CN104331856B - A kind of image zero watermarking based on real fractional Fourier transform is embedded in and extracting method - Google Patents
A kind of image zero watermarking based on real fractional Fourier transform is embedded in and extracting method Download PDFInfo
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Abstract
A kind of image zero watermarking based on real fractional Fourier transform of the present invention is embedded in and extracting method, belong to Information hiding and technical field of image processing, using real fractional Fourier algorithm, realize the dual function that watermark is embedded and encrypts, robustness after embedded watermark is stronger, safety and invisibility strengthen, and the overall performance of watermark is significantly improved, and does not change the feature of original image；The embedded method of the present invention uses generation 0, the method of 1 random matrix extracts matrix element, 0, the generation of 1 random matrix has multiformity with uncertainty, even if being aware of extracting method, correct watermark information can also not extracted so long as not using 0,1 random matrix of identical, the embedded safety of watermark is enhanced；The conversion coefficient of real fractional fourier transform as key storage, can enhance the safety and reliability of algorithm.
Description
Technical field
The invention belongs to Information hiding and technical field of image processing, and in particular to a kind of based on real fractional Fourier transform
Image zero watermarking is embedded and extracting method.
Background technology
With the development of network, people increasingly pay close attention to the safety and copyright problem of the digital picture for oneself being possessed；Letter
Breath concealing technology plays an important role in terms of the safeguard protection of digital picture；Information hiding is to enter under open network environment
The verity of the data communication of row concerning security matters, the intellectual property protection of digital product, vital document and digital signature differentiates and machine
Follow the trail of there is provided reliable security assurance information in message source after ciphertext part is divulged a secret.Digital watermark technology is Information Hiding Techniques
Important branch.
Digital watermark technology is a kind of method of effective copyright protection, content authentication and data integrity protection, one
The concern of association area researcher protected by copyright and attention since straight；Traditional digital watermark technology, is generally divided into the time
Domain watermarking algorithm and space watermark algorithm, time domain watermarking algorithm are vulnerable to external attack, and safety is bad, invisibility
Difference；And space watermark algorithm complexity is higher, allow that embedded watermark amount is less；And transform domain digital watermark is directed to noise
Robustness it is stronger, but have the shortcomings that embedding capacity is little；And traditional watermark embedding method can be more or less change figure
The feature of picture.
Current digital image watermarking algorithm, such as document are pungent happy, happy and carefree, the numeral based on Fourier Transform of Fractional Order of Wang Yue
The real-valued encryption method of image；Document is pungent happy, Zhong Jue, and the happy and carefree image digital watermark based on Real Discrete Fourier Transform is calculated
Method；Teach in said method, many algorithms all do not accomplish opposing comprehensively in terms of attack tolerant at present, most in addition
Algorithm attack tolerant can be good, more complicated to be difficult to realize.
The content of the invention
For the shortcoming of prior art, the present invention proposes that a kind of image zero watermarking based on real fractional Fourier transform is embedded in
And extracting method, to reach the dual function for realizing that watermark is embedded and encrypts, improve the robustness after embedded watermark, safety and
The purpose of invisibility.
A kind of image zero watermarking based on real fractional Fourier transform is embedded in and extracting method, comprises the following steps：
Step 1, by the watermarking images embedded image by protection, it is specific as follows：
Step 1-1, watermarking images are carried out matrixing process, that is, obtain the picture element matrix of the watermarking images, the matrix
Line number of the line number for watermarking images pixel, columns of the matrix column number for watermarking images pixel, the element of the matrix is
The pixel value of pixel；
Step 1-2, real fractional fourier transform carried out to the watermarking images after matrixing process, obtain the frequency of each pixel
Thresholding, and then the watermarking images picture element matrix after being converted, and real fractional fourier transform exponent number is recorded as first key；
Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminate each element in matrix
Between relatedness；
Step 1-4, will by protection image carry out matrixing process, that is, obtain the picture element matrix for being protected image, the square
The line number of battle array is to be protected the line number of image slices vegetarian refreshments, and the matrix column number is the columns for being protected image slices vegetarian refreshments, the matrix
Element for pixel pixel value；
Step 1-5, to matrixing process after real fractional fourier transform is carried out by protection image, obtain each pixel
Frequency domain value, so after being converted by protection image pixel matrix, and record real fractional fourier transform exponent number as second
Key；
Step 1-6, by conversion after disorder processing is carried out by element in protection image pixel matrix, eliminate each unit in matrix
Relatedness between element；
Step 1-7,0,1 random matrix of structure, the line number of the matrix are identical with protection image pixel matrix with columns, the square
