frequency reconstructed image without watermark information and with watermark information
Figure GDA00037389593700000413
The specific formula is as follows:
Figure GDA0003738959370000051
wherein L represents the length of watermark information, and is to be applied in spatial domain
Figure GDA0003738959370000052
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure GDA0003738959370000053
calculating the restored image I 1 The transformation distortion d existing between the original image I and the original image t The concrete formula is as follows:
d t ＝I-I 1 。
as a preferred technical solution, the quantization watermark extraction is performed to obtain watermark information w and recover Zernike moments, and the specific steps include:
using extracted overflow distortion d o Compensating images
Figure GDA0003738959370000054
Thereby restoring the image
Figure GDA0003738959370000055
Computing images
Figure GDA0003738959370000056
M-fold Zernike moment of order n
Figure GDA0003738959370000057
And selecting the Zernike moments
Figure GDA0003738959370000058
Regularizing to obtain Zernike moment
Figure GDA0003738959370000059
Extracting quantization watermark to obtain watermark information w, and based on the extracted quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure GDA00037389593700000510
As a preferred technical solution, the specific formula of the watermark information w is as follows:
Figure GDA00037389593700000511
where α = mod (s, 0.04)/0.04, s represents the step size in the quantized watermark.
As a preferred technical solution, the image I obtained by performing inverse Zernike transformation is described 1 The method comprises the following specific steps:
based on extracted quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure GDA0003738959370000061
The concrete formula is as follows:
Figure GDA0003738959370000062
calculating the restored Zernike matrix by using the reciprocal of the absolute value ratio of the Zernike matrix before and after the extraction of the quantization watermark as a scale coefficient
Figure GDA0003738959370000063
The specific formula is as follows:
Figure GDA0003738959370000064
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image without the watermark information and the low-frequency reconstructed image with the watermark information
Figure GDA0003738959370000065
The concrete formula is as follows:
Figure GDA0003738959370000066
wherein L represents the length of watermark information, and L represents the length of watermark information in space domain
Figure GDA0003738959370000067
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure GDA0003738959370000068
preferably, when it is determined that the image is under attack, the image I with the watermark information after the attack is calculated aw The Zernike moment of (2) comprises the following specific steps:
image I with watermark information after being attacked by calculation aw M-fold Zernike moment of order n
Figure GDA0003738959370000069
Selecting according to preset conditions
Figure GDA00037389593700000610
Regularization is carried out to obtain Zernike matrix containing watermark information
Figure GDA00037389593700000611
As a preferred technical solution, the quantization watermark extraction is performed to obtain watermark information w a The specific calculation formula is as follows:
Figure GDA0003738959370000071
where α = mod (s, 0.04)/0.04, s represents the step size in quantizing the watermark.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) The reversible robust watermarking method provided by the invention based on the Zernike moment mainly utilizes the characteristics of the Zernike moment, solves the distortion problem in the Zernike transformation process, can extract the watermark and recover the image when not attacked, can effectively extract the watermark when attacked (such as JPEG compression, stretching, rotation and the like), and has stronger robustness to geometric attack and conventional processing.
(2) The method utilizes the robustness of the quantization watermark, adopts the mode of the quantization watermark to embed the robust watermark in the original image, can resist the rotation attack of various angles based on the characteristic that the Zernike moment is invariable in rotation, has the characteristic that the expansion is invariable based on the regularization of the Zernike moment, can resist the stretching attack, and can effectively extract watermark information and restore the image.
(3) The invention can effectively extract watermark information under different signal processing, such as Gaussian noise, salt and pepper noise and other noise attacks, and meets the requirements of daily digital evidence collection and digital authentication; meanwhile, the method can be applied to different images, and a better effect can be achieved on the different images.
