CN104331856A - Image zero-watermark embedding and extraction method based on proper fraction fourier transform - Google Patents

Abstract

The invention provides an image zero-watermark embedding and extraction method based on proper fraction fourier transform, and belongs to the technical field of information hiding and image processing. A proper fraction fourier algorithm is adopted, dual effects of watermark embedding and encryption are realized, robustness is higher after watermarking embedding, security and invisibility are enhanced and the overall performance of the watermark is substantially enhanced without changing the characteristics of an original image. According to the embedding method, matrix elements are extracted by adopting a 0 and 1 random matrix generation method. Generation of 0 and 1 random matrixes has diversity and uncertainty so that correct watermark information cannot be extracted if the identical 0 and 1 random matrixes are not used even the extraction method is known, and thus security of watermark embedding is enhanced. The transform coefficient of proper fraction fourier transform can be stored as a secret key so that security and reliability of the algorithm are enhanced.

Description

A kind of image zero watermarking based on real fractional Fourier transform embeds and extracting method

Technical field

The invention belongs to Information hiding and technical field of image processing, be specifically related to a kind of image zero watermarking based on real fractional Fourier transform and embed and extracting method.

Background technology

Along with the development of network, people more and more pay close attention to safety and the copyright problem of the digital picture oneself had; Information Hiding Techniques plays an important role in the safeguard protection of digital picture; Information hiding be carry out under open network environment the data communication of concerning security matters, the intellectual property protection of digital product, vital document and digital signature authenticity differentiate and classified papers divulge a secret after message source follow the trail of and provide reliable security assurance information.Digital watermark technology is the important branch of Information Hiding Techniques.

Digital watermark technology is a kind of method of effective copyright protection, content authentication and data integrity protection, the concern of association area researcher protected by copyright all the time and attention; Traditional digital watermark technology, be generally divided into time domain watermarking algorithm and space watermark algorithm, time domain watermarking algorithm is vulnerable to external attack, and security is bad, and invisibility is poor; And space watermark algorithm complexity is higher, allow that the watermark amount of embedding is less; And transform domain digital watermark is stronger for the robustness of noise, but there is the shortcoming that embedding capacity is little; And traditional watermark embedding method can the feature of change image more or less.

Current digital image watermarking algorithm, as pungent in document happy, happy and carefree, the real-valued encryption method of the digital picture based on Fourier Transform of Fractional Order of Wang Yue; Document is pungent happy, Zhong Jue, the happy and carefree Arithmetic on Digital Watermarking of Image based on Real Discrete Fourier Transform; All teach in said method, at present a lot of algorithm does not all accomplish comprehensive opposing in attack tolerant, and But most of algorithms attack resistance performance is good in addition, more complicatedly not easily realizes.

Summary of the invention

For the shortcoming of prior art, the present invention proposes a kind of image zero watermarking based on real fractional Fourier transform and embeds and extracting method, to reach the double action realizing watermark embedment and encryption, improve the object of the robustness after embed watermark, security and invisibility.

Image zero watermarking based on real fractional Fourier transform embeds and an extracting method, comprises the following steps:

Step 1, watermarking images is embedded in protected image, specific as follows:

Step 1-1, watermarking images is carried out matrixing process, namely the picture element matrix of this watermarking images is obtained, the line number of this matrix is the line number of watermarking images pixel, and this matrix column number is the columns of watermarking images pixel, and this entry of a matrix element is the pixel value of pixel;

Step 1-2, real fractional fourier transform is carried out to the watermarking images after matrixing process, obtain the frequency domain value of each pixel, and then obtain the watermarking images picture element matrix after conversion, and record real fractional fourier transform exponent number as the first key;

Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 1-4, protected image is carried out matrixing process, namely the picture element matrix of this protected image is obtained, the line number of this matrix is the line number of protected image slices vegetarian refreshments, and this matrix column number is the columns of protected image slices vegetarian refreshments, and this entry of a matrix element is the pixel value of pixel;

