CN115861015A - Pseudo Zernike moment based robust reversible watermark embedding method and extraction method - Google Patents

Pseudo Zernike moment based robust reversible watermark embedding method and extraction method Download PDF

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CN115861015A
CN115861015A CN202210737262.0A CN202210737262A CN115861015A CN 115861015 A CN115861015 A CN 115861015A CN 202210737262 A CN202210737262 A CN 202210737262A CN 115861015 A CN115861015 A CN 115861015A
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pseudo
watermark
image
zernike
robust
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汤毅超
王春桃
边山
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South China Agricultural University
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South China Agricultural University
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Abstract

The invention relates to the technical field of digital watermarks, and discloses a robust reversible watermark embedding method and an extracting method based on a pseudo Zernike matrix, which comprise the following steps: calculating a pseudo-Zernike moment of an original image, performing self-adaptive normalization operation on the pseudo-Zernike moments of different orders, performing pseudo-Zernike inverse transformation on a difference value between the pseudo-Zernike moment obtained by calculating the image with the robust watermark and the pseudo-Zernike moment used for reconstructing the image with the robust watermark, and embedding the watermark by adopting a quantization watermarking method; when the image is not attacked, extracting watermark information of the image which is not attacked and recovering the original image; when the image is attacked, watermark information of the attacked image is extracted. The invention gives watermark intensities of different magnitudes of pseudo Zernike moments of different orders, so that the robust reversible image has stronger robustness in the face of geometric attack and conventional processing. The obtained error image is compensated to the image with the robust watermark, and the amount of distortion information is further reduced, so that large-capacity watermark embedding is realized.

Description

Robust reversible watermark embedding method and robust reversible watermark extraction method based on pseudo Zernike moment
Technical Field
The invention relates to the technical field of digital watermarks, in particular to a robust reversible watermark embedding method and a robust reversible watermark extraction method based on a pseudo Zernike matrix.
Background
The digital watermarking technology plays a role in identification by embedding digital information such as image identification, numbers, characters, serial numbers and the like into a digital medium. In recent years, the robustness research on image digital watermarking has been greatly developed, but the robustness research still has great difficulty in the face of geometric attacks such as rotation, scaling, translation and the like. The robust reversible watermark has the characteristics that when the carrier image is not attacked, the embedded watermark information can be correctly extracted and the carrier image can be completely recovered, and when the carrier image is attacked to a certain degree, the watermark information can still be correctly extracted without damage.
The prior reversible robust watermarking method comprises the steps of calculating a Zernike matrix of an image, carrying out quantitative watermarking embedding on the image based on the Zernike matrix, and judging whether the image is attacked or not through distortion information generated in the quantitative watermarking embedding process; when the image is judged not to be attacked, extracting watermark information by using the Zernike moment of the image and recovering the original image; 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 extracting the watermark information by using the Zernike moment of the image with the watermark information.
However, the above method does not consider that the distortion information is too large due to different watermark intensities required by the Zernike moments of different orders in the watermark embedding process, and the method does not compensate the distortion information generated in the positive and negative transformation process of the Zernike, which further increases the amount of the distortion information used for reversible watermark embedding, resulting in the defect that the robustness is low and the large-capacity watermark embedding cannot be satisfied.
Disclosure of Invention
The invention provides a robust reversible watermark embedding method and an extraction method based on a pseudo Zernike moment, aiming at overcoming the defects that the prior art is low in robustness and cannot meet the large-capacity watermark embedding.
In order to solve the technical problems, the technical scheme of the invention is as follows:
in a first aspect, the invention provides a pseudo-Zernike matrix-based robust reversible watermark embedding method, which comprises the following steps:
s1: an original image I is acquired.
S2: calculating n-order m-weighted pseudo-Zernike moment Z of original image I n,m 。
S3: for the pseudo Zernike moment Z n,m Performing adaptationNormalization operation is carried out to obtain normalized pseudo Zernike moment
Figure BDA0003716112970000021
S4: for normalized pseudo Zernike moment
Figure BDA0003716112970000022
Quantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->
Figure BDA0003716112970000023
And quantization distortion d quantified . Wherein, w 1 Representing robust watermark information.
S5: normalized pseudo-Zernike moments for the robust watermark
Figure BDA0003716112970000024
Carrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
Figure BDA0003716112970000025
/>
S6: for the pseudo Zernike moment with robust watermark
Figure BDA0003716112970000026
Performing inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>
Figure BDA0003716112970000027
S7: computing images with robust watermarks
Figure BDA0003716112970000028
In a pseudo-Zernike moment->
Figure BDA0003716112970000029
A pseudo Zernike moment is then calculated>
Figure BDA00037161129700000210
And a pseudo-Zernike moment->
Figure BDA00037161129700000211
The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->
Figure BDA00037161129700000212
Error image I error And image with robust watermark>
Figure BDA00037161129700000213
Performing superposition processing to obtain a superposed image>
Figure BDA00037161129700000214
S8: for the superimposed image
Figure BDA00037161129700000215
Performing watermark removing operation to obtain a watermark removed superposed image I suprimposed 。
S9: calculating an original image I and a de-watermarked superimposed image I suprumposed Rounding distortion d between rounding 。
S10: distorting said quantization by d quantified The rounding distortion d rounding And superimposing the images
Figure BDA00037161129700000216
The least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>
Figure BDA00037161129700000217
Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>
Figure BDA00037161129700000218
Wherein, w 2 Is reversible watermark information.
