CN103646376A - Digital watermark image generation method - Google Patents
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Abstract
The invention provides a digital watermark image generation method which includes the steps: acquiring a two-dimensional watermark image and a carrier image and converting the two-dimensional watermark image into a one-dimensional watermark; dividing the carrier image into a plurality of image sub-blocks and calculating the unevenness value of each image sub-block; selecting L image sub-blocks from the image sub-blocks according to the sequence of the unevenness values from large to small, and respectively compressively sensing the L image sub-blocks to generate a sensed measured value matrix; embedding the a one-dimensional watermark into the measured value matrix to generate a modified measured value of the measured value matrix; generating a watermark image according to the modified measured value. By the digital watermark image generation method, the digital watermark can achieve better robustness, concealment and security, and the attack resistance and the extraction prevention capacity of the watermark image are improved.
Description
Technical field
The invention relates to digital watermark technology, particularly about a kind of digital watermarking image generation method.
Background technology
Along with scientific and technical develop rapidly, internet is constantly universal, and digital watermark technology has obtained increasing attention as the study hotspot of information security, at aspects such as copyright protection and content authentications, has broad application prospects.Existing digital watermark technology is mainly studied in spatial domain and transform domain and is realized, and spatial domain algorithm is as least significant bit (LSB) algorithm (LSB), texture block mapping algorithm etc., and transform-domain algorithm is as dct algorithm (DCT), Algorithms of Discrete Wavelet Transform (DWT) etc.Spatial domain algorithm computing is simple, speed is fast, but robustness is poor; Transform-domain algorithm robustness is stronger, but calculation of complex.
Summary of the invention
The invention process provides a kind of digital watermarking image generation method, to guarantee that digital watermarking has better robustness, disguise and security, improves anti-attack ability and anti-extractability containing watermarking images.
To achieve these goals, the embodiment of the present invention provides a kind of digital watermarking image generation method, and this digital watermarking image generation method comprises: obtain two-dimentional watermarking images and carrier image, and convert described two-dimentional watermarking images to one dimension watermark; Described carrier image is divided into a plurality of image subblocks, calculates the unevenness value of image subblock described in each; According to described unevenness value order from big to small, from described image subblock, choose L image subblock, and a described L image subblock is carried out respectively to compressed sensing, generate the measured value matrix after one group of perception; Described one dimension watermark is embedded to described measured value matrix, generate the modification measured value of described measured value matrix; According to described modification measured value, generate containing watermarking images.
In one embodiment, described digital watermarking image generation method also comprises:
According to following scramble transformation for mula, described two-dimentional watermarking images is carried out to scramble conversion, generates original two-dimentional watermarking images:
Wherein, (X, Y) is the coordinate points of original watermark image pixel, and (X', Y') is the coordinate points of watermarking images pixel after scramble conversion, and B is the size of watermark.
Further, described original image is divided into a plurality of image subblocks, calculates the unevenness value of image subblock described in each, comprising:
Described carrier image is carried out to b * b piecemeal, utilizes following formula to calculate the unevenness value of image subblock described in each:
Wherein, B
kthe sub-block of b * b size, m
kfor sub-block B
kaverage, τ is weighting modifying factor, f (i, j) represents the image subblock of the capable j row of i in described carrier image.
Further, a described L image subblock is carried out respectively to compressed sensing, generates the measured value matrix after one group of perception, comprising:
Utilize described in sparse transfer pair image subblock described in each in L image subblock to carry out rarefaction;
It is σ that sampling rate is set, with the gaussian random matrix Φ of (b * b * σ) * b * b
las perception matrix, sparse conversion coefficient is carried out to projection, generate the individual measured value y of L * (b * b * σ)
i, described measured value y
iform described measured value matrix,
Wherein, i=1,2...b * b * σ.
Further, describedly utilize described in sparse transfer pair image subblock described in each in L image subblock to carry out rarefaction, comprising:
According to formula f=ψ x, image subblock described in each is carried out to LS-SVM sparseness,
Wherein, f is sampled signal, the base that ψ is LS-SVM sparseness, and x is sparse conversion coefficient.