Drawings
Fig. 1 is a schematic flow chart of a reversible robust watermarking method based on Zernike moment geometric attack resistance in this embodiment;
fig. 2 is a schematic flow chart of the present embodiment for determining whether an image with watermark information is attacked;
fig. 3 is a schematic flow chart of extracting a watermark and recovering an original image when the embodiment is not attacked;
fig. 4 is a schematic flowchart of extracting a watermark under an attack in this embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Examples
As shown in fig. 1, the embodiment provides a reversible robust watermarking method based on Zernike moment geometric attack resistance, which includes a watermark embedding step, a watermark extraction and image recovery step when not attacked, and a watermark extraction step when attacked;
wherein the watermark embedding step comprises the steps of:
s1: calculating the Zernike moment of the original image I;
s11: the order N (N is more than or equal to 0) of the Zernike moment is determined, in the embodiment, N =30 is taken, and A is used nm The Zernike moments of each order are expressed, where n and m satisfy the following equations:
0≤n≤N
Figure GDA0003738959370000081
base V of Zernike moment nm (x, y) is a set of perfect orthonormal bases on a unit circle, n is the order of the transform, m is the number of multiples of the transformed coefficients, V nm The specific formula of (x, y) is as follows:
V nm (x,y)＝R nm (ρ)e jmθ
wherein the content of the first and second substances,
Figure GDA0003738959370000082
θ＝tan -1 (y/x)，R nm (ρ) is a Zernike polynomial as follows:
Figure GDA0003738959370000083
therefore, a unit circle of the image needs to be made first;
s12: taking the center of an original image I with the size of M multiplied by M as the center of a circle, making an inscribed circle, taking the inscribed circle as a unit circle, calculating the Zernike moment of pixels in the unit circle, setting the pixels in the inscribed circle as f (x, y), and then constructing a Zernike base V by using the inscribed circle nm (x, y) by the Zernike group V nm (x, y) calculating Zernike moments to obtain n-order m-fold Zernike moment A nm The specific formula is as follows:
Figure GDA0003738959370000091
wherein, V nm (x,y)＝R nm (ρ)e jmθ Is a set of perfect orthonormal bases on a unit circle, R nm (ρ) is a Zernike polynomial, the specific expression being as follows:
Figure GDA0003738959370000092
Δ x and Δ y are steps of an image unit circle, and for an image of size M × M, specific expressions are as follows:
Figure GDA0003738959370000093
in this embodiment, M is equal to M =512;
s2: watermark embedding is carried out by utilizing a quantization watermark method to obtain quantization distortion d q And watermark distortion d w ；
S21: selecting the Zernike moment A nm Well satisfy (n > 0)&&(m＞0)&&Zernike moments A of (m ≠ 4 i) pq Subjecting it to a regularization operation to obtain
Figure GDA0003738959370000094
The concrete formula is as follows:
Figure GDA0003738959370000095
s22: embedding watermark information w: the method for quantizing the watermark w with the length L is used for carrying out regularized Zernike moments
Figure GDA0003738959370000101
Absolute value of (2)
Figure GDA0003738959370000102
Embedding watermark to obtain
Figure GDA0003738959370000103
The specific formula is as follows:
Figure GDA0003738959370000104
where s is the step size in the quantized watermark, s =0.02 in this example, with 100 × s being an integer greater than 1, and then the moments that are quantized are subject to quantization distortion d q And watermark distortion d w Preservation of (d) q And d w The specific formula is as follows:
Figure GDA0003738959370000105
Figure GDA0003738959370000106
s3: performing Zernike inversionTransforming to obtain image I with watermark information w ；
S31: modifying part of Zernike matrix in the process of embedding the watermark, and calculating the Zernike matrix after embedding the quantized watermark by using the reciprocal of the absolute value ratio of the Zernike matrix before and after embedding the quantized watermark as a scale coefficient
Figure GDA0003738959370000107
The specific formula is as follows:
Figure GDA0003738959370000108
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image with watermark information and the low-frequency reconstructed image without the watermark information
Figure GDA0003738959370000109