S11: generating intermediate images
Figure BDA00037161129700000219
Hash value of (H) 1 And the hash value H is added 1 Replacing intermediate images
Figure BDA00037161129700000220
The least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
Figure BDA00037161129700000221
In a second aspect, the present invention further provides a robust reversible watermark extraction method based on pseudo-Zernike moments, including:
obtaining robust reversible watermark images
Figure BDA00037161129700000222
And superimposing images>
Figure BDA00037161129700000223
The robust reversible watermark image
Figure BDA00037161129700000224
And superimposing images>
Figure BDA00037161129700000225
Generated using the pseudo-Zernike moment based robust reversible watermark embedding method of any one of claims 1-7.
Extracting the robust reversible watermark image
Figure BDA00037161129700000226
Of the first S pixels, i.e. the intermediate image
Figure BDA00037161129700000227
Hash value of H 1 And using a reversible watermarking method to &'s a robust reversible watermark image>
Figure BDA00037161129700000228
Reverting to an intermediate image
Figure BDA0003716112970000031
Extracting superimposed images
Figure BDA0003716112970000032
And replacing the intermediate image with the extraction result>
Figure BDA0003716112970000033
After the least significant bit of the first S pixels, the intermediate image at that time is generated @>
Figure BDA0003716112970000034
Hash value of (H) 2 。
When the hash value H 1 Is equal to the hash value H 2 Time, judge the reversible watermark picture of robustness
Figure BDA0003716112970000035
Non-attacked and intermediate image
Figure BDA0003716112970000036
Is not attacked, and the following steps are carried out:
extracting non-attacked intermediate images
Figure BDA0003716112970000037
The watermark information of (1).
For intermediate image not under attack
Figure BDA0003716112970000038
Performing recovery operation to the intermediate image which is not attacked
Figure BDA0003716112970000039
And restoring to the original image I.
When the hash value H 1 Is not equal to the hash value H 2 Time, judge the reversible watermark picture of robustness
Figure BDA00037161129700000310
Attacked and intermediate image +>
Figure BDA00037161129700000311
And (5) under attack, executing the following steps:
extracting an attacked intermediate image
Figure BDA00037161129700000312
The watermark information of (1).
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
(1) The invention gives watermark intensities of different magnitudes of the pseudo-Zernike moments of different orders by carrying out self-adaptive normalization operation on the pseudo-Zernike moments of different orders, so that the robust reversible image has stronger robustness in the face of geometric attacks and conventional processing.
(2) The invention obtains the pseudo Zernike moment by calculating the image with the robust watermark
Figure BDA00037161129700000313
And a pseudo-Zernike moment ≥ for reconstructing the robustly watermarked image>
Figure BDA00037161129700000314
And performing pseudo-Zernike inverse transformation on the difference value, compensating the obtained error image into the image with the robust watermark, and further reducing the distortion information quantity to realize large-capacity watermark embedding.
Drawings
Fig. 1 is a flowchart of a pseudo-Zernike moment-based robust reversible watermark embedding method according to the present invention.
Fig. 2 is a flowchart of the pseudo-Zernike moment-based robust reversible watermark extraction method of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
the technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
Referring to fig. 1, the present embodiment provides a robust reversible watermark embedding method based on pseudo-Zernike moments, which includes the following steps:
s1: an original image I is acquired.
S2: calculating n-order m-weighted pseudo-Zernike moment Z of original image I n,m 。
S3: for the pseudo Zernike moment Z n,m Performing self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
Figure BDA0003716112970000041
S4: for normalized pseudo Zernike moment
Figure BDA0003716112970000042
Quantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->
Figure BDA0003716112970000043
And quantization distortion d quantified . Wherein, w 1 Representing robust watermark information.
S5: normalized pseudo-Zernike moments for the robust watermark
Figure BDA0003716112970000044
Carrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
Figure BDA0003716112970000045
S6: for the pseudo Zernike moment with robust watermark
Figure BDA0003716112970000046
Carrying out inverse pseudo Zernike transformation and rounding operation to obtain an image with a robust watermark>
Figure BDA0003716112970000047
S7: calculating outImage with robust watermark
Figure BDA0003716112970000048
In a pseudo-Zernike moment->
Figure BDA0003716112970000049
A pseudo Zernike moment is then calculated>
Figure BDA00037161129700000410
And a pseudo-Zernike moment->
Figure BDA00037161129700000411
Performing pseudo-Zernike inverse transformation and rounding operation on the difference value to obtain an error image->
Figure BDA00037161129700000412
Error image I error And image with robust watermark->
Figure BDA00037161129700000413
Performing superposition processing to obtain a superposed image->
Figure BDA00037161129700000414
S8: for the superimposed image
Figure BDA00037161129700000415
Performing watermark removing operation to obtain a watermark removed superposed image I suprimposed 。
S9: calculating an original image I and a de-watermarked superimposed image I suprumposed Rounding distortion d between rounding 。
S10: distorting said quantization by d quantified The rounding distortion d rounding And superimposing the images
Figure BDA00037161129700000416
The least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>
Figure BDA00037161129700000417
Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>
Figure BDA00037161129700000418
Wherein, w 2 Is reversible watermark information.
