CN105427231B - A kind of SVD double-layer digital water mark methods avoiding false alarm - Google Patents
A kind of SVD double-layer digital water mark methods avoiding false alarm Download PDFInfo
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Abstract
The present invention relates to a kind of SVD double-layer digital water mark methods avoiding false alarm, including：Singular value decomposition is carried out to host image, its singular value matrix is added in watermarking images；Watermarking images to being superimposed singular value carry out singular value decomposition, and the singular value matrix of host image is replaced with its singular value matrix, constitutes the image containing first layer watermark；The eigenvalue matrix of watermarking images to being superimposed singular value carries out Hash encryption；Block DCT is carried out to the image of embedded first layer watermark, in the coefficient for the discrete cosine transform that the Hash codes of encryption gained are embedded in each sub-block, obtains the image containing second layer watermark.The present invention is suitable for the copyright protection of printed matter, this double-level watermark can keep good visual quality while increasing watermark capacity, and the false alarm problem for avoiding watermark from occurring in extraction.
Description
Technical field
The present invention relates to image procossing and information security fields.The present invention designs a kind of digital watermarking of anti-print and scan
Embedded and extracting method, this method have the characteristic for improving watermark embedding capacity, reducing identification false alarm rate, can be used for printed matter
Copyright protection.
Technical background
Have no temperately to replicate and propagate with universal and fast development, the digital content of network technology so that number production
The Copyright Protection of product is concerned, and in order to solve this problem, digital watermark technology comes into being.Digital watermark technology be by
Identification information is embedded in a kind of technology in digital content, it has substantially no effect on former digital content quality, is not easy to be ascertained and repair
Change, but identification can be extracted, for the copyright protection of digital information and anti-fake.By development for many years, digital watermark technology
Achieve certain achievement.In view of digital watermark technology realize copyright protection and it is anti-fake during, digital letter need only be changed
Breath, without increasing other costs (cost that such as special paper or specialty inks are brought), cause paper media copyright protection and
The extensive concern of anti-counterfeit field.Digital watermarking for paper media copyright protection and it is anti-fake when, often to undergo printing (print
Brush)-scan process, and print (printing)-scanning actually digital content and have passed through D/A and A/D and convert twice, while and companion
With attacks such as noise to a certain degree, fuzzy, geometric transformations, cause digital content by prodigious loss or distortion, so that
Watermark information is difficult to retain in digital content, to lose copyright protection and anti-fake effect.However, current bill, product packet
The forgery and imitation of the paper media such as dress, certificate, vital document bring prodigious loss to mechanisms such as enterprise, finance, urgently
Replace tradition anti-fake and a kind of new technology of copyright protection it is expected that this digital watermark technology without application cost can become.Cause
This, digital watermarking realizes that paper media is anti-fake and copyright protection, and there is huge applications values, are also faced with prodigious technology and choose
War.The robust performance for especially improving anti-printing (the printing)-scanning of digital watermark technology is the basic premise of energy practical application, is
One project for being worth research and breaking through.
In recent years, the digital watermarking algorithm of printing-scanning attack can be resisted by occurring some.Data of literatures is consulted,
Substantially there are two types of the digital watermarking algorithms of type to achieve certain effect in terms of resisting printing-scanning attack at present.It is a kind of
It is in discrete cosine transform (Discreet Cosine Transformation, DCT), discrete Fourier transform (Discreet
Fourier Transformation, DFT) etc. it is embedded on the basis of Spectrum Conversions.Seek in original image DCT/DFT coefficients
Basicly stable region (essentially mid-frequency region) embedded watermark letter after vision is insensitive and printing-scanning attack digital watermarking
Breath.For example, the patent of Wang Quan et al.《Anti printing and scanning coloured image blind watermark method based on DCT coefficient statistical property》, in