The specific formula is as follows:
Figure GDA00037389593700001010
s32: in the spatial domain
Figure GDA00037389593700001011
Adding the original image I to obtain an image I with watermark information w The concrete formula is as follows:
Figure GDA0003738959370000111
s33: image I with watermark information w Performing rounding operation to obtain image
Figure GDA0003738959370000112
S4: processing the transformation distortion d existing in the positive and negative transformation process of Zernike t Although the Zernike moments are orthogonal transforms on the unit circles, due to computational accuracy problems,the more the number of the calculated orders is, the more the accumulated error is, and therefore, the distortion d needs to be converted t Carrying out treatment;
s41: similar to steps S11 and S12, the image with the watermark information is calculated
Figure GDA0003738959370000113
M-fold Zernike moment of order n
Figure GDA0003738959370000114
Obtain the Zernike moment of the corresponding transformation
Figure GDA0003738959370000115
Regularizing the same to obtain
Figure GDA0003738959370000116
S42: and (3) performing quantitative watermark extraction to obtain watermark information w, wherein the specific formula is as follows:
Figure GDA0003738959370000117
where α = mod (s, 0.04)/0.04, and α =0.005 in this example, the quantization distortion d is reused q And watermark distortion d w Recovering Zernike moments
Figure GDA0003738959370000118
The specific formula is as follows:
Figure GDA0003738959370000119
s43: calculating the restored Zernike moments by using the inverse of the absolute value ratio of the Zernike moments before and after the extraction of the quantized watermark as a proportionality coefficient
Figure GDA00037389593700001110
The specific formula is as follows:
Figure GDA00037389593700001111
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image without the watermark information and the low-frequency reconstructed image with the watermark information
Figure GDA00037389593700001112
The specific formula is as follows:
Figure GDA0003738959370000121
in the spatial domain
Figure GDA0003738959370000122
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure GDA0003738959370000123
s44: calculating the restored image I 1 The transformation distortion d existing between the original image I and the original image t The concrete formula is as follows:
d t ＝I-I 1
s5: processing distortion by reversible watermarking method, and embedding the combined distortion information into the reversible watermarking method
Figure GDA0003738959370000124
Then obtain
Figure GDA0003738959370000125
Generating
Figure GDA0003738959370000126
Embedding the hash value H into a reversible watermarking method
Figure GDA0003738959370000127
To getTo the image
Figure GDA0003738959370000128
S51: for images
Figure GDA0003738959370000129
Carrying out overflow saturation treatment, namely setting the value of the pixel value larger than 255 as 255 and setting the value of the pixel value smaller than 0 as 0 to obtain an image
Figure GDA00037389593700001210
Simultaneously preserving overflow distortion d possibly existing in overflow saturation treatment process o ；
S52: distortion d of quantization by reversible watermarking q Distortion d of watermark w Distortion of overflow d o And transformation distortion d t Embedding in images
Figure GDA00037389593700001211
In (1), obtaining an image
Figure GDA00037389593700001212
S53: generating an image
Figure GDA00037389593700001213
Embedding the hash value H into the image by a reversible watermarking method
Figure GDA00037389593700001214
Obtaining an image
Figure GDA00037389593700001215
As shown in fig. 2, the specific steps of determining whether the image is attacked or not are as follows:
s6: method for reversible watermarking from images
Figure GDA00037389593700001216
Extracts the hash value H 1 And restoring the image
Figure GDA00037389593700001217
Generating an image
Figure GDA0003738959370000131
Hash value of (H) 2 Judgment of H 1 And H 2 Judging whether the images are equal or not, and judging whether the images are attacked or not;
image processing method
Figure GDA0003738959370000132
Method for extracting hash value H by reversible watermark 1 And restoring the image
Figure GDA0003738959370000133
Generating an image
Figure GDA0003738959370000134
Hash value of (H) 2 Judgment of H 1 And H 2 Whether they are equal;
if H is present 1 And H 2 Equality, illustrate images