Step 1-5, real fractional fourier transform is carried out to the protected image after matrixing process, obtain the frequency domain value of each pixel, and then obtain the protected image pixel matrix after conversion, and record real fractional fourier transform exponent number as the second key;

Step 1-6, element in the protected image pixel matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 1-7, structure 0,1 stochastic matrix, the line number of this matrix is identical with protection image pixel matrix with columns, and in this matrix, the number of 1 is identical with element number in the picture element matrix of watermarking images, and records this 0,1 stochastic matrix as the 3rd key;

Step 1-8, by the protected image pixel matrix and 0 after scramble, 1 stochastic matrix is multiplied, and obtains a new matrix, then presses leu from top to bottom time by the non-zero element extraction in this matrix out, obtains and extracts matrix;

Step 1-9, with obtain extraction matrix deduct the watermarking images picture element matrix after scramble, obtain cipher key matrix, using this matrix as the 4th key;

Step 1-10, complete zero watermarking telescopiny;

Step 2, preserve the protected image after the first key, the second key, the 3rd key, the 4th key and embed watermark;

Protected image after step 3, the first key according to storing, the second key, the 3rd key, the 4th key and embed watermark, carries out watermark extracting, specific as follows:

Step 3-1, the protected image of embed watermark is carried out matrixing process, namely the picture element matrix of the protected image of this embed watermark is obtained, the line number of this matrix is the line number of the protected image slices vegetarian refreshments of embed watermark, this matrix column number is the columns of the protected image slices vegetarian refreshments of embed watermark, and this entry of a matrix element is the pixel value of pixel;

Step 3-2, according to the second key stored, real fractional fourier transform is carried out to the protected image of the embed watermark after matrixing process, obtains the frequency domain value of each pixel, and then obtain the protected image pixel matrix of embed watermark after conversion;

Step 3-3, element in the protected image pixel matrix of the embed watermark after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 3-4, by conversion after the protected image pixel matrix of embed watermark and 0 of storage, 1 stochastic matrix, namely the 3rd double secret key answers element multiplication, obtains a new matrix, press leu more from top to bottom secondary by the non-zero element extraction in this matrix out, obtain and extract matrix;

Step 3-5, by the extraction matrix that obtains and cipher key matrix, namely the 4th key subtracts each other, and obtains the watermarking images picture element matrix after scramble;

Step 3-6, the watermarking images picture element matrix after scramble is carried out being inverted unrest, namely obtain watermarking images picture element matrix;

Step 3-7, according to the first key preserved, carry out real fraction Fourier inverse transformation to acquisition watermarking images picture element matrix, obtain the time-domain value of a pixel, the matrix after conversion is original watermark image picture element matrix, completes the extraction to embed watermark image.

Disorder processing described in step 1-3, step 1-6 and step 3-3, by the first row element in matrix and last column element switch, second row element and row element switch second from the bottom, by that analogy, complete the scramble of matrix rows element, then by first row element in matrix and last column element switch, secondary series element and column element switch second from the bottom, by that analogy, the scramble of each column element of matrix is completed.

Advantage of the present invention:

The present invention's zero watermarking algorithm solves the protection problem of digital picture, is creationaryly applied among zero watermarking algorithm by real fractional fourier transform, and innovation is mainly manifested in the following aspects:

1, traditional water mark method feature changing original image more or less in the process of embed watermark, but our zero watermarking algorithm of adopting, under the prerequisite not changing primitive image features, embed watermark information, plays the effect to protect image

2, the present invention applies real fractional fourier transform and is applied among zero watermarking algorithm, and compared to the existing method for digital image copyright protection, the quantity of information of this algorithm embed watermark is larger, and attack resistance performance is stronger, and security is higher;

3, the present invention is in the process of watermark embedment and extraction, application construction 0 cleverly, the method of 1 stochastic matrix carries out watermark embedment, not only serve the effect of scramble, eliminate image coherent element relevance, and 0,1 stochastic matrix there is uncertainty, add the safety and reliability of algorithm;