State's patent, Patent No. CN103559676A.Another kind of is wavelet transform (Discreet Wavelet
Transformation, DWT) combine singular value decomposition (Singular Value Decomposition, SVD), that is, utilize DWT
The strong low-frequency image of attack resistance stability is obtained, then SVD decomposition is carried out to low-frequency image, watermark information is embedded in the unusual of SVD
In value coefficient.For example, the patent of Ye Tianyu《Robust zero watermarking based on singular value decomposition, harr wavelet transformations and mean value computation
Algorithm》, Chinese patent, Patent No.：CN102129659A.It is found by the numerous studies that numerous scholars have carried out, printing-
The attack that scanning process is generated in actual application environment, not only D/A and the sampling in A/D conversions and quantization, prints-sweeps
The attacks such as the noise generated due to equipment limitation in environment, fuzzy are retouched, loss and the distortion of information can be aggravated.Therefore, in reality
In, the attack suffered by embedded watermark signal is not simple group of the different attacks of one or more of simple emulation experiment
It closes, but the result of Various Complex signal synthesis effect.This make the digital watermark method based on DCT visual quality of images,
It is difficult to seek to equalization point between the robust performance of anti-print and scan and embedded watermark information capacity.Moreover, print and scan mistake
On the robustness of embedded watermark information, there is also prodigious influences for the difference of equipment, arrange parameter in journey.In contrast,
DWT and SVD in the digital watermark method of DWT combinations SVD can obtain the more stable feature of image, more strong to obtain
Robustness, and the capacity of embedded watermark information is larger.Therefore, the digital watermark method of DWT combinations SVD is in anti-print and scan
Aspect obtain preferable effect.But in these methods, in order to increase embedded watermark information capacity and improve embedded images
Visual quality, it is practical that the watermark information SVD singular values decomposed substantially are hidden in original image DWT changing images
In singular value.When extracting watermark information, the watermarking images and the unusual value difference after original image DWT transformation that first obtain scanning
It is different, recycle the singular vector reconstructuring water-mark information of this unusual value difference and original watermark.However, actually singular vector is only structure
At the key message of any image (such as watermarking images), singular value size is to influence the power of final image.As a result, if there is
Piece image is not embedded in watermark information, and after print and scan is handled, the singular value of DWT transformation changes, and will obtain
Obtain watermark information.It is without embedded watermark, but has identified watermark, thereby produces false alarm problem.It is beaten actual
In print-scanning process, different degrees of variation, therefore such digital watermark method usually can all occur for the singular value of DWT transformation
The problem of false alarm inevitably occurs, this makes digital watermarking lose the value of the practical application of copyright protection.
Invention content
It is an object of the present invention to for there are problems that in existing anti-print and scan digital watermarking algorithm false alarm and
The problem of high power capacity is difficult to balance with high quality proposes a kind of SVD double-layer digital water mark methods avoiding false alarm.
The technical solution adopted by the present invention is a kind of SVD double-layer digital water mark methods avoiding false alarm, including watermark insertion
With two processes of watermark extracting, implement according to the following steps：
First, the insertion of watermark, specifically includes following steps：
Step A1 decomposes host image H and watermarking images W using SVD, is denoted as H=U respectivelyHSHVH TAnd W=
UWSWVW T；
Step A2, by watermarking images W insertion host image singular value matrixs SH, obtain new image arrayIt calculates such as
Under：
Wherein, α is embedment strength, and α ∈ [0.01,0.1]；
Step A3, by the singular value matrix S of host imageHReplace with imageSingular value matrix through SVD operation gainedObtain the image H of embedded first layer watermark informationW, calculate as follows：
Step A4 will be superimposed the watermarking images of singular valueFeature value vector matrix UWAnd VWOne-dimensional square is lined up by row
Battle array uWAnd vW, the one-dimensional matrix is encrypted using SHA-256 Hash Encryption Algorithm, obtains corresponding Hash codes RUWith
RV：
RU=Harshing(SHA-256)(uW),
RV=Harshing(SHA-256)(vW),
And RUAnd RVBinary coded form is converted to, then to binary RUAnd RVLogic xor operation is carried out, is obtained