Further, described described one dimension watermark is embedded to described measured value matrix, generates the modification measured value of described measured value matrix, comprising:
According to following formula, described one dimension watermark is embedded to described measured value matrix, generate the modification measured value after embed watermark
Wherein, λ
i=round (y
i/ δ), round is the bracket function that rounds off, and mod is modular arithmetic function, δ=ad (B
k) be quantization step, a is constant.
Further, mod (λ
i+ w
n, 2) represent to each measured value and watermark value and do Modulo-two operation, if λ
i+ w
nthe value of doing Modulo-two operation is 1, uses
replace described modification measured value
work as λ
i+ w
nthe value of doing Modulo-two operation is 0, uses
replace revising measured value
Further, the modification measured value described in described basis generates containing watermarking images, comprising:
According to described modification measured value, carry out signal reconstruction, generate minimum 1 norm of sparse conversion coefficient x;
Described minimum 1 norm is carried out to contrary sparse conversion to be generated containing watermarking images.
Further, the modification measured value described in described basis carries out signal reconstruction, generates minimum 1 norm of sparse conversion coefficient x, comprising:
Bring described modification measured value into following formula and carry out signal reconstruction, generate minimum 1 norm of sparse conversion coefficient x
Wherein, Φ
l=Φ
ψ, Φ is perception waveform, y
i=Φ f.
The number of times that described one dimension watermark is embedded to described measured value matrix is: L * (b * b * σ)/(n * n), n * n represents the size of watermarking images.
The beneficial effect of the embodiment of the present invention is, digital watermarking image generation method of the present invention has guaranteed that digital watermarking has better robustness, disguise and security, reduce the complexity of embed watermark algorithm, and improved anti-attack ability and anti-extractability containing watermarking images; In addition, should containing watermarking images, when extracting watermark, not need the participation of original image, greatly reduced carrying cost.
Accompanying drawing explanation
In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.
Fig. 1 is that the digital watermarking image of the embodiment of the present invention generates method flow diagram;
Fig. 2 is that the embodiment of the present invention is carried out respectively compressed sensing to image subblock, generates the method flow diagram of the measured value matrix after one group of perception;
Fig. 3 is that the embodiment of the present invention generates the method flow diagram containing watermarking images according to revising measured value.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, those of ordinary skills, not making the every other embodiment obtaining under creative work prerequisite, belong to the scope of protection of the invention.
One of main core technology of the present invention is in carrier image, to have used compressed sensing technology, for embodiments of the invention are better described, before describing the digital watermarking image generation method of the embodiment of the present invention in detail, the compressed sensing technology that paper the present invention uses.
Compressed sensing mainly comprises rarefaction representation, the measurement structure of matrix and three significant process of the reconstruction of signal of signal], its core concept recovers original high dimensional signal by a small amount of information exactly.
In the embodiment of the present invention, establish and treat that acquired original signal (being the signal of carrier image) is f, f is carried out on one group of perception waveform Φ to perception, be about to f and project to Φ above, can obtain one group of measured value y:
y=Φf (1)
The compressed sensing that the present invention adopts is exactly to recover by the measured value y of the data volume much smaller than acquired original signal f the full detail of acquired original signal f.But acquired original signal f itself is not sparse conventionally, therefore need first by sparse conversion, to carry out LS-SVM sparseness:
f=ψx (2)
From formula (2), the sparse conversion coefficient x on the base ψ of Discrete Change is sparse, and formula (2) is updated in formula (1), obtains formula (3):
y=Φψx (3)
Make Φ
l=Φ
ψ, formula (3) can be write as:
y=Φ
Lx (4)
Wherein, Φ
lfor compressed sensing matrix.
By solution formula (4) is approximate, solve x like this, just can by formula (2), solve acquired original signal f again.But be one by the process that y solves x, owe to determine problem, need to separate a complicated optimization problem, as shown in Equation (5):
The process that solves x is the restructuring procedure of signal namely, is in fact minimum 1 norm solving with the x of a constraint condition, in formula (5), and y=Φ
lx is constraint condition.
Illustrate the restructuring procedure of signal below:
Conventional restructing algorithm comprises the methods such as greedy algorithm and convex optimized algorithm at present.The present invention adopts calculated amount orthogonal matching pursuit algorithm (OMP) relatively little, that rebuild better effects if, easily realization in greedy algorithm to realize signal reconstruction, and its input, output and calculation procedure are as follows:
Input: compressed sensing matrix Φ
l, measure vectorial y, degree of rarefication k;
Initialization: residual error r
0=y, indexed set J
0=Φ, iterations t=1.