In battle array, 1 number is identical with element number in the picture element matrix of watermarking images, and it is close as the 3rd to record 0,1 random matrix
Key；
Step 1-8, by scramble after be multiplied by protection image pixel matrix and 0,1 random matrix, obtain a new square
Battle array, then press leu from top to bottom time by the non-zero element extraction in the matrix out, obtain extraction matrix；
Step 1-9, the watermarking images picture element matrix after scramble is deducted with the matrix that extracts for obtaining, obtain cipher key matrix, will
The matrix is used as the 4th key；
Step 1-10, complete zero watermarking telescopiny；
Being schemed by protection after step 2, preservation first key, the second key, the 3rd key, the 4th key and embedded watermark
Picture；
Being protected after step 3, the first key according to storage, the second key, the 3rd key, the 4th key and embedded watermark
Shield image, carries out watermark extracting, specific as follows：
Step 3-1, by embedded watermark by protection image carry out matrixing process, that is, obtain being protected for the embedded watermark
The picture element matrix of image, the line number of the matrix is the line number by protection image slices vegetarian refreshments of embedded watermark, and the matrix column number is
The columns by protection image slices vegetarian refreshments of embedded watermark, the element of the matrix are the pixel value of pixel；
Step 3-2, according to the second key of storage, protected image to carry out real point the embedded watermark after matrixing process
Count Fourier transformation, the frequency domain value of each pixel of acquisition, and then the embedded watermark after being converted is protected image pixel square
Battle array；
Step 3-3, by conversion after embedded watermark by protection image pixel matrix in element carry out disorder processing, eliminate
Relatedness in matrix between each element；
Step 3-4, by conversion after embedded watermark by protection image pixel matrix with storage 0,1 random matrix, i.e.,
3rd key corresponding element is multiplied, and obtains a new matrix, then carries the non-zero element in the matrix by leu from top to bottom
Take out, obtain and extract matrix；
Step 3-5, by obtain extraction matrix and cipher key matrix, i.e. the 4th key subtract each other, obtain scramble after watermark figure
As picture element matrix；
Step 3-6, the watermarking images picture element matrix after scramble is carried out inverting unrest, that is, obtain watermarking images picture element matrix；
Step 3-7, according to preserve first key, to obtain watermarking images picture element matrix carry out real fraction Fourier inversion
Change, obtain the time-domain value of a pixel, the matrix after conversion is original watermark image picture element matrix, complete to embedded watermark figure
The extraction of picture.
Disorder processing described in step 1-3, step 1-6 and step 3-3, will the first row element and last column in matrix
Element exchange position, the second row element and row element exchange position second from the bottom, by that analogy, complete putting for matrix rows element
Disorderly, then by the first column element in matrix and last column element exchange position, the second column element is exchanged with column element second from the bottom
Position, by that analogy, completes the scramble of each column element of matrix.
Advantage of the present invention：
The present invention solves the protection problem of digital picture with zero watermarking algorithm, and creative should by real fractional fourier transform
Among for zero watermarking algorithm, innovation is mainly manifested in the following aspects：
1st, the more or less feature for changing original image during embedded watermark of traditional water mark method, but
The zero watermarking algorithm that we adopt, on the premise of primitive image features are not changed, is embedded in watermark information, plays and image is protected
Effect
2nd, among the real fractional fourier transform of present invention application is applied to zero watermarking algorithm, compared to existing for numeral
The method of image copyright protection, the quantity of information of the embedded watermark of this algorithm are bigger, and attack tolerant can be higher, and safety is higher；
3rd, the present invention is embedded and during extracting in watermark, cleverly application construction 0, and the method for 1 random matrix is carried out
Watermark is embedded in, and has not only acted as the effect of scramble, eliminates image coherent element relatedness, and 0, and 1 random matrix has not
Definitiveness, increased the safety and reliability of algorithm；
4th, the result of calculation of traditional algorithm is plural number, and in this algorithm, the result of real fractional fourier transform is real number, more
Plus beneficial to storage, transmission and process, while being greatly reduced the complexity of algorithm, make invention be more prone to realize；
In sum, the present invention proposes that a kind of image zero watermarking based on real fractional Fourier transform is embedded in and extraction side
Method, the real fractional Fourier algorithm of employing realize the dual function that watermark is embedded and encrypts, be embedded in the robustness after watermark compared with
By force, safety and invisibility strengthen, and the overall performance of watermark is significantly improved, and does not change the feature of original image；The present invention is embedding
The method for entering uses the method for 0,1 random matrix of generation and extracts matrix element, and the generation of 0,1 random matrix has multiformity
With uncertainty, even if being aware of extracting method, correct water can not also be extracted so long as not using 0,1 random matrix of identical
Official seal ceases, and enhances the embedded safety of watermark；The conversion coefficient of real fractional fourier transform can be enhanced as key storage
The safety and reliability of algorithm.