S11: generating intermediate images
Figure BDA00037161129700000419
Hash value of (H) 1 And the hash value H is added 1 Replacing intermediate images
Figure BDA00037161129700000420
The least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
Figure BDA00037161129700000421
In the specific implementation process, the self-adaptive normalization operation is carried out on the pseudo-Zernike moments of different orders, and the watermark intensities of the pseudo-Zernike moments of different orders and different sizes are given, so that the robust reversible image has stronger robustness in the aspects of geometric attack and conventional processing. Calculating a pseudo-Zernike moment from an image with a robust watermark
Figure BDA00037161129700000422
And a pseudo-Zernike moment ≥ for reconstructing the robustly watermarked image>
Figure BDA00037161129700000423
And performing pseudo-Zernike inverse transformation on the difference value, compensating the obtained error image into an image with the robust watermark, and further reducing the distortion information amount to realize large-capacity watermark embedding.
Example 2
This embodiment makes an adjustment on the basis of the pseudo-Zernike moment-based robust reversible watermark embedding method proposed in embodiment 1.
S1: an original image I is acquired.
S2: calculating n-order m-fold pseudo-Zernike moment Z of the original image I n,m 。
In this embodiment, an inscribed circle of the original image I is made with the center of the original image I having a size of B × B as the center of a circle and B as a positive integer, and a pseudo Zernike basis V is constructed based on the inscribed circle n,m (x s ,y t ) (ii) a Using the inscribed circle as a unit circle and according to the pseudo Zernike base V n,m (x, y) calculating the n-th order m-fold pseudo-Zernike moment Z of the pixel in the unit circle n,m The specific expression is as follows:
Figure BDA0003716112970000051
V nm (x，y)＝R nm (r)e imθ
Figure BDA0003716112970000052
Figure BDA0003716112970000053
θ＝tan -1 (y/x)
Figure BDA0003716112970000054
wherein the pseudo Zernike group V n,m (x s ,y t ) Is a set of perfect orthogonal bases on a unit circle, R nm (r) is a pseudo Zernike polynomial, x s The s-th abscissa, y, representing the original image I t Denotes the t-th ordinate, Δ x, of the original image I s Representing the step size, Δ y, of the abscissa of a unit circle in the original image I t Denotes the step size of the ordinate, f (x), of a unit circle in the original image I s ,y t ) Representing pixels within a unit circle, k is an integer from 0 to (n-m).
In this embodiment, the value of B is 512.
S3: for the pseudo ZernikeMoment Z n,m Self-adaptive normalization operation is carried out to obtain normalized pseudo-Zernike moment
Figure BDA0003716112970000055
The specific expression is as follows:
Figure BDA0003716112970000056
Figure BDA0003716112970000057
wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the repeated number of the pseudo-Zernike matrix embedded in the ith watermark bit, i is the ith watermark bit, j is the bit value corresponding to the ith watermark bit, Z 00 A 0 th order, 0 times the pseudo-Zernike moment, N is the upper limit of the order N,
Figure BDA0003716112970000058
for adaptive normalization of weights, T start Gamma is a global parameter for adjusting the strength of the watermark, which is the starting value of the adaptive normalized weight.
In the present example, N =26,t start ＝2400，γ＝10。
The self-adaptive normalization scheme is adopted for different pseudo-Zernike moment orders, self-adaptive normalization weights with different sizes are adopted, watermark information with different strengths is embedded into the pseudo-Zernike moments with different orders, robustness of resisting geometric attack and conventional processing is improved, watermarks can be extracted and recovered when the watermarks are not attacked, and the watermarks can be effectively extracted when the watermarks are attacked.
S4: to normalized pseudo Zernike moment
Figure BDA0003716112970000061
Quantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->
Figure BDA0003716112970000062
And quantization distortion d quantified (ii) a Wherein, w 1 Representing robust watermark information d quantified The specific expression is as follows:
Figure BDA0003716112970000063
Figure BDA0003716112970000064
Figure BDA0003716112970000065
wherein, beta i (j) Expressed as constraint beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being a quantization step; d dec_i Represent
Figure BDA0003716112970000066
To a fraction thereof nearest integer, e.g. if +>
Figure BDA0003716112970000067
Then
Figure BDA0003716112970000068
At this time D dec_i ＝0.3。
In this embodiment, the quantization step Δ =32.
The novel quantization watermark embedding method adopted in the embodiment adopts rounding operation, so that the robust quantization watermark is only embedded into the pseudo-Zernike moment
Figure BDA0003716112970000069
While the pseudo-Zernike moments Z of the original image I n,m The fractional part of the watermark is preserved, so that the distortion degree caused by different watermark information is the same, the distortion information quantity for reversible watermark embedding is obviously reduced,and large-capacity watermark embedding is realized. The pseudo-Zernike moment absolute value has the characteristic of invariant rotation scaling, can effectively resist the attack of rotation scaling, and can effectively extract watermark information and restore images when not attacked. />
S5: for the normalized pseudo-Zernike moment with robust watermark
Figure BDA00037161129700000610
Carrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
Figure BDA00037161129700000611
The specific expression is as follows:
Figure BDA00037161129700000612
s6: for the pseudo Zernike moment with robust watermark
Figure BDA00037161129700000613
Carrying out inverse pseudo Zernike transformation and rounding operation to obtain an image with a robust watermark>
Figure BDA00037161129700000614
The specific expression is as follows:
Figure BDA00037161129700000615
where L represents the length of the robust watermark information.