One new binary signal R, and take first 64 of R to be used as second layer watermark information, it is denoted as Rw；
Step A5, the image to carrying first layer watermark information carries out piecemeal DCT operations, by second of watermark information RwIt is embedding
Enter into direct current (DC) the coefficient Ci of each sub-block, wherein i=1,2,3....., 64, wherein step includes：
(a) the image H of first layer watermark will be carriedWIt is divided into 8 × 8 sub-block, DCT operations is implemented to each sub-block, obtains each
The DC coefficients c of sub-blocki, and calculate its average value
(b) each sub-block DC coefficients c is calculatediWith its average valueBetween difference：
(c) according to second layer watermark information RwThe positions i bit values Rw(i) and diff (ci) the corresponding son of symbol modification
The DC coefficients c of blocki, concrete operations are：If RwAnd diff (c (i)=1iWhen) >=0, current sub-block DC coefficients ciIncrease | diff (ci)
|；If RwAnd diff (c (i)=1i) < 0 when, current sub-block DC coefficients ciReduce | diff (ci)|；If RwAnd diff (c (i)=0i)
When >=0, current sub-block DC coefficients ciReduce 2 times | diff (ci)|；If RwAnd diff (c (i)=0i) < 0 when, current sub-block DC
Coefficient ciIncrease by 2 times | diff (ci)|；
(d) DCT inverse transformations are carried out to each sub-block for changing coefficient, obtains the image of embedded two layers of watermark information
Then, the extraction of watermark, specifically includes following steps：
The image H ' of watermark to be extracted and original host image H are divided into 8 × 8 sub-block by step B1, and to each sub-block
Implement DCT operations, obtains the DC coefficients of each sub-block respectivelyWithAnd according to a pair of of DC of the two corresponding position sub-block
CoefficientWithBinary signal R ', i=1,2,3....., 64 are generated, wherein containing following steps：
(a) DC coefficients are calculated separatelyWithWith its respective average valueWithDifference：
(b) it is examined in diff (c from left to right, from top to bottomi W) and diff (ci H) symbol, obtain one group 64
Binary data R '：As diff (ci W) >=0 and diff (ci H) >=0 or diff (ci W) < 0 and diff (ci H) < 0 when, binary system
Bit value R ' (i)=1 of the positions i of data R '；As diff (ci W) < 0 and diff (ci H) > 0 or diff (ci W) > 0 and diff
(ci H) < 0 when, bit value R ' (i)=0 of the positions i of binary data R '；
Step B2, due to original watermark image W and the image for being superimposed host image singular valueCharacteristic having the same to
Amount, therefore by watermarking images W through the eigenvectors matrix U obtained by SVD operationsWAnd VWOne-dimensional matrix u is lined up by rowWAnd vW, it is used in combination
SHA-256 Hash Encryption Algorithm is encrypted the one-dimensional signal to obtain Hash codes RUAnd RV, then by Hash codes be converted to two into
Coding form processed, using logic exclusive or to binary RUAnd RVIt is operated, obtains binary signal R, take first 64 of R, i.e.,
Obtain embedded second layer watermark information Rw；
Step B3, the second layer watermark information R that the binary signal R ' that judgment step B1 is obtained and step B2 is obtainedw?
Next step extraction operation is carried out if the value of the two is identical with property, if the value of the two is different, terminates the operation for extracting watermark,
It indicates in the image of watermark to be extracted without carrying watermark information；
Step B4, by singular value matrix Ss of the original watermark image W through SVD operation gainedWReplace with the figure of watermark to be extracted
As singular value matrix Ss of the H ' through SVD operation gainedH′, obtain new image
According to the singular value matrix S of host imageH, imageAnd embedment strength α, extract first layer watermarking images
W ', it is specific as follows：
The invention has the advantages that improving false alarm rate high problem when being embedded in watermark based on SVD methods, it can resist and beat
Print scanning attack, avoids false alarm phenomenon from generating at the capacity for improving watermark insertion, can be used for the copyright protection of printed matter.
Description of the drawings
Fig. 1 a are the flow charts of watermark telescopiny of the present invention, and Fig. 1 b are the flow charts of watermark extraction process of the present invention；
Fig. 2 a are the host images used in the embodiment of the present invention, and Fig. 2 b are the watermark figures used in the embodiment of the present invention
Picture, Fig. 2 c are the images after embedded two layers of watermark in the embodiment of the present invention, and Fig. 2 d are passed through to Fig. 2 c in the embodiment of the present invention
Konica Minolta C6000 digital printers print and Microtek 1000XL Plus scanner scanning gained images, figure
2e is in the embodiment of the present invention to the watermarking images of Fig. 2 d extractions.