Description of the drawings
Watermarking images telescopiny flow charts of the Fig. 1 for an embodiment of the present invention；
Watermarking images of the Fig. 2 for an embodiment of the present invention；
Fig. 3 is the image after the watermarking images reality fractional fourier transform of an embodiment of the present invention；
Original images of the Fig. 4 for an embodiment of the present invention；
Fig. 5 is the image after the original image reality fractional fourier transform of an embodiment of the present invention；
Watermarking images extraction process flow charts of the Fig. 6 for an embodiment of the present invention；
Watermarking images of the Fig. 7 for the extraction of an embodiment of the present invention；
Fig. 8 attacks experimental result schematic diagram for the white Gaussian noise of an embodiment of the present invention, wherein, figure (a) is variance
For 0.003 when the watermarking images that extract, scheme the watermarking images extracted when (b) is 0.006 for variance, figure (c) is 0.009 for variance
When the watermarking images that extract, scheme the watermarking images extracted when (d) is 0.03 for variance；
Fig. 9 attacks experimental result schematic diagram for the salt-pepper noise of an embodiment of the present invention, wherein, figure (a) is strong for noise
Spend for 0.03 when the watermarking images that extract, scheme the watermarking images extracted when (b) is 0.05 for noise intensity, figure (c) is strong for noise
Spend for 0.08 when the watermarking images that extract；
Figure 10 attacks experimental result schematic diagram for the JPEG compression of an embodiment of the present invention, wherein, figure (a) is JPEG product
The watermarking images extracted when prime factor is 90, scheme the watermarking images extracted when (b) is 60 for JPEG quality factor, and figure (c) is
The watermarking images that JPEG quality factor are extracted when being 30, scheme the watermarking images extracted when (d) is 10 for JPEG quality factor, figure
E watermarking images that () is extracted when being 5 for JPEG quality factor；
Figure 11 attacks experimental results schematic diagram for the Gassian low-pass filter of an embodiment of the present invention, wherein, scheme (a)
The watermarking images extracted when being 0.5 for standard deviation, scheme the watermarking images extracted when (b) is 0.7 for standard deviation, and figure (c) is standard
The watermarking images that difference is extracted when being 0.9.
Specific embodiment
Below in conjunction with the accompanying drawings an embodiment of the present invention is described further.
A kind of image zero watermarking based on real fractional Fourier transform is embedded in and extracting method, comprises the following steps：
Step 1, by the watermarking images embedded image by protection, method flow diagram is as shown in figure 1, specific as follows：
Step 1-1, watermarking images are carried out matrixing process, that is, obtain the picture element matrix of the watermarking images, the matrix
Line number of the line number for watermarking images pixel, columns of the matrix column number for watermarking images pixel, the element of the matrix is
The pixel value of pixel；
In the embodiment of the present invention, Fig. 2 is the watermarking images that the present embodiment is adopted, and reads digital watermarking image, to digital water
Watermark image carries out matrix disposal, obtains the picture element matrix P=(p of watermarking imagesS, q)S×Q, the wherein row of S representing matrixs, Q represent square
The row of battle array；PS, qFor the s rows of the picture element matrix P of watermarking images, the element on q column positions；Watermarking images are gray level image,
Pixel value PS, q∈ [0,255].
Step 1-2, real fractional fourier transform carried out to the watermarking images after matrixing process, obtain the frequency of each pixel
Thresholding, and then the watermarking images picture element matrix after being converted, and real fractional fourier transform exponent number is recorded as first key；
In the embodiment of the present invention, by the picture element matrix P=(p of watermarking imagesS, q)S×Q, real fractional fourier transform is carried out, it is real
Coefficient in fractional fourier transform is alpha, beta；The picture element matrix P of the watermarking images after real fractional fourier transform1=
(p1s, q)S×Q, p1s, qThe picture element matrix P of the watermarking images being expressed as after real fractional fourier transform1S rows, on q column positions
Element, p1s, qFor real number.