S7: computing images with robust watermarks
Figure BDA0003716112970000071
Is based on the pseudo-Zernike moment->
Figure BDA0003716112970000072
A pseudo Zernike moment is then calculated>
Figure BDA0003716112970000073
And a pseudo-Zernike moment->
Figure BDA0003716112970000074
The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->
Figure BDA0003716112970000075
Then the error image I error And image with robust watermark->
Figure BDA0003716112970000076
Performing superposition processing to obtain a superposed image->
Figure BDA0003716112970000077
The specific expression is as follows:
Figure BDA0003716112970000078
Figure BDA0003716112970000079
in this embodiment, although the pseudo Zernike moments are orthogonal transformation on the unit circle, information loss is caused in the positive and negative transformation processes, and at this time, distortion information is compensated to the image with the robust watermark by constructing an error image
Figure BDA00037161129700000710
The information loss degree can be reduced. There is therefore a need for robust watermarked images +>
Figure BDA00037161129700000711
The calculated pseudo-Zernike moment->
Figure BDA00037161129700000712
And a pseudo-Zernike moment @usedto reconstruct the image>
Figure BDA00037161129700000713
The difference between them is inverse pseudo-Zernike transformed.
S8: for the superimposed image
Figure BDA00037161129700000714
Performing watermark removing operation to obtain a watermark removed superposed image I suprimposed The method comprises the following specific steps:
computing a superimposed image
Figure BDA00037161129700000715
In a pseudo-Zernike moment->
Figure BDA00037161129700000716
For the pseudo Zernike moment
Figure BDA00037161129700000717
Performing adaptive normalization operation to obtain a normalized pseudo-Zernike moment->
Figure BDA00037161129700000718
By extracting the normalized pseudo-Zernike moments
Figure BDA00037161129700000719
Quantization distortion d of quantified Obtaining a normalized pseudo-Zernike moment->
Figure BDA00037161129700000720
For the normalized pseudo-Zernike moment
Figure BDA00037161129700000721
Inverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-suprimposed The calculation formula is as follows:
Figure BDA00037161129700000722
calculating the pseudo Zernike moment Z n,m-suprimposed With the pseudo-Zernike moment
Figure BDA00037161129700000723
Performs pseudo-Zernike inverse transformation and rounding operation on the difference value, and combines the rounding operation result and the superimposed image->
Figure BDA00037161129700000724
Performing superposition processing to obtain a watermark-removed superposed image I suprimposed The calculation formula is as follows:
Figure BDA0003716112970000081
s9: calculating an original image I and a de-watermarked superimposed image I suprimposed Rounding distortion d between rounding The expression is as follows:
d rounding ＝I-I suprimposed
s10: distorting said quantization d using a reversible watermarking method quantified The rounding distortion d rounding And superimposing the images
Figure BDA0003716112970000082
The least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>
Figure BDA0003716112970000083
Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>
Figure BDA0003716112970000084
Wherein, w 2 Is reversible watermark information.
S11: generating intermediate images
Figure BDA0003716112970000085
Hash value of H 1 And the hash value H is added 1 Replacing intermediate images
Figure BDA0003716112970000086
The least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
Figure BDA0003716112970000087
In this embodiment, an SHA-256 algorithm is used to generate an intermediate image
Figure BDA0003716112970000088
Hash value of (H) 1 。
Example 3
Referring to fig. 2, the present embodiment provides a robust reversible watermark extraction method based on pseudo-Zernike moments, including:
obtaining robust reversible watermark images
Figure BDA0003716112970000089
And the superimposed image pick>
Figure BDA00037161129700000810
The robust reversible watermark image
Figure BDA00037161129700000811
And the superimposed image pick>
Figure BDA00037161129700000812
Generated using the pseudo-Zernike moment based robust reversible watermark embedding method as described in example 1 or 2.