Specific implementation mode
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
The method for being embedded in watermark in the picture using the present invention is as shown in Figure 1a, is as follows：
1st step decomposes host image H and watermarking images W using SVD, is denoted as H=U respectivelyHSHVH TAnd W=
UWSWVW T；
2nd step, by watermarking images W insertion host image singular value matrixs SH, obtain new image arrayIt calculates as follows：
Wherein, α is embedment strength, and takes α=0.01；
3rd step, by the singular value matrix S of host imageHReplace with imageSingular value matrix through SVD operation gained
Obtain the image H of embedded first layer watermark informationW, calculate as follows：
4th step will be superimposed the watermarking images of singular valueFeature value vector matrix UWAnd VWOne-dimensional matrix is lined up by row
uWAnd vW, the one-dimensional matrix is encrypted using SHA-256 Hash Encryption Algorithm, obtains corresponding Hash codes RUAnd RV：
RU=Harshing(SHA-256)(uW),
RV=Harshing(SHA-256)(vW),
And RUAnd RVBinary coded form is converted to, then to binary RUAnd RVLogic xor operation is carried out, is obtained
One new binary signal R, and take first 64 of R to be used as second layer watermark information, it is denoted as Rw；
5th step, the image to carrying first layer watermark information carries out piecemeal DCT operations, by second of watermark information RwIt is embedding
Enter into the DC coefficients of each sub-block, wherein step includes：
(a) the image H of first layer watermark will be carriedWIt is divided into 8 × 8 sub-block, DCT operations is implemented to each sub-block, obtains each
The DC coefficients c of sub-blocki, and calculate its average value
(b) each sub-block DC coefficients c is calculatediWith its average valueBetween difference：
(c) according to second layer watermark information RwThe positions i bit values Rw(i) and diff (ci) the corresponding son of symbol modification
The DC coefficients c of blocki, concrete operations are：If RwAnd diff (c (i)=1iWhen) >=0, current sub-block DC coefficients ciIncrease | diff (ci)
|；If RwAnd diff (c (i)=1i) < 0 when, current sub-block DC coefficients ciReduce | diff (ci)|；If RwAnd diff (c (i)=0i)
When >=0, current sub-block DC coefficients ciReduce 2 times | diff (ci)|；If RwAnd diff (c (i)=0i) < 0 when, current sub-block DC
Coefficient ciIncrease by 2 times | diff (ci)|；
(d) DCT inverse transformations are carried out to each sub-block for changing coefficient, obtains the image of two layers of watermark information of embedded quantity
The method for extracting watermark in the image of watermark to be extracted using the present invention is as shown in Figure 1 b, is as follows：
The image H ' of watermark to be extracted and original host image H are divided into 8 × 8 sub-block by the 1st step, and to each sub-block
Implement DCT operations, obtains the DC coefficients of each sub-block respectivelyWithAnd according to a pair of of DC of the two corresponding position sub-block
CoefficientWithGenerate binary signal R ', wherein i=1,2,3....., 64, wherein containing following steps：
(a) DC coefficients are calculated separatelyWithWith its respective average valueWithDifference：
(b) it is examined in diff (c from left to right, from top to bottomi W) and diff (ci H) symbol, obtain one group 64
Binary data R '：As diff (ci W) >=0 and diff (ci H) >=0 or diff (ci W) < 0 and diff (ci H) < 0 when, binary system
Bit value R ' (i)=1 of the positions i of data R '；As diff (ci W) < 0 and diff (ci H) > 0 or diff (ci W) > 0 and diff
(ci H) < 0 when, bit value R ' (i)=0 of the positions i of binary data R '；
2nd step, due to original watermark image W and the image for being superimposed host image singular valueCharacteristic having the same to
Amount, therefore by watermarking images W through the eigenvectors matrix U obtained by SVD operationsWAnd VWOne-dimensional matrix u is lined up by rowWAnd vW, it is used in combination
SHA-256 Hash Encryption Algorithm is encrypted the one-dimensional signal to obtain Hash codes RUAnd RV, then by Hash codes be converted to two into
Coding form processed, using logic exclusive or to binary RUAnd RVIt is operated, obtains binary signal R, take first 64 of R, i.e.,
Obtain embedded second layer watermark information Rw；
3rd step, the second layer watermark information R that the binary signal R ' that judgment step B1 is obtained and step B2 is obtainedw?