Real fractional fourier transform is carried out to the watermarking images after matrixing process specific as follows：
Build fractional fourier transform formula as follows：
Wherein,Fractional fourier transform operator is represented, α represents fractional fourier transform exponent number, value model
Enclose for (0,1)；F (t) represents a continuous signal, t express times；Conversion kernel function is represented,Wherein, u represents α score fields, exp ()
Represent the exponential of e；ψ=α pi/2s represent the angle of phase place, and j represents imaginary part；N represents positive integer；δ () represents that impact swashs
Encourage.
The fractional fourier transform formula of structure is carried out into sliding-model control, discrete fraction Fourier transformation is obtained：
Wherein, vkIt is an orthonormal characteristic vector, and requires characteristic vector vkIt is similar to the spy of Fourier transformation
Levy function (continuous Hermite-Gaussian functions)；vN-1Orthogonal characteristic vector is represented, i represents centrifugal pump；K represents discrete
Time.
Real discrete fraction Fourier transformation is obtained according to formula (2)：
Wherein, Re () represents real part；Im () represents imaginary part；X={ x1, x2, x3..., xN}TRepresent letter of the length for N
Number, in the embodiment of the present invention, N is even number；Represent signal x regressand values；
Real fractional fourier transform matrix can be obtained from above is：
Watermarking images picture element matrix to be transformed is substituted into, building two-dimensional discrete reality fractional fourier transform is：
Wherein,[] represents two dimension reality fractional fourier transform operator；X represents watermarking images picture element matrix；
Represent N × N reality fractional fourier transform matrixes；Represent M × M reality fractional fourier transform matrixes, αLAnd αRIt is respectively two-dimentional
Real fractional fourier transform exponent number, in the embodiment of the present invention, αLFor α (alpha), αRFor β (beta)；Y represents the image after conversion
Watermarking images picture element matrix after picture element matrix or conversion；
In the embodiment of the present invention, real fractional fourier transform, the change in real fractional fourier transform are carried out to digital picture
Coefficient alpha is changed, the span of beta is [0,1], with the increase of conversion coefficient, image is gradually turned from time domain to frequency domain
Become, conversion coefficient voluntarily can be chosen as needed, in the embodiment of the present invention, alpha=0.3, beta=0.3.Watermarking images
The image carried out after real fractional fourier transform is as shown in Figure 3.
Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminate each element in matrix
Between relatedness；Will the first row element and last column element exchange position in matrix, the second row element with it is second from the bottom
Row element exchange position, by that analogy, completes the scramble of matrix rows element, then by the first column element in matrix and last string
Element exchange position, the second column element and column element exchange position second from the bottom, by that analogy, complete putting for each column element of matrix
Disorderly.
Watermarking images information P in the embodiment of the present invention, after being replaced2=(p2s, q)S×Q, the image information after conversion
It is still the matrix of S × Q, p2 S, qRepresent digital watermarking image information P2S rows, the element on q column positions；The present invention is implemented
In example, the watermarking images picture element matrix after real fractional fourier transform isBy the matrix after the matrix scrambling it is
Watermarking images line number S is recorded, columns Q is used for the foundation of hereinafter 0,1 random matrix, and record watermarking images divide in fact
The value of number Fourier transformation conversion exponent number alpha and beta is stored as first key, can strengthen the peace of embedded watermarking images
Quan Xing.
Step 1-4, will by protection image carry out matrixing process, that is, obtain the picture element matrix for being protected image, the square
The line number of battle array is to be protected the line number of image slices vegetarian refreshments, and the matrix column number is the columns for being protected image slices vegetarian refreshments, the matrix
Element for pixel pixel value；
In the embodiment of the present invention, Fig. 4 reads the number of pending copyright protection to adopt in the present embodiment by protection image
Word image, carries out matrixing process to which, obtains the picture element matrix L=(l for being protected imageR, c)R×C, wherein R representing matrixs
Row, the row of C representing matrixs, lR, cThe r rows of the picture element matrix L of image, the element on c column positions, l are protected for thisR, c
∈ [0,255].
Step 1-5, to matrixing process after real fractional fourier transform is carried out by protection image, obtain each pixel
Frequency domain value, so after being converted by protection image pixel matrix, and record real fractional fourier transform exponent number as second
Key；
In the embodiment of the present invention, by by the picture element matrix L=(l of protection imageR, c)R×CReal fractional fourier transform is carried out,
Real fractional fourier transform coefficient alpha, beta.Image information L is obtained after real fractional fourier transform1=
(l1r, c)R×C, l1r, cFor digital image information L1R rows, the element on c column positions.In the embodiment of the present invention, after conversion
Image is as shown in Figure 5.