Extracting the robust reversible watermark image
Figure BDA00037161129700000813
Of the first S pixels, i.e. the intermediate image
Figure BDA00037161129700000814
OfValue of Hi H 1 And using a reversible watermarking method to combine the robust reversible watermark image->
Figure BDA00037161129700000815
Restore to intermediate image
Figure BDA00037161129700000816
Extracting superimposed images
Figure BDA00037161129700000817
And replacing the intermediate image with the extraction result>
Figure BDA00037161129700000818
After the least significant bit of the first S pixels, the intermediate image at that time is generated @>
Figure BDA00037161129700000819
Hash value of (H) 2 ；/>
When the hash value H 1 Is equal to the hash value H 2 Time-lapse judging robust reversible watermark image
Figure BDA00037161129700000820
Non-attacked and intermediate image
Figure BDA00037161129700000821
Is not attacked, and the following steps are carried out:
extracting non-attacked intermediate images
Figure BDA00037161129700000822
The watermark information of (2), the specific steps include:
extracting non-attacked intermediate images
Figure BDA00037161129700000823
Least significant bit, quantization distortion d of the first S pixels of quantified And rounding distortion d rounding And using a reversible watermark blockThe intermediate image which is not attacked is->
Figure BDA0003716112970000091
Restoration to an image with a robust watermark>
Figure BDA0003716112970000092
Computing images with robust watermarks
Figure BDA0003716112970000093
Is based on the pseudo-Zernike moment->
Figure BDA0003716112970000094
And combining said pseudo-Zernike moment in a manner known per se>
Figure BDA0003716112970000095
Performing adaptive normalization to obtain a normalized pseudo-Zernike moment>
Figure BDA0003716112970000096
According to normalized pseudo-Zernike moments
Figure BDA0003716112970000097
Extraction of robust watermark information w using quantization watermarking method 1 The expression is as follows:
Figure BDA0003716112970000098
Figure BDA0003716112970000099
wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the repeated number of the pseudo-Zernike matrix embedded in the ith watermark bit, i is the ith watermark bit, j is the bit value corresponding to the ith watermark bit, beta i (j) Representing a constraint of beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being a quantization step;
for intermediate image not under attack
Figure BDA00037161129700000910
Performing a restore operation to combine the intermediate image>
Figure BDA00037161129700000911
Restoring the original image I, specifically comprising:
according to the quantization distortion d quantified The normalized pseudo Zernike moments
Figure BDA00037161129700000912
Conversion into a pseudo-Zernike moment->
Figure BDA00037161129700000913
The expression is as follows:
Figure BDA00037161129700000914
for the pseudo Zernike moment
Figure BDA00037161129700000915
Inverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-temporary ；
For the pseudo Zernike moment Z n,m-temporary Carrying out pseudo Zernike inverse transformation and rounding operation to obtain a watermark removed superposed image I suprimposed The expression is as follows:
Figure BDA00037161129700000916
wherein L represents the length of the robust watermark information;
according to rounding distortion d rounding Superimposing the watermark removed image I suprimposed Converting into an original image I, wherein the expression is as follows:
I＝I suprimposed +d rounding 。
when the hash value H 1 Is not equal to the hash value H 2 Time-lapse judging robust reversible watermark image
Figure BDA0003716112970000101
Attacked and intermediate image
Figure BDA0003716112970000102
And (5) under attack, executing the following steps:
extracting an attacked intermediate image
Figure BDA0003716112970000103
The watermark information of (2), the specific steps include:
when the hash value H 1 Is not equal to the hash value H 2 Extracting the attacked intermediate image
Figure BDA0003716112970000104
The step of watermarking information of (1) comprises:
computing an attacked intermediate image
Figure BDA0003716112970000105
Is based on the pseudo-Zernike moment->
Figure BDA0003716112970000106
For the pseudo-Zernike moment->
Figure BDA0003716112970000107
Performing self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
Figure BDA0003716112970000108
For normalized pseudo Zernike moment
Figure BDA0003716112970000109
Performing quantization watermark extraction operation to obtain an attacked intermediate image->
Figure BDA00037161129700001010
Watermark information w of attack The expression is as follows:
Figure BDA00037161129700001011
Figure BDA00037161129700001012
wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the weight of the pseudo-Zernike moment embedded in the ith watermark bit, i is the ith watermark bit, j is the bit value corresponding to the ith watermark bit, and beta i (j) Representing a constraint of beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being the quantization step.
In this embodiment, the reversible watermarking method is implemented based on prediction error expansion and histogram translation technologies, and includes the following specific steps:
a diamond mode prediction scheme is adopted, all pixel points in an image are divided into two mutually crossed sets which are respectively called a cross set and a point set, wherein the cross set is used for embedding information, and the point set is used for calculating a predicted value.
Wherein, the central pixel u i,j Is predicted by its surrounding pixel points (v) i-1,j ,v i+1,j ,v i,j-1 ,v i,j+1 ) Is calculated to obtain the average value of (1). By centering the central pixel u i,j And subtracting the actual value from the predicted value to obtain the prediction error of the pixel point. The prediction error of all the cross-set pixel points can be obtained by the same method.
Further calculating the local variance of all cross-set pixel points and performing ascending order arrangement to obtain the distortion d suitable for embedding quantization quantified Rounding distortion d rounding A sequence of prediction errors with the least significant bits of the first S pixels of the image.
Finally, the quantization is distorted by using a histogram translation methodd quantified Rounding distortion d rounding And the least significant bit of the first S pixels of the picture is embedded in the ordered prediction error sequence.
In the specific implementation process, only robust reversible watermark images are needed to be verified when copyright information is verified
Figure BDA0003716112970000111
The value of the least significant bit of the first N pixels in the middle, i.e. the intermediate image->
Figure BDA0003716112970000112
Hash value of H 1 Is extracted, the intermediate image obtained at this time is->
Figure BDA0003716112970000113
The least significant bits of the first N pixels of (a) are all "0" (because the content is fetched).
Then the superimposed image is processed
Figure BDA0003716112970000114
Replaces the intermediate image->
Figure BDA0003716112970000115
Is valid (because the superimposed image |)>
Figure BDA0003716112970000116
Is less significant and the intermediate image->
Figure BDA0003716112970000117
Is identical) when the intermediate image @>
Figure BDA0003716112970000118
Is recovered to generate its hash value H 2 ；H 1 Representing intermediate images when embedding watermarks
Figure BDA0003716112970000119
Hash value of H 2 Is representative ofIntermediate image/device when taking watermark>
Figure BDA00037161129700001110
Hash of H 1 And H 2 The identity of the two proves that the image is not attacked.