(1) find out residual error r
twith compressed sensing matrix Φ
lthe inner product g of each row
t=Φ
l tr
t-1in greatest member, ρ
i=argmax|g
t| [i];
(4) upgrade residual error r
t=y-Φ
lx
t, t=t+1;
(5) judge whether iterations meets t>k, satisfied stop iteration,
r=r
t, output
and r; Do not meet, return to execution step (1).
Describe the digital watermarking image generation method of the embodiment of the present invention below in detail:
As shown in Figure 1, the embodiment of the present invention provides a kind of digital watermarking image generation method, and this digital watermarking image generation method comprises:
Step 101: obtain two-dimentional watermarking images and carrier image, and convert described two-dimentional watermarking images to one dimension watermark;
Step 102: described carrier image is divided into a plurality of image subblocks, calculates the unevenness value of image subblock described in each;
Step 103: according to described unevenness value order from big to small, choose L image subblock from described image subblock, and a described L image subblock is carried out respectively to compressed sensing, generate the measured value matrix after one group of perception;
Step 104: described one dimension watermark is embedded to described measured value matrix, generate the modification measured value of described measured value matrix;
Step 105: generate containing watermarking images according to described modification measured value.
Known by the flow process shown in Fig. 1, the present invention is divided into a plurality of image subblocks by carrier image, and choose more much higher sub-block of unevenness value, a plurality of sub-blocks carry out respectively obtaining containing watermarking images after compressed sensing and watermark embedding operation, guaranteed that digital watermarking has better robustness, disguise and security, and improved anti-attack ability and anti-extractability containing watermarking images; In addition, should containing watermarking images, when extracting watermark, not need the participation of original image, greatly reduced carrying cost.
When the present invention specifically implements, in one embodiment, before converting two-dimentional watermarking images to one dimension watermark by step 101, in order better to strengthen security and the robustness of watermarking images, can also to two-dimentional watermarking images, carry out scramble conversion according to following scramble transformation for mula, generate original two-dimentional watermarking images:
In formula (6), (X, Y) is the coordinate points of original watermark image pixel, and (X', Y') is the coordinate points of watermarking images pixel after scramble conversion, and B is the size of watermarking images.
After obtaining original two-dimentional watermarking images by formula (6), then by step 101, convert original two-dimentional watermarking images to one dimension watermark w
n(i) (w
n(i)=0,1}, 1≤i≤n * n).
During the concrete enforcement of step 102, original image can be carried out to b * b piecemeal, be divided into a plurality of image subblocks, then utilize following formula (7) to calculate the unevenness value of each image subblock:
In formula (7), m * m represents the size of described carrier image M, B
kthe image subblock of b * b size, m
kfor image subblock B
kaverage, τ is weighting modifying factor, f (i, j) represents the image subblock of the capable j row of i in carrier image M.
Unevenness d (the B of image subblock
k) larger, this image subblock homogeneity is poorer, and texture information is relatively abundant, and vision capacity is large.Based on this principle, in step 103, all image subblocks are queued up according to order from big to small, then select successively from big to small limited L image subblock capacious, to embed more jumbo watermark, guarantee the robustness of watermark.Wherein, L=1,2... (m * m)/(b * b).
As shown in Figure 2, during the concrete enforcement of step 103, L image subblock carried out respectively to compressed sensing, generates the measured value matrix after one group of perception, comprising:
Step 201: utilize sparse transfer pair described in each image subblock carry out rarefaction;
Step 202: it is σ that sampling rate is set, with the gaussian random matrix Φ of (b * b * σ) * b * b
las perception matrix, sparse conversion coefficient is carried out to projection, generate the individual measured value y of L * (b * b * σ)
i.
Measured value y
iformed this measured value matrix, wherein, i=1,2...b * b * σ.