Figure GDA0003738959370000135
Recovered images without attack
Figure GDA0003738959370000136
And images
Figure GDA0003738959370000137
To match, to the image
Figure GDA0003738959370000138
Extracting the watermark and recovering the original image under the condition of not being attacked;
if H is present 1 And H 2 Inequality, indicating a picture
Figure GDA0003738959370000139
Attacked and restored image
Figure GDA00037389593700001310
And images
Figure GDA00037389593700001311
Inconsistency, pair
Figure GDA00037389593700001312
Watermark extraction under the condition of attack is carried out;
as shown in fig. 3, the specific steps of extracting the watermark and recovering the image when the attack is not received are as follows:
s7: method for reversible watermarking from images
Figure GDA00037389593700001313
Extracts distortion information therefrom, and restores the image
Figure GDA00037389593700001314
Specifically, the image is taken
Figure GDA00037389593700001315
Method for extracting quantization distortion d by reversible watermark q Distortion d of watermark w And overflow distortion d o And transformation distortion d t And recovering the image with the watermark information
Figure GDA00037389593700001316
S8: using overflow distortion d o Compensating images
Figure GDA00037389593700001317
Restoring images
Figure GDA00037389593700001318
Computing images
Figure GDA00037389593700001319
Then, carrying out quantitative watermark extraction to obtain watermark information w and recovering the Zernike moment;
s81: using extracted overflow distortion d o Compensating images
Figure GDA00037389593700001320
Thereby restoring the image
Figure GDA00037389593700001321
S82: similar to step S11 and step S12, an image is calculated
Figure GDA00037389593700001322
M-fold Zernike moment of order n
Figure GDA00037389593700001323
Selected according to the same conditions
Figure GDA00037389593700001324
Regularizing the same to obtain
Figure GDA00037389593700001325
S83: similar to step S42, the quantization watermark extraction is carried out to obtain watermark information w, and the extracted quantization distortion d is utilized q And watermark distortion d w Recovering Zernike moments
Figure GDA00037389593700001326
The specific formula of the watermark information w is as follows:
Figure GDA0003738959370000141
wherein α =0.005;
s9: performing Zernike inverse transformation to obtain an image I 1 By transformation distortion d t For image I 1 Compensating and recovering an original image I;
s91: similar to step S43, zernike inverse transformation is performed to restore the image i 1 ；
By extractionThe quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure GDA0003738959370000142
The concrete formula is as follows:
Figure GDA0003738959370000143
calculating the restored Zernike matrix by using the reciprocal of the absolute value ratio of the Zernike matrix before and after the extraction of the quantization watermark as a scale coefficient
Figure GDA0003738959370000144
The specific formula is as follows:
Figure GDA0003738959370000145
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image without the watermark information and the low-frequency reconstructed image with the watermark information
Figure GDA0003738959370000146
The concrete formula is as follows:
Figure GDA0003738959370000147
in the spatial domain
Figure GDA0003738959370000148
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure GDA0003738959370000149
s92: using extracted transformation distortion d t Compensated image I 1 And thus recovering the image I, the specific formula is as follows:
I＝I 1 +d t
as shown in fig. 4, the watermark extraction when attacked is as follows:
s10: image I with watermark information after being attacked by calculation aw Obtaining the Zernike matrix containing the watermark information after the attack;
specifically, similarly to steps S11 and S12, the image I with watermark information after being attacked is extracted aw M-fold Zernike moment of order n
Figure GDA0003738959370000151
Selected under the same conditions
Figure GDA0003738959370000152
Regularizing it to obtain
Figure GDA0003738959370000153
S11: performing quantitative watermark extraction to obtain watermark information w a ；
Specifically, quantization watermark extraction is performed to obtain watermark information w a The concrete formula is as follows:
Figure GDA0003738959370000154
where α = mod (s, 0.04)/0.04, and α =0.005 is taken in this embodiment.