In this embodiment, for the pseudo-Zernike matrix-based robust reversible watermark embedding method and extraction, 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:
table 1: bit error rate result table when picture Lena is attacked (256 bits embedded robust watermark)
Figure BDA00037161129700001111
As shown in Table 1, the embedded robust watermark is 256bits, the error rate exceeds 20% and is represented by- ", and the experimental result based on the picture Lena shows that the method of the embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100: 1, rotation attack from 0 degree to 360 degrees and scaling attack with a stretching factor of 0.5 to 2.0, and Gaussian noise attack with a mean value of 0 and a variance of 0.01 to 0.03.
Table 2: error rate result table when picture Peppers is attacked (256 bits embedded robust watermark)
Figure BDA0003716112970000121
As shown in table 2, the experimental results based on the pictures Peppers show 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: 1, rotational attack of 0 to 360 degrees, and scaling attack with a stretch factor of 0.5 to 2.0, and gaussian noise attack with a mean value of 0 and a variance of 0.01 to 0.03.
Table 3: bit error rate result table (256 bits embedded with robust watermark) when picture Barbara is attacked
Figure BDA0003716112970000122
/>
Figure BDA0003716112970000131
As shown in table 3, the experimental results based on the pictures barbarbarbarbara show 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: 1, rotational attack of 0 to 360 degrees, and scaling attack with a tensile factor of 0.5 to 2.0, and gaussian noise attack with a mean value of 0 and a variance of 0.01 to 0.03.
Table 4: bit error rate result table when picture Baboon is attacked (256 bits embedded robust watermark)
Figure BDA0003716112970000132
As shown in table 4, the experimental results based on the picture babon show 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: 1, rotational attack of 0 to 360 degrees and scaling attack with a stretch factor of 0.5 to 2.0, and gaussian noise attack with a mean value of 0 and a variance of 0.01 to 0.03.
In this embodiment, the gray level images of the Lena picture, the Peppers picture, the barbarbarba picture and the Baboon picture are used as experimental objects, and the four groups of pictures have different characteristics, for example, the Lena picture includes a flat block, clear and fine lines, gradually changing light and shade, and color depth; the pictures Peppers have the characteristics of more bright and dark areas, similar colors inside the blocks and large color difference among the blocks; the picture Barbara has a large number of regular textures; the picture Baboon has a large amount of irregular textures and the like. Various pictures in daily life have the characteristics, so that the four groups of pictures are taken as experimental objects, so that the experimental result has popularization; the size of the selected picture is 512 × 512, and the difference between different images is not large, 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.
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (11)

1. The robust reversible watermark embedding method based on the pseudo Zernike moment is characterized by comprising the following steps of:
s1: acquiring an original image I;
s2: calculating n-order m-weighted pseudo-Zernike moment Z of original image I n,m ；
S3: for the pseudo Zernike moment Z n,m Performing self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
Figure RE-FDA0003802870840000011
S4: to normalized pseudo Zernike moment
Figure RE-FDA0003802870840000012
Quantitative watermark embedding is carried out to obtain normalized pseudo-Zernike moments which are subjected to robust watermark combination>
Figure RE-FDA0003802870840000013
And quantization distortion d quantified (ii) a Wherein, w 1 Representing robust watermark information;
s5: for the normalized pseudo-Zernike moment with robust watermark
Figure RE-FDA0003802870840000014
Carrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
Figure RE-FDA0003802870840000015
S6: for the pseudo Zernike moment with robust watermark
Figure RE-FDA0003802870840000016
Performing inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>
Figure RE-FDA0003802870840000017
S7: computing images with robust watermarks
Figure RE-FDA0003802870840000018
Is based on the pseudo-Zernike moment->
Figure RE-FDA0003802870840000019
The pseudo-Zernike moment is then calculated>
Figure RE-FDA00038028708400000110
And a pseudo-Zernike moment->
Figure RE-FDA00038028708400000111
The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->
Figure RE-FDA00038028708400000112
Will error the pictureI error And image with robust watermark>
Figure RE-FDA00038028708400000113
Performing superposition processing to obtain a superposed image>
Figure RE-FDA00038028708400000114
S8: for the superimposed image
Figure RE-FDA00038028708400000115
Performing watermark removing operation to obtain a watermark removed superposed image I suprimposed ；
S9: calculating an original image I and a de-watermarked superimposed image I suprimposed Rounding distortion d between rounding ；
S10: distorting said quantization by d quantified The rounding distortion d rounding And superimposing the images
Figure RE-FDA00038028708400000116
The least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>
Figure RE-FDA00038028708400000117
In (d), an intermediate image is obtained which contains a robust watermark and a reversible watermark>
Figure RE-FDA00038028708400000118
Wherein w 2 Is reversible watermark information;
s11: generating intermediate images
Figure RE-FDA00038028708400000119
Hash value of (H) 1 And the hash value H is added 1 Replace the intermediate image pick>
Figure RE-FDA00038028708400000120
The least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
Figure RE-FDA00038028708400000121
2. The pseudo-Zernike moment-based robust reversible watermark embedding method according to claim 1, wherein in S2, the n-order m-weighted pseudo-Zernike moment Z of the original image I is calculated n,m The method comprises the following specific steps:
taking the center of an original image I with the size of BxB as the circle center, B as a positive integer, making an inscribed circle of the original image I, and constructing a pseudo Zernike base V based on the inscribed circle n,m (x s ,y t ) (ii) a Using the inscribed circle as a unit circle according to the pseudo Zernike base V n,m (x, y) calculating the m-th order pseudo-Zernike moment Z of the pixels in the unit circle n,m The specific expression is as follows:
Figure RE-FDA0003802870840000021
wherein, the pseudo Zernike group V n,m (x s ,y t ) Is a set of perfect orthogonal bases on a unit circle, x s The s-th abscissa, y, representing the original image I t Denotes the t-th ordinate, Δ x, of the original image I s Represents the abscissa step length, Δ y, of a unit circle in the original image I t Represents the ordinate step size, f (x), of a unit circle in the original image I s ,y t ) Representing the pixels within the unit circle.
