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 PDFInfo
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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
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
S4: for normalized pseudo Zernike momentQuantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->And quantization distortion d quantified . Wherein, w 1 Representing robust watermark information.
S5: normalized pseudo-Zernike moments for the robust watermarkCarrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->/>
S6: for the pseudo Zernike moment with robust watermarkPerforming inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>
S7: computing images with robust watermarksIn a pseudo-Zernike moment->A pseudo Zernike moment is then calculated>And a pseudo-Zernike moment->The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->Error image I error And image with robust watermark>Performing superposition processing to obtain a superposed image>
S8: for the superimposed imagePerforming 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 imagesThe least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>Wherein, w 2 Is reversible watermark information.
S11: generating intermediate imagesHash value of (H) 1 And the hash value H is added 1 Replacing intermediate imagesThe least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
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 imagesAnd superimposing images>The robust reversible watermark imageAnd superimposing images>Generated using the pseudo-Zernike moment based robust reversible watermark embedding method of any one of claims 1-7.
Extracting the robust reversible watermark imageOf the first S pixels, i.e. the intermediate imageHash value of H 1 And using a reversible watermarking method to &'s a robust reversible watermark image>Reverting to an intermediate image
Extracting superimposed imagesAnd replacing the intermediate image with the extraction result>After the least significant bit of the first S pixels, the intermediate image at that time is generated @>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 robustnessNon-attacked and intermediate imageIs not attacked, and the following steps are carried out:
For intermediate image not under attackPerforming recovery operation to the intermediate image which is not attackedAnd 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 robustnessAttacked and intermediate image +>And (5) under attack, executing the following steps:
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 watermarkAnd a pseudo-Zernike moment ≥ for reconstructing the robustly watermarked image>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
S4: for normalized pseudo Zernike momentQuantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->And quantization distortion d quantified . Wherein, w 1 Representing robust watermark information.
S5: normalized pseudo-Zernike moments for the robust watermarkCarrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
S6: for the pseudo Zernike moment with robust watermarkCarrying out inverse pseudo Zernike transformation and rounding operation to obtain an image with a robust watermark>
S7: calculating outImage with robust watermarkIn a pseudo-Zernike moment->A pseudo Zernike moment is then calculated>And a pseudo-Zernike moment->Performing pseudo-Zernike inverse transformation and rounding operation on the difference value to obtain an error image->Error image I error And image with robust watermark->Performing superposition processing to obtain a superposed image->
S8: for the superimposed imagePerforming 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 imagesThe least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>Wherein, w 2 Is reversible watermark information.
S11: generating intermediate imagesHash value of (H) 1 And the hash value H is added 1 Replacing intermediate imagesThe least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
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 watermarkAnd a pseudo-Zernike moment ≥ for reconstructing the robustly watermarked image>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:
V nm (x,y)=R nm (r)e imθ
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 momentThe specific expression is as follows:
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,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 momentQuantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->And quantization distortion d quantified (ii) a Wherein, w 1 Representing robust watermark information d quantified The specific expression is as follows:
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 RepresentTo a fraction thereof nearest integer, e.g. if +>ThenAt 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 momentWhile 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 watermarkCarrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->The specific expression is as follows:
s6: for the pseudo Zernike moment with robust watermarkCarrying out inverse pseudo Zernike transformation and rounding operation to obtain an image with a robust watermark>The specific expression is as follows:
where L represents the length of the robust watermark information.
S7: computing images with robust watermarksIs based on the pseudo-Zernike moment->A pseudo Zernike moment is then calculated>And a pseudo-Zernike moment->The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->Then the error image I error And image with robust watermark->Performing superposition processing to obtain a superposed image->The specific expression is as follows:
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 imageThe information loss degree can be reduced. There is therefore a need for robust watermarked images +>The calculated pseudo-Zernike moment->And a pseudo-Zernike moment @usedto reconstruct the image>The difference between them is inverse pseudo-Zernike transformed.