It should be noted that：If watermarking images are the same with by protection image reality fractional Fourier change, only need to remember
The coefficient of the real fractional fourier transform of record watermarking images；If both are different, need also exist for recording by protection image
Real fractional fourier transform coefficient is stored as the second key.
Step 1-6, by conversion after disorder processing is carried out by element in protection image pixel matrix, eliminate each unit in matrix
Relatedness between element；
In the embodiment of the present invention, the image to passing through real fractional fourier transform enters line shuffle, the image array after scramble
For L2=(l2r, c)R×C, l2r, cFor digital image information L2R rows, the element on c column positions, in the embodiment of the present invention, figure
5 is image of the original image after real fractional fourier transform, and the matrix after real fractional fourier transform is
Matrix after scramble is
Step 1-7,0,1 random matrix of structure, the line number of the matrix are identical with protection image pixel matrix with columns, the square
In battle array, 1 number is identical with element number in the picture element matrix of watermarking images, and it is close as the 3rd to record 0,1 random matrix
Key；
In the embodiment of the present invention, according to watermarking images and the feature by protection image, 0,1 random matrix is constructed, is generated close
Key matrix, embeds watermark data in digital picture to be protected, realizes compression and encryption to watermark information, to reach to numeral
The copyright protection of image, it is specific as follows：
The original image entered after line shuffle is carried out watermark to be embedded in, 0,1 random matrix Y=(y are generatedR, c)R×C, its size with
It is in the same size by protection image, it is the matrix of R × C, yR, c∈ [0,1]；Random 0,1 random matrix for generating, wherein 1
It is S × Q to count, and its number is in the same size with watermarking images, and 0,1 random matrix for generating is stored as the 3rd key.
In the embodiment of the present invention, the image pixel matrix of being protected after scramble isWatermarking images picture element matrix isGenerate 0,1 random matrix be
In the embodiment of the present invention, the generation of 0,1 random matrix is the key of the present invention, the 0 of generation, 1 random matrix Y=
(yR, c)R×C, R × C element is had, and wherein S × Q element is 1, thus 0 for can generating, the number of 1 random matrix
ForAnd R × C is far longer than S × Q, so the number of 0,1 random matrix is a lot, for the generation of key more has
Uncertainty, increased the embedded safety and reliability of watermark, while 0,1 random matrix is to randomly generate, it is extracting former
Equivalent to randomly selecting during beginning image respective element, the effect of scramble is served, eliminate the relatedness of original image information.
Step 1-8, by scramble after be multiplied by protection image pixel matrix and 0,1 random matrix, obtain a new square
Battle array, then press leu from top to bottom time by the non-zero element extraction in the matrix out, obtain extraction matrix；
In the embodiment of the present invention, by position 0,1 random matrix for generating corresponding with image pixel matrix is protected after scramble
The element multiplication put obtains matrix Z=(zR, c)R×C, its size with by protection image it is identical, be the matrix of R × C, in matrix Z
There is S × Q position element value not for 0, other positions are 0, in the embodiment of the present invention, by matrix after protection image scrambling be0,1 random matrix isTwo matrix corresponding elements are multiplied and are
Non-zero element in matrix Z is taken out by leu time and matrix E=(e are positioned overS, q)S×Q, its size and watermarking images one
Cause, be S × Q element, in the embodiment of the present invention, the matrix that two matrix corresponding elements are obtained after being multiplied isBy row
Non-zero element is extracted, obtaining matrix is
Step 1-9, the watermarking images picture element matrix after scramble is deducted with the matrix that extracts for obtaining, obtain cipher key matrix, will
The matrix is used as the 4th key；
In the embodiment of the present invention, the matrix E=(e that will be obtainedS, q)S×QWatermarking images after unrest are weighted therewith,
Matrix P is deducted using the element of the relevant position of matrix E2The element of correspondence position obtains matrix F=(fS, q)S×Q, the present invention
In embodiment, after scramble, watermarking images picture element matrix isBy matrixIt is corresponding with watermarking images picture element matrix after scramble
Element subtracts each other, i.e.,Using matrix as the 4th key storage.