3. The pseudo-Zernike moment-based robust reversible watermark embedding method of claim 1, wherein in S3, for the pseudo-Zernike moment Z n,m Self-adaptive normalization operation is carried out to obtain normalized pseudo-Zernike moment
Figure RE-FDA0003802870840000022
The specific expression is as follows:
Figure RE-FDA0003802870840000023
Figure RE-FDA00038028708400000211
wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the weight of the pseudo-Zernike moment embedded in the ith watermark bit, j is the bit value corresponding to the ith watermark bit, Z 00 A 0 th order, pseudo-Zernike moment, N is the upper limit of the order N,
Figure RE-FDA0003802870840000024
for adaptive normalization of weights, T start Gamma is a global parameter for adjusting the strength of the watermark, which is the starting value of the adaptive normalized weight.
4. The pseudo-Zernike moment-based robust reversible watermark embedding method of claim 1, wherein in S4, the normalized pseudo-Zernike moments are normalized
Figure RE-FDA0003802870840000025
Quantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->
Figure RE-FDA0003802870840000026
And quantization distortion d quantified The specific expression is as follows:
Figure RE-FDA0003802870840000027
Figure RE-FDA0003802870840000028
Figure RE-FDA0003802870840000029
wherein, beta i (j) Representing a constraint of beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being the quantization step, D dec_i To represent
Figure RE-FDA00038028708400000210
To the decimal between its nearest integers.
5. The pseudo-Zernike moment based robust reversible watermark embedding method of claim 1, wherein in S5, the normalized pseudo-Zernike moments with robust watermark are normalized
Figure RE-FDA0003802870840000031
Carrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
Figure RE-FDA0003802870840000032
The specific expression is as follows:
Figure RE-FDA0003802870840000033
6. the pseudo-Zernike moment-based robust reversible watermark embedding method of claim 1, wherein in S6, the pseudo-Zernike moment with robust watermark is subjected to
Figure RE-FDA0003802870840000034
Performing inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>
Figure RE-FDA0003802870840000035
The specific expression is as follows:
Figure RE-FDA0003802870840000036
where L represents the length of the robust watermark information.
7. The pseudo-Zernike moment-based robust reversible watermark embedding method of claim 1, wherein in S7, the pseudo-Zernike moment is computed
Figure RE-FDA0003802870840000037
And image with robust watermark->
Figure RE-FDA0003802870840000038
Pseudo Zernike moments of
Figure RE-FDA0003802870840000039
The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->
Figure RE-FDA00038028708400000310
The specific expression is as follows:
Figure RE-FDA00038028708400000311
the error image I error And images with robust watermarks
Figure RE-FDA00038028708400000312
Performing superposition processing to obtain a superposed image
Figure RE-FDA00038028708400000313
The specific expression is as follows:
Figure RE-FDA00038028708400000314
8. the pseudo-Zernike moment-based robust reversible watermark embedding method according to claim 1, characterized in that in S8, the superimposed image is subjected to
Figure RE-FDA00038028708400000315
Performing watermark removing operation to obtain a watermark removed superposed image I suprimposed Comprises the following steps:
computing a superimposed image
Figure RE-FDA00038028708400000316
Is based on the pseudo-Zernike moment->
Figure RE-FDA00038028708400000317
For the pseudo Zernike moment
Figure RE-FDA00038028708400000318
Performing self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
Figure RE-FDA00038028708400000319
By extracting the normalized pseudo-Zernike moments
Figure RE-FDA00038028708400000320
Quantization distortion d of quantified Obtaining the normalized pseudo-Zernike moment->
Figure RE-FDA0003802870840000041
For the normalized pseudo-Zernike moment
Figure RE-FDA0003802870840000042
Inverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-suprimposed The calculation formula is as follows:
Figure RE-FDA0003802870840000043
calculating the pseudo Zernike moment Z n,m-suprimposed With pseudo Zernike moments
Figure RE-FDA0003802870840000044
Performing pseudo-Zernike inverse transformation and rounding operation on the difference value, and combining the rounding operation result with a superimposed image->
Figure RE-FDA0003802870840000045
Performing superposition processing to obtain a watermark-removed superposed image d suprimposed The calculation formula is as follows:
Figure RE-FDA0003802870840000046
9. the robust reversible watermark extraction method based on the pseudo Zernike moment is characterized by comprising the following steps:
obtaining robust reversible watermark images
Figure RE-FDA0003802870840000047
And the superimposed image pick>
Figure RE-FDA0003802870840000048
Said robust reversible watermark image +>
Figure RE-FDA0003802870840000049
And the superimposed image pick>
Figure RE-FDA00038028708400000410
Generating by using the pseudo-Zernike moment-based robust reversible watermark embedding method according to any one of claims 1 to 7;
extracting the robust reversible watermark image
Figure RE-FDA00038028708400000411
The least significant bit of the first S pixels of (4), i.e. the intermediate image->
Figure RE-FDA00038028708400000412
Hash value of (H) 1 And using a reversible watermarking method to combine the robust reversible watermark image->
Figure RE-FDA00038028708400000413
Restored to an intermediate image>
Figure RE-FDA00038028708400000414
Extracting superimposed images
Figure RE-FDA00038028708400000415
And replacing the extracted result with the intermediate image
Figure RE-FDA00038028708400000416
After the least significant bit of the first S pixels, the intermediate image at that time is generated @>
Figure RE-FDA00038028708400000417
Hash value of (H) 2 ；
When the hash value H 1 Is equal to the hash value H 2 Time, judge the reversible watermark picture of robustness
Figure RE-FDA00038028708400000418
Non-attacked and intermediate image
Figure RE-FDA00038028708400000419
Is not attacked, and the following steps are carried out:
extracting non-attacked intermediate images
Figure RE-FDA00038028708400000420
The watermark information of (1);
for intermediate image not under attack
Figure RE-FDA00038028708400000421
Performing recovery operation to the intermediate image which is not attacked
Figure RE-FDA00038028708400000422
Recovering to an original image I;
when the hash value H 1 Is not equal to the hash value H 2 Time, judge the reversible watermark picture of robustness
Figure RE-FDA00038028708400000423
Attacked and intermediate image
Figure RE-FDA00038028708400000424
And (5) under attack, executing the following steps:
extracting an attacked intermediate image
Figure RE-FDA00038028708400000425
The watermark information of (1).