S8: for the superimposed imagePerforming watermark removing operation to obtain a watermark removed superposed image I suprimposed The method comprises the following specific steps:
For the pseudo Zernike momentPerforming adaptive normalization operation to obtain a normalized pseudo-Zernike moment->
By extracting the normalized pseudo-Zernike momentsQuantization distortion d of quantified Obtaining a normalized pseudo-Zernike moment->
For the normalized pseudo-Zernike momentInverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-suprimposed The calculation formula is as follows:
calculating the pseudo Zernike moment Z n,m-suprimposed With the pseudo-Zernike momentPerforms pseudo-Zernike inverse transformation and rounding operation on the difference value, and combines the rounding operation result and the superimposed image->Performing superposition processing to obtain a watermark-removed superposed image I suprimposed The calculation formula is as follows:
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 imagesThe least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>Obtaining an intermediate image ^ comprising the robust watermark and the reversible watermark>Wherein, w 2 Is reversible watermark information.
S11: generating intermediate imagesHash value of H 1 And the hash value H is added 1 Replacing intermediate imagesThe least significant bit of the first N pixels, resulting in a robust reversible watermark image ≥>
In this embodiment, an SHA-256 algorithm is used to generate an intermediate imageHash 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 imagesAnd the superimposed image pick>The robust reversible watermark imageAnd the superimposed image pick>Generated using the pseudo-Zernike moment based robust reversible watermark embedding method as described in example 1 or 2.
Extracting the robust reversible watermark imageOf the first S pixels, i.e. the intermediate imageOfValue of Hi H 1 And using a reversible watermarking method to combine the robust reversible watermark image->Restore to intermediate image
Extracting superimposed imagesAnd replacing the intermediate image with the extraction result>After the least significant bit of the first S pixels, the intermediate image at that time is generated @>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 imageNon-attacked and intermediate imageIs not attacked, and the following steps are carried out:
extracting non-attacked intermediate imagesThe watermark information of (2), the specific steps include:
extracting non-attacked intermediate imagesLeast 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->Restoration to an image with a robust watermark>
Computing images with robust watermarksIs based on the pseudo-Zernike moment->And combining said pseudo-Zernike moment in a manner known per se>Performing adaptive normalization to obtain a normalized pseudo-Zernike moment>
According to normalized pseudo-Zernike momentsExtraction of robust watermark information w using quantization watermarking method 1 The expression is as follows:
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 attackPerforming a restore operation to combine the intermediate image>Restoring the original image I, specifically comprising:
according to the quantization distortion d quantified The normalized pseudo Zernike momentsConversion into a pseudo-Zernike moment->The expression is as follows:
for the pseudo Zernike momentInverse 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:
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 imageAttacked and intermediate imageAnd (5) under attack, executing the following steps:
extracting an attacked intermediate imageThe 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 imageThe step of watermarking information of (1) comprises:
computing an attacked intermediate imageIs based on the pseudo-Zernike moment->For the pseudo-Zernike moment->Performing self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
For normalized pseudo Zernike momentPerforming quantization watermark extraction operation to obtain an attacked intermediate image->Watermark information w of attack The expression is as follows:
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 verifiedThe value of the least significant bit of the first N pixels in the middle, i.e. the intermediate image->Hash value of H 1 Is extracted, the intermediate image obtained at this time is->The least significant bits of the first N pixels of (a) are all "0" (because the content is fetched).