Step 1-10, complete zero watermarking telescopiny；
Step 2, preserve first key, the second key, the 3rd key, the 4th key and by protection image；
After watermark is embedded, image can publish use, need to retain real fractional fourier transform coefficient respectively
Alpha, beta, 0,1 random matrix Y=(yR, c)R×C, matrix F=(fS, q)S×QAnd the original backup by protection image.
In the embodiment of the present invention, with the 3rd key 0,1 random matrix as basic matrix, by matrix F=(fS, q)S×QUnit
Element, by row inject 0,1 random matrix neutral element position, with same method by first key and the second key be inserted into 0,1 with
Combination key matrix is formed in machine matrix；Finally, combination key matrix carries out kept secure；Copyright owner retains above number
According to, extract watermark during need use.
Step 3, according to storage first key, the second key, the 3rd key, the 4th key and by protection image, carry out
Watermark extracting, method flow diagram is as shown in fig. 6, specific as follows：
Step 3-1, by embedded watermark by protection image carry out matrixing process, that is, obtain being protected for the embedded watermark
The picture element matrix of image, the line number of the matrix is the line number by protection image slices vegetarian refreshments of embedded watermark, and the matrix column number is
The columns by protection image slices vegetarian refreshments of embedded watermark, the element of the matrix are the pixel value of pixel；
In the embodiment of the present invention, the backup by protection image containing watermarking images is read, being protected for the embedded watermark is obtained
Picture element matrix L=(the l of shield imageR, c)R×C, watermark carrier image information is R × C, lR, cRepresenting matrix information L r rows, c row
Element, LR, c∈ [0,255]；
Step 3-2, according to the second key of storage, protected image to carry out real point the embedded watermark after matrixing process
Count Fourier transformation, the frequency domain value of each pixel of acquisition, and then the embedded watermark after being converted is protected image pixel square
Battle array；
In the embodiment of the present invention, combination key matrix is read, extract the second key reality fractional fourier transform coefficient
Matrix information L is carried out real fractional fourier transform by alpha, beta, watermarking images carrier image information L after being converted1
=(l1r, c)R×C, R represents the line number of watermark carrier image matrix Jing after real fractional fourier transform, the columns of C representing matrixs,
l1r, cFor digital image information L1R rows, the element on c column positions.
Step 3-3, by conversion after embedded watermark by protection image pixel matrix in element carry out disorder processing, eliminate
Relatedness in matrix between each element；
In the embodiment of the present invention, by watermarking images carrier image information L after conversion1Scramble obtains matrix information L2=
(l2r, c)R×C.Image be size be R × C matrix, l2r, cFor the r rows of digital image information L2, the unit on c column positions
Element.
Step 3-4, by conversion after embedded watermark by protection image pixel matrix with storage 0,1 random matrix, i.e.,
3rd key is multiplied, and obtains a new matrix, then press from top to bottom leu it is secondary by the non-zero element extraction in the matrix out,
Obtain and extract matrix；
In the embodiment of the present invention, combination key matrix is read, extract the 3rd key 0,1 random matrix Y=(yR, c)R×CWith
Four watermark keys, obtain the watermarking images picture element matrix after scramble, specific as follows：
0,1 random matrix Y=(yR, c)R×CWhen being that watermark is embedded, produced random matrix, containing after its size and scramble
Watermark carrier image information is consistent；Scramble is protected into image array L containing watermark2=(l2r, c)R×CWith it is embedded when 0,1 with
Machine matrix Y=(yR, c)R×CCorrespondence position element multiplication, obtains matrix Z=(zR, c)R×C, in matrix Z, have R rows and C row, and square
The number of the non-zero elements of battle array Z is consistent with 0,1 random matrix Y, is S × Q；In the embodiment of the present invention, by the watermark quilt after scramble
Protection image arrayWith 0,1 random matrixCorresponding element is multiplied, i.e.,
Read matrix Z in non-zero element and by its assignment in matrix E=(eS, q)S×Q, read cipher key matrix F=(fS, q)S×Q,
The element of matrix F relevant position is deducted using the element of the relevant position of matrix E, that is, obtains the watermarking images information after scramble
P2=(p2 S, q)S×Q, the matrix in the embodiment of the present invention, after multiplicationNon-zero element is extracted by row is
Step 3-5, by obtain extraction matrix and cipher key matrix, i.e. the 4th key subtract each other, obtain scramble after watermark figure
As picture element matrix；
In the embodiment of the present invention, by matrixWith matrixCorresponding element subtracts each other i.e.MatrixThe as watermarking images matrix of scramble.