10. The pseudo-Zernike moment based robust reversible watermark extraction method of claim 9,
when the hash value H 1 Is equal to the hash value H 2 Extracting the intermediate image not under attack
Figure RE-FDA0003802870840000051
The step of watermarking information of (1) comprises:
extracting non-attacked intermediate images
Figure RE-FDA0003802870840000052
Least significant bit, quantization distortion d of the first S pixels of quantified And rounding distortion d rounding And using a reversible watermarking method to ^ the intermediate image not attacked>
Figure RE-FDA0003802870840000053
Restored as image with robust watermark->
Figure RE-FDA0003802870840000054
Computing images with robust watermarks
Figure RE-FDA0003802870840000055
Is based on the pseudo-Zernike moment->
Figure RE-FDA0003802870840000056
And combining said pseudo-Zernike moment in a manner known per se>
Figure RE-FDA0003802870840000057
Performing adaptive normalization operation to obtain a normalized pseudo-Zernike moment->
Figure RE-FDA0003802870840000058
According to normalized pseudo-Zernike moments
Figure RE-FDA0003802870840000059
Extraction of robust watermark information w using quantization watermarking method 1 The expression is as follows:
Figure RE-FDA00038028708400000510
/>
Figure RE-FDA00038028708400000511
wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the weight of the pseudo-Zernike moment embedded in the ith watermark bit, i is the ith watermark bit, j is the bit value corresponding to the ith watermark bit, and beta i (j) Expressed as constraint beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being a quantization step;
the pair of unappressed intermediate images
Figure RE-FDA00038028708400000512
Performing recovery operation to the intermediate image which is not attacked
Figure RE-FDA00038028708400000513
The step of restoring to the original image I comprises:
according to the quantization distortion d quantified The normalized pseudo Zernike moments
Figure RE-FDA00038028708400000514
Conversion into pseudo-Zernike moments>
Figure RE-FDA00038028708400000515
The expression is as follows:
Figure RE-FDA00038028708400000516
for the pseudo Zernike moment
Figure RE-FDA00038028708400000517
Inverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-temporary ；
For the pseudo Zernike moment Z n,m-temporary Carrying out pseudo Zernike inverse transformation and rounding operation to obtain a watermark removed superposed image I suprimposed The expression is as follows:
Figure RE-FDA0003802870840000061
wherein L represents a length of the robust watermark information;
according to rounding distortion d rounding Superimposing the watermark removed image I suprimposed Converting into an original image I, wherein the expression is as follows:
I＝I suprimposed +d rounding 。
11. the pseudo-Zernike moment based robust reversible watermark extraction method according to claim 9,
when the hash value H 1 Is not equal to the hash value H 2 Extracting the attacked intermediate image
Figure RE-FDA0003802870840000062
The step of watermarking information of (1) comprises:
computing an attacked intermediate image
Figure RE-FDA0003802870840000063
In a pseudo-Zernike moment->
Figure RE-FDA0003802870840000064
For the pseudo Zernike moment
Figure RE-FDA0003802870840000065
Performing adaptive normalization to obtain a normalized pseudo-Zernike moment>
Figure RE-FDA0003802870840000066
For normalized pseudo Zernike moment
Figure RE-FDA0003802870840000067
Performing quantization watermark extraction operation to obtain an attacked intermediate image->
Figure RE-FDA0003802870840000068
Watermark information w of attack The expression is as follows: />
Figure RE-FDA0003802870840000069
Figure RE-FDA00038028708400000610
Wherein n is i Order of pseudo-Zernike moment for embedding ith watermark bit, m i Is the repeated number of the pseudo-Zernike matrix embedded in the ith watermark bit, i is the ith watermark bit, j is the bit value corresponding to the ith watermark bit, beta i (j) Representing a constraint of beta i (1)＝β i (0) A jitter value of + Δ/2, Δ being the quantization step.
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