In this embodiment, for the reversible robust watermarking method, the error rate of an image with watermark information after being attacked is below 20%, which is considered as having better robustness, and the specific experimental results are as follows:
as shown in table 1 below, the robust watermark embedded in the table is 60bits, the error rate exceeding 20% is represented by "-", and the experimental result based on the picture Lena shows that the method of the present embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100, rotational attack from 0 to 360 degrees, tensile attack with a tensile factor of 0.5 to 2.0, gaussian noise with a mean value of 0, variance of 0.01 to 0.03, and salt and pepper noise attack with a density of 0.01;
table 1: bit error rate result table (embedded robust watermark is 60 bits) when picture Lena is attacked
Figure GDA0003738959370000161
As shown in table 2 below, the experimental results based on the picture ae show that the present embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100, rotational attack from 0 to 360 degrees, tensile attack with a tensile factor of 0.5 to 2.0, gaussian noise with a mean value of 0, a variance of 0.01 to 0.03, and salt and pepper noise attack with a density of 0.01 to 0.03;
table 2 bit error rate result table when picture Aerial is attacked (embedded robust watermark is 60 bits)
Figure GDA0003738959370000171
Figure GDA0003738959370000181
As shown in table 3 below, the experimental results based on the picture babon show that the present embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100, rotational attack of 0 to 360 degrees, tensile attack with a tensile factor of 0.5 to 2.0, gaussian noise with a mean value of 0, variance of 0.01 to 0.03, and salt and pepper noise attack with a density of 0.01 to 0.03;
table 3 table of bit error rate results when picture babon is attacked (embedded robust watermark is 60 bits)
Figure GDA0003738959370000182
Figure GDA0003738959370000191
In this example, a Lena picture, an initial picture and a Baboon gray image are used as experimental objects, and the three groups of pictures have different characteristics, such as that the Lena picture includes flat blocks, clear and fine lines, gradually changing light and shadow, and color depth levels; the Aeriol picture has a sharp outline and is bright and dark; the picture Baboon has the characteristics of continuous pixel values, smooth edges and the like. Various pictures in daily life have the characteristics, so that the three groups of pictures are taken as experimental objects, so that the experimental result has popularization; the picture size selected by the embodiment is 512 × 512, and different images have small difference, so that the method can be popularized to various images.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (10)

1. A reversible robust watermarking method based on Zernike moment geometric attack resistance is characterized by comprising the following steps:
calculating the Zernike moment of the original image I to obtain the n-order m-fold Zernike moment A nm ；
Watermark embedding is carried out by adopting a quantization watermark method to obtain quantization distortion d q And watermark distortion d w ；
Zernike inverse transformation is carried out to obtain an image I with watermark information w Obtaining an image after a rounding operation
Figure FDA0003743244730000011
Processing the transformation distortion d existing in the positive and negative transformation process of Zernike t ；
For images
Figure FDA0003743244730000012
Performing overflow saturation processing to obtain an image
Figure FDA0003743244730000013
And overflow distortion d o ；
Distortion of quantization d by reversible watermarking q Distortion d of watermark w Distortion of overflow d o And transformation distortion d t Embedding in images
Figure FDA0003743244730000014
In (1), obtaining an image
Figure FDA0003743244730000015
Generating images
Figure FDA0003743244730000016
The hash value H is embedded into the image by adopting a reversible watermarking method
Figure FDA0003743244730000017
Obtaining an image
Figure FDA0003743244730000018
Using reversible watermarking methods to extract images from images
Figure FDA0003743244730000019
Extracts the hash value H 1 And recovering the obtained image
Figure FDA00037432447300000110
Generating images
Figure FDA00037432447300000111
Hash value of (H) 2 Judgment of H 1 And H 2 Judging whether the images are equal or not, and judging whether the images are attacked or not;
determining an image
Figure FDA00037432447300000112
When not attacked, the reversible watermarking method is adopted to extract images
Figure FDA00037432447300000113