The result of calculation of 4, traditional algorithm is plural number, and in this algorithm, the result of real fractional fourier transform is real number, is more beneficial to storage, transmission and process, also greatly reduces the complexity of algorithm simultaneously, makes invention be more prone to realize;

In sum, the present invention proposes a kind of image zero watermarking based on real fractional Fourier transform and embeds and extracting method, the real fractional Fourier algorithm adopted, achieve the double action of watermark embedment and encryption, robustness after embed watermark is stronger, security and invisibility strengthen, and the overall performance of watermark significantly improves, and does not change the feature of original image; What the method that the present invention embeds adopted is generation 0, the method of 1 stochastic matrix extracts matrix element, 0, the generation of 1 stochastic matrix has diversity with uncertain, even if be aware of extracting method, also can not extract correct watermark information so long as not 0,1 identical stochastic matrix of use, enhance the security of watermark embedment; The conversion coefficient of real fractional fourier transform can be used as key storage, enhances the safety and reliability of algorithm.

Accompanying drawing explanation

Fig. 1 is the watermarking images telescopiny process flow diagram of an embodiment of the present invention;

Fig. 2 is the watermarking images of an embodiment of the present invention;

Fig. 3 is the image after the real fractional fourier transform of watermarking images of an embodiment of the present invention;

Fig. 4 is the original image of an embodiment of the present invention;

Fig. 5 is the image after the real fractional fourier transform of original image of an embodiment of the present invention;

Fig. 6 is the watermarking images leaching process process flow diagram of an embodiment of the present invention;

Fig. 7 is the watermarking images of the extraction of an embodiment of the present invention;

Fig. 8 is that the white Gaussian noise of an embodiment of the present invention attacks experimental result schematic diagram, wherein, the watermarking images of figure (a) for extracting when variance is 0.003, the watermarking images of figure (b) for extracting when variance is 0.006, the watermarking images of figure (c) for extracting when variance is 0.009, the watermarking images of figure (d) for extracting when variance is 0.03;

Fig. 9 is that the salt-pepper noise of an embodiment of the present invention attacks experimental result schematic diagram, wherein, the watermarking images of figure (a) for extracting when noise intensity is 0.03, the watermarking images of figure (b) for extracting when noise intensity is 0.05, the watermarking images of figure (c) for extracting when noise intensity is 0.08;

Figure 10 is the JPEG compression attack experimental result schematic diagram of an embodiment of the present invention, wherein, the watermarking images of figure (a) for extracting when JPEG quality factor are 90, the watermarking images of figure (b) for extracting when JPEG quality factor are 60, the watermarking images of figure (c) for extracting when JPEG quality factor are 30, the watermarking images of figure (d) for extracting when JPEG quality factor are 10, the watermarking images of figure (e) for extracting when JPEG quality factor are 5;

Figure 11 is that the Gassian low-pass filter of an embodiment of the present invention attacks experimental results schematic diagram, wherein, the watermarking images of figure (a) for extracting when standard deviation is 0.5, the watermarking images of figure (b) for extracting when standard deviation is 0.7, the watermarking images of figure (c) for extracting when standard deviation is 0.9.

Embodiment

Below in conjunction with accompanying drawing, an embodiment of the present invention is described further.

Image zero watermarking based on real fractional Fourier transform embeds and an extracting method, comprises the following steps:

Step 1, embed in protected image by watermarking images, method flow diagram is as shown in Figure 1, specific as follows:

Step 1-1, watermarking images is carried out matrixing process, namely the picture element matrix of this watermarking images is obtained, the line number of this matrix is the line number of watermarking images pixel, and this matrix column number is the columns of watermarking images pixel, and this entry of a matrix element is the pixel value of pixel;

In the embodiment of the present invention, Fig. 2 is the watermarking images that the present embodiment adopts, and reads digital watermarking image, carries out matrix disposal, obtain the picture element matrix P=(p of watermarking images to digital watermarking image _{s, q}) _{s × Q}, the wherein row of S representing matrix, the row of Q representing matrix; P _{s, q}for the s of the picture element matrix P of watermarking images is capable, the element on q column position; Watermarking images is gray level image, pixel value P _{s, q}∈ [0,255].