Step 3-6, the watermarking images picture element matrix after scramble is carried out inverting unrest, that is, obtain watermarking images picture element matrix；
Watermarking images picture element matrix P in the embodiment of the present invention, after the scramble that will be obtained2=(p2s, q)S×QReversely put
Matrix P is obtained disorderly1=(p1s, q)S×Q, in the embodiment of the present invention, the scramble watermarking images matrix for obtaining isInvert disorderly as square
Battle array
Matrix P1What is represented is the watermarking images picture element matrix of real fractional fourier transform, reads real fractional fourier transform
Coefficient alpha, beta, i.e. first key, by matrix P1Carry out reverse reality fractional fourier transform and obtain watermarking images letter
Breath P=(pS, q)S×Q。
Step 3-7, carry out real fraction Fourier inverse transformation to obtaining watermarking images picture element matrix, obtain a pixel when
Thresholding, the matrix after conversion are original watermark image picture element matrix, complete the extraction to being embedded in watermarking images.
The extraction process of so far watermark terminates, and watermarking images are the legitimacy of provable copyright owner, and the present invention is implemented
The watermarking images extracted in example are as shown in Figure 7.
Separately below with various common attack patterns to being carried out attack experiment, Binding experiment by protection image containing watermark
Data and experimental result and accompanying drawing are illustrating the superiority of present embodiment：
As shown in figure (a) in Fig. 8, to being attacked by the white Gaussian noise that protection image carries out 0.003 (variance) containing watermark,
Watermarking images are extracted, the NC values for extracting watermark are：0.9980, shown in figure (b), the protected image containing watermark is carried out
The white Gaussian noise of 0.006 (variance) is attacked, and extracts the NC values of watermarking images：0.9890, shown in figure (c), to the quilt containing watermark
The image of protection carries out the white Gaussian noise of 0.009 (variance) and attacks, and extracts the NC values of watermarking images：0.9947, scheme (d) institute
Show, the white Gaussian noise that 0.03 (variance) is carried out to the protected image containing watermark is attacked, and extracts the NC values of watermarking images：
0.9858；Thus explanation is protected image to have superperformance under white Gaussian noise attack containing watermark.
As shown in figure (a) in Fig. 9, image is protected being attacked by the salt-pepper noise that noise intensity is 0.03 containing watermark,
The watermarking images NC values of extraction：0.9915, shown in figure (b), attacked by the salt-pepper noise that noise intensity is 0.05, extraction
Watermarking images NC values：0.9951, shown in figure (c), attacked by the salt-pepper noise that noise intensity is 0.08, the watermark figure of extraction
As NC values：0.9962.Illustrate that being attacked for salt-pepper noise by protection image containing watermark has good resistivity.
As shown in figure (a) in Figure 10, image is protected when the JPEG compression that JPEG quality factor are 90 is attacked containing watermark,
The watermarking images NC values of extraction：0.9985, shown in figure (b), when JPEG quality factor are 60, the watermarking images NC values of extraction：
0.9999, shown in figure (c), when JPEG quality factor are 30, the watermarking images NC values of extraction：0.9983, shown in figure (d), JPEG
When quality factor are 10, the watermarking images NC values of extraction：0.9997, shown in figure (e), when JPEG quality factor are 5, the water of extraction
Watermark image NC value：0.9976.Illustrate to be protected image performance when being attacked by JPEG compression good containing watermark.
As shown in figure (a) in Figure 11, image is protected to be attacked by the Gassian low-pass filter that standard deviation is 0.5 containing watermark
When, the watermarking images NC values of extraction：0.9973, shown in figure (b), when standard deviation is 0.7, the watermarking images NC values of extraction：
0.9896, shown in figure (c), when standard deviation is 0.9, the watermarking images NC values of extraction：0.9984..Illustrate to be protected figure containing watermark
As also showing good robustness when being attacked by Gassian low-pass filter.
From above experimental data, the present embodiment all has preferable resistivity to various attacks, with preferable
Robustness.And realize easy, simplicity.The present embodiment has certain superiority feasibility as can be seen here.
To being carried out noise by protection image containing watermark, compress, the various attacks test Lu Bangxing such as shearing, experimental result is such as
Shown in table 1：
Table 1：Various common attack experimental results
From experimental result as can be seen that to various common attack modes, this algorithm can ensure that the watermark NC values extracted exist
More than 0.9, or even most of NC values are higher than 0.95, with preferable robustness.