To extract the quantization distortion d q Distortion d of watermark w Distortion of overflow d o And transformation distortion d t And restoring the image
Figure FDA00037432447300000114
Based on overflow distortion d o Compensating images
Figure FDA00037432447300000115
Restoring images
Figure FDA00037432447300000116
Computing images
Figure FDA00037432447300000117
Obtaining the Zernike matrix containing the watermark information by the Zernike matrix, and carrying out quantitative watermark extraction to obtain watermark information w and recover the Zernike matrix;
performing Zernike inverse transformation to obtain an image I 1 Applying transformation distortion dt to image I 1 Compensating and recovering an original image I;
determining an image
Figure FDA00037432447300000118
When the attack is received, calculating the Zernike moment of the image with the watermark information after the attack is received, and obtaining the Zernike moment containing the watermark information after the attack is received;
quantitative watermark extraction is carried out to obtain watermark information w a 。
2. The Zernike moment-based geometric attack resistant reversible robust watermarking method according to claim 1, wherein the Zernike moment of the original image I is calculated by the specific steps of:
determining the order N of the Zernike moment, taking the center of an original image I with the size of M multiplied by M as the center of a circle, making an inscribed circle, taking the inscribed circle as a unit circle, solving the Zernike moment of a pixel in the unit circle, and constructing a Zernike base V based on the inscribed circle nm (x, y) by the Zernike group V nm (x, y) calculating Zernike moments to obtain n-order m-fold Zernike moment A nm The specific calculation formula is as follows:
Figure FDA0003743244730000021
where Δ x and Δ y represent the step size of the image unit circle, f (x) i ，y j ) Representing the pixels within the unit circle.
3. The Zernike moment geometric attack resistant reversible robust watermarking method according to claim 2, wherein the watermark embedding is performed by using a quantization watermarking method to obtain quantization distortion d q And watermark distortion d w The method comprises the following specific steps:
selecting Zernike moment A nm In which the Zernike moment A satisfies the predetermined conditions pq Regularization is carried out to obtain Zernike moment
Figure FDA0003743244730000022
Using quantization watermarking method to align Zernike matrix
Figure FDA0003743244730000023
Absolute value of (2)
Figure FDA0003743244730000024
Embedding watermark to obtain
Figure FDA0003743244730000025
The specific formula is as follows:
Figure FDA0003743244730000026
the quantization distortion d q And watermark distortion d w The specific formula of (A) is as follows:
Figure FDA0003743244730000027
Figure FDA0003743244730000028
where s represents the step size in the quantized watermark and w represents the watermark information.
4. The reversible robust watermarking method based on Zernike moment geometric attack resistance as claimed in claim 3, wherein the inverse Zernike transformation is performed to obtain image I with watermark information w The method comprises the following specific steps:
calculating the Zernike matrix after embedding the quantization watermark by using the reciprocal of the absolute value ratio of the Zernike matrix before and after embedding the quantization watermark as a scale coefficient
Figure FDA0003743244730000031
The concrete formula is as follows:
Figure FDA0003743244730000032
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image with watermark information and the low-frequency reconstructed image without the watermark information
Figure FDA0003743244730000033
The specific formula is as follows:
Figure FDA0003743244730000034
wherein L represents the length of watermark information, and is to be applied in spatial domain
Figure FDA0003743244730000035
Adding the original image I to obtain an image I with watermark information w The concrete formula is as follows:
Figure FDA0003743244730000036
5. the Zernike moment geometric attack resistant reversible robust watermarking method according to claim 4, wherein the transformation distortion d existing in the Zernike positive and negative transformation process is processed t The method comprises the following specific steps:
computing images with watermark information
Figure FDA0003743244730000037
M-fold Zernike moment of order n
Figure FDA0003743244730000038
Obtaining the corresponding Zernike moment
Figure FDA0003743244730000039
Regularization is carried out to obtain
Figure FDA00037432447300000310