Step 1-2, real fractional fourier transform is carried out to the watermarking images after matrixing process, obtain the frequency domain value of each pixel, and then obtain the watermarking images picture element matrix after conversion, and record real fractional fourier transform exponent number as the first key;

In the embodiment of the present invention, by the picture element matrix P=(p of watermarking images _{s, q}) _{s × Q}, carry out real fractional fourier transform, the coefficient in real fractional fourier transform is alpha, beta; The picture element matrix P of the watermarking images after real fractional fourier transform ₁=(p _{1s, q}) _{s × Q}, p _{1s, q}be expressed as the picture element matrix P of the watermarking images after real fractional fourier transform ₁s capable, the element on q column position, p _{1s, q}for real number.

Real fractional fourier transform carries out to the watermarking images after matrixing process specific as follows:

Build fractional fourier transform formula as follows:

Wherein, represent fractional fourier transform operator, α represents fractional fourier transform exponent number, and span is (0,1); F (t) represents a continuous signal, and t represents the time; represent transformation kernel function, wherein, u represents α score field, and exp () represents the exponential of e; ψ=α pi/2 represents the angle of phase rotating, and j represents imaginary part; N represents positive integer; δ () represents excited by impact.

The fractional fourier transform formula of structure is carried out sliding-model control, obtains discrete fraction Fourier transform:

Wherein, v _kbe an orthonormal proper vector, and require proper vector v _kbe similar to the fundamental function (continuous Hermite-Gaussian function) of Fourier transform; v _n-1represent orthogonal proper vector, i represents discrete value; K represents discrete time.

Real discrete fraction Fourier transform is obtained according to formula (2):

$\begin{array}{c}y=\left[\begin{array}{c}\mathrm{Re}\left(F^{\mathrm{\α}}\right)\mathrm{Re}\left(\hat{x}\right)-\mathrm{Im}\left(F^{\mathrm{\α}}\right)\mathrm{Im}\left(\hat{x}\right)\\ \mathrm{Im}\left(F^{\mathrm{\α}}\right)\mathrm{Re}\left(\hat{x}\right)+\mathrm{Re}\left(F^{\mathrm{\α}}\right)\mathrm{Im}\left(\hat{x}\right)\end{array}\right]=\left[\begin{array}{cc}\mathrm{Re}\left(F^{\mathrm{\α}}\right)& -\mathrm{Im}\left(F^{\mathrm{\α}}\right)\\ \mathrm{Im}\left(F^{\mathrm{\α}}\right)& \mathrm{Re}\left(F^{\mathrm{\α}}\right)\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\hat{x})\\ \mathrm{Im}\left(\hat{x}\right)\end{array}\right]\\ =R^{\mathrm{\α}}\·x\end{array}---\left(3\right)$

Wherein, Re () represents real part; Im () represents imaginary part; X={x ₁, x ₂, x ₃..., x _n} ^trepresent that length is the signal of N, in the embodiment of the present invention, N is even number; represent signal x regressand value;

Can obtain real fractional fourier transform matrix from be above:

$R^{\mathrm{\α}}=\left[\begin{array}{cc}\mathrm{Re}\left(F^{\mathrm{\α}}\right)& -\mathrm{Im}\left(F^{\mathrm{\α}}\right)\\ \mathrm{Im}\left(F^{\mathrm{\α}}\right)& \mathrm{Re}\left(F^{\mathrm{\α}}\right)\end{array}\right]---\left(4\right)$

Substitute into watermarking images picture element matrix to be transformed, building the real fractional fourier transform of two-dimensional discrete is:

$Y=R^{({\mathrm{\α}}_L,{\mathrm{\α}}_R)}\left[X\right]=R^{{\mathrm{\α}}_L}\·X\·R^{{\mathrm{\α}}_R}---\left(5\right)$