During the concrete enforcement of step 201, can first according to above-mentioned formula (2), to each image subblock, carry out LS-SVM sparseness, then sampling rate is set is σ, with the gaussian random matrix Φ of (b * b * σ) * b * b
las perception matrix, sparse conversion coefficient is carried out to projection, generate the individual measured value y of L * (b * b * σ)
i, L sub-block obtains L * (b * b * σ) individual measured value, perception matrix Φ altogether
las key, preserve, during in order to watermark extracting, use.
It should be noted that, sparse conversion comprises discrete transform and continuous transformation etc., and discrete transform can be wavelet transform (DWT), discrete cosine transform (DCT) and discrete Fourier transformation (DFT) etc., the present invention only describes with wavelet transform, is not intended to limit.
Be the code of the algorithm of step 201 correspondence below:
During the concrete enforcement of step 104, can the one dimension watermark obtaining of conversion in step 101 be embedded to the measured value matrix after perception according to following quantitative formula (8), according to quantitative formula (8) step-by-step, revise the measured value y in measured value matrix
i, generate the modification measured value after embed watermark
Wherein, λ
i=round (y
i/ δ), round is the bracket function that rounds off, and mod is modular arithmetic function, δ=ad (B
k) be quantization step, a is constant.
Quantization step δ=ad (B in formula (8)
k) the piece unevenness value d (B that obtains in formula (7)
k) determine d (B
k) value larger, sub-block capacity is larger, thus quantization step δ=ad (B
k) large, just can embed more watermark information, so quantization step δ=ad (B herein
k) be adaptive, there is certain dirigibility, the watermark information that can embed according to actual needs changes.
In one embodiment, mod (λ
i+ w
n, 2) can represent to each measured value and watermark value and do Modulo-two operation, if λ
i+ w
nthe value of doing Modulo-two operation is 1, uses
replace revising measured value
if λ
i+ w
nthe value of doing Modulo-two operation is 0, uses
replace revising measured value
Utilize this formula (8), can arrive and obtain security, robustness and disguised all high watermarks, and then it is all high containing watermarking images to obtain security, robustness and disguise.
Provide the code of the algorithm of step 104 correspondence below:
In step 104, to each image subblock, all to carry out watermark embedding, therefore one dimension watermark embeds the number of times of measured value matrix, be: L * (b * b * σ)/(n * n), n * n represents the size of watermarking images.
As shown in Figure 3, during the concrete enforcement of step 105, comprise the steps:
Step 301: carry out signal reconstruction according to described modification measured value, generate minimum 1 norm of sparse conversion coefficient x, particularly, need to bring described modification measured value into following formula and carry out signal reconstruction, by asking for minimum 1 norm of the sparse x of sparse conversion
generate the approximate signal of sparse conversion coefficient x:
In formula (9), qualifications is
be above-mentioned formula (4), just changed the measured value y in formula (4) into modification measured value y herein
i, x has changed into
concrete signal reconstruction, refers to above-mentioned about compressed sensing technology introduction.
Step 302: described minimum 1 norm is carried out to contrary sparse conversion and generate containing watermarking images.
In the step 201 of Fig. 2, utilize each image subblock of sparse transfer pair to carry out LS-SVM sparseness, in order to obtain containing watermarking images, the needs that can manage it carry out contrary sparse conversion, by the minimum of sparse conversion coefficient x 1 norm
generate containing watermarking images
the contrary sparse inverse transformation that is transformed to sparse conversion, contrary sparse conversion comprises contrary discrete transform and contrary continuous transformation etc., the contrary sparse conversion that wavelet transform is corresponding is inverse discrete wavelet transform (IDWT), contrary sparse conversion corresponding to discrete cosine transform is inverse discrete cosine transform (IDCT), the contrary sparse transfer pair of discrete Fourier transformation should be inverse discrete Fourier transform (IDFT) etc., the present invention only describes with inverse discrete wavelet transform, is not intended to limit.
Due to the leaching process of watermark and the telescopiny of watermark reciprocal, therefore be not described in detail, be briefly described as follows:
Image containing watermark is carried out to 16 * 16 piecemeals (16 * 16 just illustrate, and are not intended to limit), according to above-mentioned formula (7), calculate respectively unevenness, select a limited L image block, relend the key Φ preserving while helping watermark to embed
lrespectively each sub-block is carried out to compressed sensing, then carry out watermark extracting, its corresponding watermark extracting formula is:
Wherein:
floor is downward bracket function.