Next step extraction operation is carried out if the value of the two is identical with property, if the value of the two is different, terminates the operation for extracting watermark,
It indicates in the image of watermark to be extracted without carrying watermark information；
This step can avoid false alarm to avoid but watermarking images are extracted using following step when no embedded watermark
The generation of phenomenon；
4th step, by singular value matrix Ss of the original watermark image W through SVD operation gainedWReplace with the figure of watermark to be extracted
As singular value matrix Ss of the H ' through SVD operation gainedH′, obtain new image
According to the singular value matrix S of host imageH, imageAnd embedment strength α, extract first layer watermarking images
W ', it is specific as follows：
Embodiment illustrates that the present invention is used for protecting literary property of presswork by taking image shown in Fig. 2 as an example.
Host image and watermarking images shown in Fig. 2 are coloured image, when applying the invention to coloured image：It is embedding
Before entering watermark, it is necessary first to coloured image be divided into the image in three channels of red, green, blue, then schemed to the host of triple channel
As the watermarking images for the corresponding triple channel of method insertion for being utilized respectively the embedded watermark of the present invention, it is finally synthesizing the threeway of embedded watermark
Road image；Before extracting watermark, the image of watermark to be extracted is divided into the image in three channels of red, green, blue first, then to three
Channel image is utilized respectively the watermarking images of the corresponding triple channel of method extraction of present invention extraction watermark, finally by the threeway of extraction
Road watermarking images synthesize coloured image.
In practical operation：First, watermarking images shown in tiling Fig. 2 b (image size is 225 × 225) are replicated, its figure is made
As size is identical as the size of host image shown in Fig. 2 a (image size is 512 × 512)；Then, using the present invention as schemed
The method of embedded watermark, the watermarking images of subchannel are respectively embedded in the host image of corresponding channel shown in 1a, are synthesized
Channel obtains carrying the image of two layers of watermark information, as shown in Figure 2 c, wherein strength factor α=0.01 of embedded watermark；It connects
, will be carried shown in Fig. 2 c on Konica Minolta C6000 digital printers the image of two layers of watermark information with
The output resolution ratio the output for printing of 600dpi, then with Microtek 1000XL Plus scanners with the scanning resolution of 300dpi
The image of the output for printing is scanned, as a result as shown in Figure 2 d；Finally, using the method for extraction watermark of the invention as shown in Figure 1 b from
The watermarking images that corresponding channel is extracted in Fig. 2 d of subchannel, synthesize triple channel watermarking images, and extraction result is as shown in Figure 2 e.
In order to illustrate the advantageous effect of the method for the present invention, the watermark figure that the watermarking images that this is extracted are paved into duplication is calculated
The texture paging index (SSIM) of picture, result 0.7288.It can be seen that carrying the image of watermark information by printing and sweeping
The attack for retouching process remains to extract the watermarking images for showing copyright.
The foregoing is merely the specific implementation modes in the present invention, but scope of protection of the present invention is not limited thereto.Appoint
What those skilled in the art within the technical scope disclosed by the invention, can be converted or be substituted.The transformation carried out
It should be all included within the scope of the present invention with replacing.Therefore, protection scope of the present invention should be with the protection of claims
Subject to range.
Claims (3)
1. a kind of SVD double-layer digital water mark methods avoiding false alarm, which is characterized in that including watermark insertion and watermark extracting two
Process is implemented according to the following steps：
First, the insertion of watermark, specifically includes following steps：
Step A1 decomposes host image H and watermarking images W using SVD, is denoted as H=U respectivelyHSHVH TAnd W=UWSWVW T；
Step A2, by watermarking images W insertion host image singular value matrixs SH, obtain new image arrayIt calculates as follows：
Wherein, α is embedment strength, and α ∈ [0.01,0.1]；
Step A3, by the singular value matrix S of host imageHReplace with imageSingular value matrix through SVD operation gained?