Wherein, [] represents two-dimentional real fractional fourier transform operator; X represents watermarking images picture element matrix; represent the real fractional fourier transform matrix of N × N; represent the real fractional fourier transform matrix of M × M, α _land α _rbe respectively two-dimentional real fractional fourier transform exponent number, in the embodiment of the present invention, α _lfor α (alpha), α _rfor β (beta); Y represents the watermarking images picture element matrix after the image pixel matrix after conversion or conversion;

In the embodiment of the present invention, real fractional fourier transform is carried out to digital picture, conversion coefficient alpha in real fractional fourier transform, the span of beta is [0,1], along with the increase of conversion coefficient, image is changed to frequency domain by time domain gradually, and conversion coefficient can be chosen as required voluntarily, in the embodiment of the present invention, alpha=0.3, beta=0.3.Watermarking images carries out the image after real fractional fourier transform as shown in Figure 3.

Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix; By the first row element in matrix and last column element switch, second row element and row element switch second from the bottom, by that analogy, complete the scramble of matrix rows element, again by first row element in matrix and last column element switch, secondary series element and column element switch second from the bottom, by that analogy, complete the scramble of each column element of matrix.

In the embodiment of the present invention, obtain the watermarking images information P after displacement ₂=(p _{2s, q}) _{s × Q}, the image information after conversion is still the matrix of S × Q, p ² _{s, q}representative digit watermarking images information P ₂s capable, the element on q column position; In the embodiment of the present invention, the watermarking images picture element matrix after real fractional fourier transform is $\left[\begin{array}{cc}1& 7\\ 6& 5\end{array}\right],$ By the matrix after this matrix scrambling be $\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right].$

Record watermarking images line number S, columns Q is used for the foundation of 0,1 stochastic matrix hereinafter, and the value of record watermarking images real fractional fourier transform conversion exponent number alpha and beta, as the first encryption key storage, can strengthen the security of embed watermark image.

Step 1-4, protected image is carried out matrixing process, namely the picture element matrix of this protected image is obtained, the line number of this matrix is the line number of protected image slices vegetarian refreshments, and this matrix column number is the columns of protected image slices vegetarian refreshments, and this entry of a matrix element is the pixel value of pixel;

In the embodiment of the present invention, Fig. 4 is the protected image adopted in the present embodiment, reads the digital picture of pending copyright protection, carries out matrixing process to it, obtains the picture element matrix L=(l of this protected image _{r, c}) _{r × C}, the wherein row of R representing matrix, the row of C representing matrix, l _{r, c}for the r of the picture element matrix L of this protected image is capable, the element on c column position, l _{r, c}∈ [0,255].

Step 1-5, real fractional fourier transform is carried out to the protected image after matrixing process, obtain the frequency domain value of each pixel, and then obtain the protected image pixel matrix after conversion, and record real fractional fourier transform exponent number as the second key;

In the embodiment of the present invention, by the picture element matrix L=(l of protected image _{r, c}) _{r × C}carry out real fractional fourier transform, real fractional fourier transform coefficient alpha, beta.Image information L is obtained after real fractional fourier transform ₁=(l _{1r, c}) _{r × C}, l _{1r, c}for digital image information L ₁r capable, the element on c column position.In the embodiment of the present invention, the image after conversion as shown in Figure 5.

If it is to be noted that watermarking images changes the same with the real fractional Fourier of protected image, then only need the coefficient of the real fractional fourier transform recording watermarking images; If both are different, then need the real fractional fourier transform coefficient recording protected image as the second encryption key storage equally.