Be the code of watermark extracting some algorithm below:
By digital watermarking image generation method of the present invention, guaranteed that digital watermarking has better robustness, disguise and security, reduce the complexity of embed watermark algorithm, and improved anti-attack ability and anti-extractability containing watermarking images; In addition, should containing watermarking images, when extracting watermark, not need the participation of original image, greatly reduced carrying cost.
The disguise of lower surface analysis digital watermarking of the present invention and the complexity of embed watermark algorithm:
The disguise of 1 digital watermarking of the present invention:
Generally with Y-PSNR (English full name, PSNR) as evaluation criterion, the image visual effect of its reflection after embed watermark, PSNR value is larger, illustrates that to contain the quality of watermarking images higher, disguise is better, its formula is:
In formula (11), the size that M * N is original image, L is original image maximum gradation value, I is original image,
for containing watermarking images.
Table 1 is the disguise contrast of algorithm in the algorithm invented herein and prior art:
The contrast of table 1 PSNR value
This paper algorithm | Prior art algorithm | |
PSNR value | 34.68dB | 34.41dB |
As can be seen from Table 1, the PSNR value of algorithm gained of the present invention digital watermarking exceeds 0.27dB than the PSNR value of the resulting watermark of existing middle algorithm, illustrates that algorithm of the present invention compares with algorithm of the prior art, has better disguise.
The complexity of the algorithm of 2 embed watermarks of the present invention:
In prior art, generally entire image is done to wavelet transform, carry out rarefaction, then the low frequency coefficient of embed watermark not has also been carried out to compressed sensing operation, increased so unnecessary trouble.And first the present invention carries out piecemeal processing to image, only choose a limited L sub-block and carried out compressed sensing processing, greatly improved the efficiency of computing.Table 2 provides algorithm in algorithm of the present invention and prior art and same Lena image is being embedded to needed contrast operation time of same watermark:
Table 2 contrast operation time
This paper algorithm | Prior art algorithm | |
The embed watermark time used | 11.3s | 19.1s |
As can be seen from Table 2, algorithm embed watermark of the present invention operation time used is than few 7.8s of the time used of algorithm in prior art, illustrate algorithm of the present invention operation time complexity lower than algorithm of the prior art.
Those skilled in the art should understand, embodiments of the invention can be provided as method, system or computer program.Therefore, the present invention can adopt complete hardware implementation example, implement software example or in conjunction with the form of the embodiment of software and hardware aspect completely.And the present invention can adopt the form that wherein includes the upper computer program of implementing of computer-usable storage medium (including but not limited to magnetic disk memory, CD-ROM, optical memory etc.) of computer usable program code one or more.
The present invention is with reference to describing according to process flow diagram and/or the block scheme of the method for the embodiment of the present invention, equipment (system) and computer program.Should understand can be in computer program instructions realization flow figure and/or block scheme each flow process and/or the flow process in square frame and process flow diagram and/or block scheme and/or the combination of square frame.Can provide these computer program instructions to the processor of multi-purpose computer, special purpose computer, Embedded Processor or other programmable data processing device to produce a machine, the instruction of carrying out by the processor of computing machine or other programmable data processing device is produced for realizing the device in the function of flow process of process flow diagram or a plurality of flow process and/or square frame of block scheme or a plurality of square frame appointments.
These computer program instructions also can be stored in energy vectoring computer or the computer-readable memory of other programmable data processing device with ad hoc fashion work, the instruction that makes to be stored in this computer-readable memory produces the manufacture that comprises command device, and this command device is realized the function of appointment in flow process of process flow diagram or a plurality of flow process and/or square frame of block scheme or a plurality of square frame.
These computer program instructions also can be loaded in computing machine or other programmable data processing device, make to carry out sequence of operations step to produce computer implemented processing on computing machine or other programmable devices, thereby the instruction of carrying out is provided for realizing the step of the function of appointment in flow process of process flow diagram or a plurality of flow process and/or square frame of block scheme or a plurality of square frame on computing machine or other programmable devices.
In the present invention, applied specific embodiment principle of the present invention and embodiment are set forth, the explanation of above embodiment is just for helping to understand method of the present invention and core concept thereof; , for one of ordinary skill in the art, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention meanwhile.