To the image H of embedded first layer watermark informationW, calculate as follows：
Step A4 will be superimposed the watermarking images of singular valueFeature value vector matrix UWAnd VWOne-dimensional matrix u is lined up by rowWWith
vW, the one-dimensional matrix is encrypted using SHA-256 Hash Encryption Algorithm, obtains corresponding Hash codes RUAnd RV：
RU=Harshing(SHA-256)(uW),
RV=Harshing(SHA-256)(vW),
And RUAnd RVBinary coded form is converted to, then to binary RUAnd RVLogic xor operation is carried out, obtains one
New binary signal R, and take first 64 of R to be used as second layer watermark information, it is denoted as Rw；
Step A5 will carry the image H of first layer watermark informationWIt is divided into 8 × 8 sub-block, and DCT operations is implemented to each sub-block, it will
Second layer watermark information RwIt is embedded into direct current (DC) the coefficient C of each sub-blockiIn, it carries out DCT inverse transformations and obtains carrying two layers of watermark letter
The image of breathWherein, i=1,2,3....., 64；
Then, the extraction of watermark, specifically includes following steps：
The image H ' of watermark to be extracted and original host image H are divided into 8 × 8 sub-block, and implemented to each sub-block by step B1
DCT is operated, and obtains the DC coefficients of each sub-block respectivelyWithAnd according to a pair of of DC coefficients of the two corresponding position sub-blockWithGenerate binary signal R ', wherein i=1,2,3....., 64；
Step B2, due to original watermark image W and the image for being superimposed host image singular valueEigen vector having the same, because
This is by watermarking images W through the eigenvectors matrix U obtained by SVD operationsWAnd VWOne-dimensional matrix u is lined up by rowWAnd vW, SHA- is used in combination
256 Hash Encryption Algorithm are encrypted one-dimensional matrix to obtain Hash codes RUAnd RV, Hash codes are then converted into binary coding
Form, using logic exclusive or to binary RUAnd RVIt is operated, obtains binary signal R, take first 64 of R, that is, obtain embedding
The second layer watermark information R enteredw；
Step B3, the second layer watermark information R that the binary signal R ' that judgment step B1 is obtained and step B2 is obtainedwMatching,
If the value of the two is identical, next step extraction operation is carried out, if the value of the two is different, terminates the operation for extracting watermark, indicates
Without carrying watermark information in the image of watermark to be extracted；
Step B4, by singular value matrix Ss of the original watermark image W through SVD operation gainedWReplace with the image H ' of watermark to be extracted
Singular value matrix S through SVD operation gainedH′, obtain new image
According to the singular value matrix S of host imageH, imageAnd embedment strength α, first layer watermarking images W ' is extracted, specifically
It is as follows：
2. a kind of SVD double-layer digital water mark methods avoiding false alarm according to claim 1, it is characterised in that：The step
In rapid A5, by second layer watermark information RwIt is embedded into each sub-block DC coefficients C of imageiIn operation, wherein i=1,2,3.....,
64, the specific method is as follows：
First, each sub-block DC coefficients c is calculatediWith its average valueBetween difference diff (ci)：
Then, according to second layer watermark information RwThe positions i bit values Rw(i) and diff (ci) the corresponding sub-block of symbol modification
DC coefficients ci, concrete operations are：If RwAnd diff (c (i)=1iWhen) >=0, current sub-block DC coefficients ciIncrease | diff (ci)|；
If RwAnd diff (c (i)=1i) < 0 when, current sub-block DC coefficients ciReduce | diff (ci)|；If RwAnd diff (c (i)=0i)≥
When 0, current sub-block DC coefficients ciReduce 2 times | diff (ci)|；If RwAnd diff (c (i)=0i) < 0 when, current sub-block DC systems
Number ciIncrease by 2 times | diff (ci)|。
3. according to a kind of SVD double-layer digital water mark methods avoiding false alarm according to claim 1, it is characterised in that：Institute
It states in step B1, according to DC coefficientsWithGenerate the operation of binary signal R ', wherein i=1,2,3....., 64, specifically
Method is as follows：
First, DC coefficients are calculated separatelyWithWith its respective average valueWithDifference：
Then, it is examined in diff (c from left to right, from top to bottomi W) and diff (ci H) symbol, obtain one group 64 two into
Data R ' processed：As diff (ci W) >=0 and diff (ci H) >=0 or diff (ci W) < 0 and diff (ci H) < 0 when, binary data
Bit value R ' (i)=1 of the positions i of R '；As diff (ci W) < 0 and diff (ci H) > 0 or diff (ci W) > 0 and diff (ci H)
When < 0, bit value R ' (i)=0 of the positions i of binary data R '.
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| CN111984943B (en) * | 2020-07-29 | 2023-08-22 | 南京信息工程大学 | DWT-SVD digital watermarking method based on artificial bee colony algorithm |
| CN112232428B (en) * | 2020-10-23 | 2021-11-16 | 上海电力大学 | Image hash acquisition method based on three-dimensional characteristics and energy change characteristics |
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