Step 1-6, element in the protected image pixel matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

In the embodiment of the present invention, carry out scramble to the image through real fractional fourier transform, the image array after scramble is L ₂=(l _{2r, c}) _{r × C}, l _{2r, c}for digital image information L ₂r capable, the element on c column position, in the embodiment of the present invention, Fig. 5 is the image of original image after real fractional fourier transform, and the matrix after real fractional fourier transform is $\left[\begin{array}{ccc}8& 3& 5\\ 9& 6& 7\\ 4& 2& 1\end{array}\right],$ Matrix after scramble is $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right];$

Step 1-7, structure 0,1 stochastic matrix, the line number of this matrix is identical with protection image pixel matrix with columns, and in this matrix, the number of 1 is identical with element number in the picture element matrix of watermarking images, and records this 0,1 stochastic matrix as the 3rd key;

In the embodiment of the present invention, according to the feature of watermarking images and protected image, structure 0; 1 stochastic matrix, generates cipher key matrix, by watermark embedment in digital picture to be protected; realize the compression to watermark information and encryption, to reach the copyright protection to digital picture, specific as follows:

The original image carried out after scramble is carried out watermark embedment, generates 0,1 stochastic matrix Y=(y _{r, c}) _{r × C}, its size and protected image in the same size, be the matrix of R × C, y _{r, c}∈ [0,1]; 0,1 stochastic matrix of stochastic generation, wherein the number of 1 is S × Q, its number and watermarking images in the same size, is stored by 0,1 stochastic matrix generated as the 3rd key.

In the embodiment of the present invention, the protected image pixel matrix after scramble is $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right],$ Watermarking images picture element matrix is $\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right],$ 0,1 stochastic matrix generated is $\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right].$

In the embodiment of the present invention, the generation of 0,1 stochastic matrix is key of the present invention, 0,1 stochastic matrix Y=(y of generation _{r, c}) _{r × C}, total R × C element, and wherein S × Q element is 1, therefore can generate 0, the number of 1 stochastic matrix is and R × C is far longer than S × Q, so 0, the number of 1 stochastic matrix is a lot, generation for key has uncertainty more, adds the safety and reliability of watermark embedment, and simultaneously 0,1 stochastic matrix is random generation, it is equivalent to randomly draw when extracting original image respective element, serves the effect of scramble, eliminates the relevance of original image information.

Step 1-8, by the protected image pixel matrix and 0 after scramble, 1 stochastic matrix is multiplied, and obtains a new matrix, then presses leu from top to bottom time by the non-zero element extraction in this matrix out, obtains and extracts matrix;

In the embodiment of the present invention, the element multiplication of the protected image pixel matrix correspondence position after 0,1 stochastic matrix generated and scramble is obtained matrix Z=(z _{r, c}) _{r × C}, its size is identical with protected image, is the matrix of R × C, and have S × Q position element value not to be 0 in matrix Z, other positions are 0, and in the embodiment of the present invention, after protected image scrambling, matrix is $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right],$ 0,1 stochastic matrix is $\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right],$ Two matrix corresponding elements are multiplied namely $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right]\·*\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 7& 0& 9\\ 0& 3& 0\end{array}\right].$

Element non-zero in matrix Z is taken out by leu and is positioned over matrix E=(e _{s, q}) _{s × Q}, its size is consistent with watermarking images, is S × Q element, and in the embodiment of the present invention, the matrix obtained after two matrix corresponding elements are multiplied is $\left[\begin{array}{ccc}1& 0& 0\\ 7& 0& 9\\ 0& 3& 0\end{array}\right],$ Extract non-zero element by row, obtaining matrix is $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right].$

Step 1-9, with obtain extraction matrix deduct the watermarking images picture element matrix after scramble, obtain cipher key matrix, using this matrix as the 4th key;

In the embodiment of the present invention, by the matrix E=(e obtained _{s, q}) _{s × Q}watermarking images with it after unrest is weighted, and namely utilizes the element of the relevant position of matrix E to deduct matrix P ₂the element of correspondence position obtains matrix F=(f _{s, q}) _{s × Q}, in the embodiment of the present invention, after scramble, watermarking images picture element matrix is $\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right],$ By matrix $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right]$ Subtract each other with watermarking images picture element matrix corresponding element after scramble, namely $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right]\·-1*\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right]=\left[\begin{array}{cc}-4& -3\\ 0& 8\end{array}\right],$ Using matrix as the 4th key storage.