Claims (10)
1. a digital watermarking image generation method, is characterized in that, described method comprises:
Obtain two-dimentional watermarking images and carrier image, and convert described two-dimentional watermarking images to one dimension watermark;
Described carrier image is divided into a plurality of image subblocks, calculates the unevenness value of image subblock described in each;
According to described unevenness value order from big to small, from described image subblock, choose L image subblock, and a described L image subblock is carried out respectively to compressed sensing, generate the measured value matrix after one group of perception;
Described one dimension watermark is embedded to described measured value matrix, generate the modification measured value of described measured value matrix;
According to described modification measured value, generate containing watermarking images.
2. method according to claim 1, is characterized in that, described convert two-dimentional watermarking images to one dimension watermark before, described method also comprises:
According to following scramble transformation for mula, described two-dimentional watermarking images is carried out to scramble conversion, generates original two-dimentional watermarking images:
Wherein, (X, Y) is the coordinate points of original watermark image pixel, and (X', Y') is the coordinate points of watermarking images pixel after scramble conversion, and B is the size of watermark.
3. method according to claim 1 and 2, is characterized in that, described original image is divided into a plurality of image subblocks, calculates the unevenness value of image subblock described in each, comprising:
Described carrier image is carried out to b * b piecemeal, utilizes following formula to calculate the unevenness value of image subblock described in each:
Wherein, m * m represents the size of described carrier image, B
kthe sub-block of b * b size, m
kfor sub-block B
kaverage, τ is weighting modifying factor, f (i, j) represents the image subblock of the capable j row of i in described carrier image.
4. method according to claim 3, is characterized in that, a described L image subblock is carried out respectively to compressed sensing, generates the measured value matrix after one group of perception, comprising:
Utilize described in sparse transfer pair image subblock described in each in L image subblock to carry out rarefaction;
It is σ that sampling rate is set, with the gaussian random matrix Φ of (b * b * σ) * b * b
las perception matrix, sparse conversion coefficient is carried out to projection, generate the individual measured value y of L * (b * b * σ)
i, described measured value y
iform described measured value matrix,
Wherein, i=1,2...b * b * σ.
5. method according to claim 4, is characterized in that, describedly utilizes described in sparse transfer pair image subblock described in each in L image subblock to carry out rarefaction, comprising:
According to formula f=ψ x, image subblock described in each is carried out to LS-SVM sparseness,
Wherein, f is sampled signal, the base that ψ is LS-SVM sparseness, and x is sparse conversion coefficient.
6. method according to claim 5, is characterized in that, described described one dimension watermark is embedded to described measured value matrix, generates the modification measured value of described measured value matrix, comprising:
According to following formula, described one dimension watermark is embedded to described measured value matrix, generate the modification measured value after embed watermark
Wherein, λ
i=round (y
i/ δ), round is the bracket function that rounds off, and mod is modular arithmetic function, δ=ad (B
k) be quantization step, a is constant.
7. method according to claim 6, is characterized in that, mod (λ
i+ w
n, 2) represent to each measured value and watermark value and do Modulo-two operation, if λ
i+ w
nthe value of doing Modulo-two operation is 1, uses
replace described modification measured value
work as λ
i+ w
nthe value of doing Modulo-two operation is 0, uses
replace revising measured value
8. method according to claim 7, is characterized in that, the modification measured value described in described basis generates containing watermarking images, comprising:
According to described modification measured value, carry out signal reconstruction, generate minimum 1 norm of sparse conversion coefficient x;
Described minimum 1 norm is carried out to contrary sparse conversion to be generated containing watermarking images.
9. method according to claim 8, is characterized in that, the modification measured value described in described basis carries out signal reconstruction, generates minimum 1 norm of sparse conversion coefficient x, comprising:
Bring described modification measured value into following formula and carry out signal reconstruction, generate minimum 1 norm of sparse conversion coefficient x
Wherein, Φ
l=Φ
ψ, Φ is perception waveform, y
i=Φ f.
10. method according to claim 6, is characterized in that, the number of times that described one dimension watermark is embedded to described measured value matrix is: L * (b * b * σ)/(n * n), n * n represents the size of watermarking images.
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