Then the superimposed image is processedReplaces the intermediate image->Is valid (because the superimposed image |)>Is less significant and the intermediate image->Is identical) when the intermediate image @>Is recovered to generate its hash value H 2 ;H 1 Representing intermediate images when embedding watermarksHash value of H 2 Is representative ofIntermediate image/device when taking watermark>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)
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)
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
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)
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
S4: to normalized pseudo Zernike momentQuantitative watermark embedding is carried out to obtain normalized pseudo-Zernike moments which are subjected to robust watermark combination>And quantization distortion d quantified (ii) a Wherein, w 1 Representing robust watermark information;
s5: for the normalized pseudo-Zernike moment with robust watermarkCarrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->
S6: for the pseudo Zernike moment with robust watermarkPerforming inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>
S7: computing images with robust watermarksIs based on the pseudo-Zernike moment->The pseudo-Zernike moment is then calculated>And a pseudo-Zernike moment->The difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->Will error the pictureI error And image with robust watermark>Performing superposition processing to obtain a superposed image>
S8: for the superimposed imagePerforming 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 imagesThe least significant bit of the first N pixels of is embedded in the image ≥ with a robust watermark>In (d), an intermediate image is obtained which contains a robust watermark and a reversible watermark>Wherein w 2 Is reversible watermark information;
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:
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 momentThe specific expression is as follows:
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,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 normalizedQuantitative watermark embedding is carried out to obtain a normalized pseudo-Zernike moment->And quantization distortion d quantified The specific expression is as follows:
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 normalizedCarrying out inverse operation of self-adaptive normalization to obtain a pseudo Zernike moment->The specific expression is as follows:
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 toPerforming inverse transformation and rounding operation of pseudo Zernike to obtain an image/based on robust watermark>The specific expression is as follows:
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 computedAnd image with robust watermark->Pseudo Zernike moments ofThe difference value is subjected to pseudo Zernike inverse transformation and rounding operation to obtain an error image->The specific expression is as follows:
the error image I error And images with robust watermarksPerforming superposition processing to obtain a superposed imageThe specific expression is as follows:
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 toPerforming watermark removing operation to obtain a watermark removed superposed image I suprimposed Comprises the following steps:
For the pseudo Zernike momentPerforming self-adaptive normalization operation to obtain normalized pseudo-Zernike moment
By extracting the normalized pseudo-Zernike momentsQuantization distortion d of quantified Obtaining the normalized pseudo-Zernike moment->
For the normalized pseudo-Zernike momentInverse operation of self-adaptive normalization is carried out to obtain a pseudo Zernike moment Z n,m-suprimposed The calculation formula is as follows:
calculating the pseudo Zernike moment Z n,m-suprimposed With pseudo Zernike momentsPerforming pseudo-Zernike inverse transformation and rounding operation on the difference value, and combining the rounding operation result with a superimposed image->Performing superposition processing to obtain a watermark-removed superposed image d suprimposed The calculation formula is as follows:
9. the robust reversible watermark extraction method based on the pseudo Zernike moment is characterized by comprising the following steps:
obtaining robust reversible watermark imagesAnd the superimposed image pick>Said robust reversible watermark image +>And the superimposed image pick>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 imageThe least significant bit of the first S pixels of (4), i.e. the intermediate image->Hash value of (H) 1 And using a reversible watermarking method to combine the robust reversible watermark image->Restored to an intermediate image>
Extracting superimposed imagesAnd replacing the extracted result with the intermediate imageAfter the least significant bit of the first S pixels, the intermediate image at that time is generated @>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 robustnessNon-attacked and intermediate imageIs not attacked, and the following steps are carried out:
for intermediate image not under attackPerforming recovery operation to the intermediate image which is not attackedRecovering 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 robustnessAttacked and intermediate imageAnd (5) under attack, executing the following steps:
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 attackThe step of watermarking information of (1) comprises:
extracting non-attacked intermediate imagesLeast 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>Restored as image with robust watermark->
Computing images with robust watermarksIs based on the pseudo-Zernike moment->And combining said pseudo-Zernike moment in a manner known per se>Performing adaptive normalization operation to obtain a normalized pseudo-Zernike moment->
According to normalized pseudo-Zernike momentsExtraction of robust watermark information w using quantization watermarking method 1 The expression is as follows:
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 imagesPerforming recovery operation to the intermediate image which is not attackedThe step of restoring to the original image I comprises:
according to the quantization distortion d quantified The normalized pseudo Zernike momentsConversion into pseudo-Zernike moments>The expression is as follows:
for the pseudo Zernike momentInverse 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:
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 imageThe step of watermarking information of (1) comprises:
computing an attacked intermediate imageIn a pseudo-Zernike moment->For the pseudo Zernike momentPerforming adaptive normalization to obtain a normalized pseudo-Zernike moment>
For normalized pseudo Zernike momentPerforming quantization watermark extraction operation to obtain an attacked intermediate image->Watermark information w of attack The expression is as follows: />
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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