Claims (2)
1. a kind of image zero watermarking based on real fractional Fourier transform is embedded in and extracting method, it is characterised in that：Including following
Step：
Step 1, by the watermarking images embedded image by protection, it is specific as follows：
Step 1-1, watermarking images are carried out matrixing process, that is, obtain the picture element matrix of the watermarking images, the line number of the matrix
For the line number of watermarking images pixel, columns of the matrix column number for watermarking images pixel, the element of the matrix is pixel
The pixel value of point；
Step 1-2, real fractional fourier transform carried out to the watermarking images after matrixing process, obtain the frequency domain of each pixel
Value, and then the watermarking images picture element matrix after being converted, and real fractional fourier transform exponent number is recorded as first key；
Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminated in matrix between each element
Relatedness；
Step 1-4, will by protection image carry out matrixing process, that is, obtain the picture element matrix for being protected image, the matrix
Line number is to be protected the line number of image slices vegetarian refreshments, and the matrix column number is the columns for being protected image slices vegetarian refreshments, the unit of the matrix
Pixel value of the element for pixel；
Step 1-5, to matrixing process after real fractional fourier transform is carried out by protection image, obtain the frequency domain of each pixel
Value, and then protected image pixel matrix after being converted, and real fractional fourier transform exponent number is recorded as the second key；
Step 1-6, by conversion after disorder processing is carried out by element in protection image pixel matrix, eliminate in matrix each element it
Between relatedness；
Step 1-7,0,1 random matrix of structure, the line number of the matrix are identical with protection image pixel matrix with columns, in the matrix
1 number is identical with element number in the picture element matrix of watermarking images, and records 0,1 random matrix as the 3rd key；
Step 1-8, by scramble after be multiplied by protection image pixel matrix and 0,1 random matrix corresponding element, obtain one it is new
Matrix, then press leu from top to bottom time by the non-zero element extraction in the matrix out, obtain and extract matrix；
Step 1-9, the watermarking images picture element matrix after scramble is deducted with the matrix that extracts for obtaining, obtain cipher key matrix, by the square
Battle array is used as the 4th key；
Step 1-10, complete zero watermarking telescopiny；
Step 2, preserve first key, the second key, the 3rd key, the 4th key and by protection image；
Step 3, according to storage first key, the second key, the 3rd key, the 4th key and by protection image, carry out watermark
Extract, it is specific as follows：
Step 3-1, by embedded watermark by protection image carry out matrixing process, that is, obtain the embedded watermark by protection image
Picture element matrix, the line number of the matrix is the line number by protection image slices vegetarian refreshments of embedded watermark, and the matrix column number is embedded
The columns by protection image slices vegetarian refreshments of watermark, the element of the matrix are the pixel value of pixel；
Step 3-2, according to storage the second key, to matrixing process after embedded watermark protected image to carry out real fraction Fu
In leaf transformation, obtain the frequency domain value of each pixel, and then image pixel matrix protected in the embedded watermark after being converted；
Step 3-3, by conversion after embedded watermark disorder processing carried out by element in protection image pixel matrix, eliminate matrix
Relatedness between middle each element；
Step 3-4, by conversion after embedded watermark by protection image pixel matrix with storage 0,1 random matrix, i.e., the 3rd
Key corresponding element is multiplied, and obtains a new matrix, then goes out the non-zero element extraction in the matrix successively by row from top to bottom
Come, obtain and extract matrix；
Step 3-5, by obtain extraction matrix and cipher key matrix, i.e. the 4th key subtract each other, obtain scramble after watermarking images picture
Prime matrix；
Step 3-6, the watermarking images picture element matrix after scramble is carried out inverting unrest, that is, obtain watermarking images picture element matrix；
Step 3-7, according to preserve first key, to obtain watermarking images picture element matrix carry out real fraction Fourier inversion
Change, obtain the time-domain value of each pixel, the matrix after conversion is original watermark image picture element matrix, complete to embedded watermark figure
The extraction of picture.
2. the image zero watermarking based on real fractional Fourier transform according to claim 1 is embedded in and extracting method, and which is special
Levy and be, the disorder processing described in step 1-3, step 1-6 and step 3-3 will the first row element and last column in matrix
Element exchange position, the second row element and row element exchange position second from the bottom, by that analogy, complete putting for matrix rows element
Disorderly, then by the first column element in matrix and last column element exchange position, the second column element is exchanged with column element second from the bottom
Position, by that analogy, completes the scramble of each column element of matrix.
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