Performing quantitative watermark extraction to obtain watermark information w;
using the quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure FDA00037432447300000311
The specific formula is as follows:
Figure FDA00037432447300000312
calculating the restored Zernike moment based on the inverse of the absolute value ratio of the Zernike moments before and after the extraction of the quantized watermark as the scale coefficient
Figure FDA0003743244730000041
The specific formula is as follows:
Figure FDA0003743244730000042
performing Zernike inverse transformation to obtain the difference between the low-frequency reconstructed image without watermark information and with watermark information
Figure FDA0003743244730000043
The concrete formula is as follows:
Figure FDA0003743244730000044
wherein L represents the length of watermark information, and is to be applied in spatial domain
Figure FDA0003743244730000045
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure FDA0003743244730000046
calculating the restored image I 1 The transformation distortion dt existing between the original image I is specifically represented as follows:
d t ＝I-I 1 。
6. the Zernike moment anti-geometric attack reversible robust watermarking method according to claim 5, wherein the quantization watermark extraction is performed to obtain watermark information w and recover the Zernike moment, and the specific steps include:
using extracted spillover distortion d o Compensating images
Figure FDA0003743244730000047
Thereby restoring the image
Figure FDA0003743244730000048
Computing images
Figure FDA0003743244730000049
M-fold Zernike moment of order n
Figure FDA00037432447300000410
And selecting Zernike moments
Figure FDA00037432447300000411
Regularizing to obtain Zernike moment
Figure FDA00037432447300000412
Extracting quantization watermark to obtain watermark information w, and based on the extracted quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure FDA00037432447300000413
7. The Zernike moment geometric attack resistant reversible robust watermarking method according to claim 6, wherein the watermark information w is specifically formulated as follows:
Figure FDA0003743244730000051
where α = mod (s, 0.04)/0.04, s represents the step size in the quantized watermark.
8. The Zernike moment-based reversible robust watermarking method against geometric attacks according to claim 7, wherein the inverse Zernike transformation is performed to obtain an image I 1 The method comprises the following specific steps:
based on extracted quantization distortion d q And watermark distortion d w Recovering Zernike moments
Figure FDA0003743244730000052
The specific formula is as follows:
Figure FDA0003743244730000053
calculating the restored Zernike matrix by using the reciprocal of the absolute value ratio of the Zernike matrix before and after the extraction of the quantization watermark as a scale coefficient
Figure FDA0003743244730000054
The specific formula is as follows:
Figure FDA0003743244730000055
then, zernike inverse transformation is carried out to obtain the difference between the low-frequency reconstructed image without the watermark information and the low-frequency reconstructed image with the watermark information
Figure FDA0003743244730000056
The specific formula is as follows:
Figure FDA0003743244730000057
wherein L represents the length of watermark information, and is to be applied in spatial domain
Figure FDA0003743244730000058
And image I with watermark information w Performing an addition operation to obtain an image I 1 The concrete formula is as follows:
Figure FDA0003743244730000061
9. the Zernike moment geometric attack resistant reversible robust watermarking method according to claim 1, wherein the decision is image
Figure FDA0003743244730000062
When the attack is received, the Zernike moment with the watermark information image after the attack is calculated, and the specific steps comprise:
image I with watermark information after being attacked by calculation aw M-fold Zernike moment of order n
Figure FDA0003743244730000063
Selecting according to preset conditions
Figure FDA0003743244730000064
Regularization is carried out to obtain Zernike moment containing watermark information
Figure FDA0003743244730000065
10. The Zernike moment geometric attack resistant reversible robust watermarking method according to claim 9, wherein the quantization watermark extraction is performed to obtain watermark information w a The specific calculation formula is as follows:
Figure FDA0003743244730000066
where α = mod (s, 0.04)/0.04, s represents the step size in the quantized watermark.
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