Step 1-10, complete zero watermarking telescopiny;

Step 2, preserve the first key, the second key, the 3rd key, the 4th key and protected image;

After watermark embedment, image can publish use, needs to retain real fractional fourier transform coefficient alpha, beta respectively, 0,1 stochastic matrix Y=(y _{r, c}) _{r × C}, matrix F=(f _{s, q}) _{s × Q}and the backup of original protected image.

In the embodiment of the present invention, with the 3rd key 0,1 stochastic matrix as basis matrix, by matrix F=(f _{s, q}) _{s × Q}element, by the neutral element position of row reeve 0,1 stochastic matrix, with same method, the first key and the second key are inserted into 0, in 1 stochastic matrix, form combination key matrix; Finally, combination key matrix carries out kept secure; Copyright owner retains above data, needs to use in the process extracting watermark.

Step 3, the first key according to storing, the second key, the 3rd key, the 4th key and protected image, carry out watermark extracting, method flow diagram is as shown in Figure 6, specific as follows:

Step 3-1, the protected image of embed watermark is carried out matrixing process, namely the picture element matrix of the protected image of this embed watermark is obtained, the line number of this matrix is the line number of the protected image slices vegetarian refreshments of embed watermark, this matrix column number is the columns of the protected image slices vegetarian refreshments of embed watermark, and this entry of a matrix element is the pixel value of pixel;

In the embodiment of the present invention, read the backup of the protected image containing watermarking images, obtain the picture element matrix L=(l of the protected image of this embed watermark _{r, c}) _{r × C}, watermark carrier image information is R × C, l _{r, c}representing matrix information L r is capable, the element of c row, L _{r, c}∈ [0,255];

Step 3-2, according to the second key stored, real fractional fourier transform is carried out to the protected image of the embed watermark after matrixing process, obtains the frequency domain value of each pixel, and then obtain the protected image pixel matrix of embed watermark after conversion;

In the embodiment of the present invention, read combination key matrix, extract the second key real fractional fourier transform coefficient alpha, beta, carries out real fractional fourier transform by matrix information L, obtains the watermarking images carrier image information L after converting ₁=(l _{1r, c}) _{r × C}, R represents the line number of watermark carrier image matrix after real fractional fourier transform, the columns of C representing matrix, l _{1r, c}for digital image information L ₁r capable, the element on c column position.

Step 3-3, element in the protected image pixel matrix of the embed watermark after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

In the embodiment of the present invention, by the watermarking images carrier image information L after conversion ₁scramble obtains matrix information L ₂=(l _{2r, c}) _{r × C}.The matrix of image to be size be R × C, l _{2r, c}for the r of digital image information L2 is capable, the element on c column position.

Step 3-4, by the protected image pixel matrix of embed watermark and 0,1 stochastic matrix of storage after conversion, namely the 3rd key is multiplied, and obtains a new matrix, then it is secondary by the non-zero element extraction in this matrix out press leu from top to bottom, acquisition extraction matrix;

In the embodiment of the present invention, read combination key matrix, extract the 3rd key 0,1 stochastic matrix Y=(y _{r, c}) _{r × C}with the 4th watermark keys, obtain the watermarking images picture element matrix after scramble, specific as follows:

0,1 stochastic matrix Y=(y _{r, c}) _{r × C}when being watermark embedment, the stochastic matrix produced, its size with after scramble containing watermark carrier image information consistent; By scramble containing the protected image array L of watermark ₂=(l _{2r, c}) _{r × C}with 0,1 stochastic matrix Y=(y when embedding _{r, c}) _{r × C}correspondence position element multiplication, obtains matrix Z=(z _{r, c}) _{r × C}, there are R capable and C row in matrix Z, and the number and 0 of the non-zero element of matrix Z, 1 stochastic matrix Y is consistent, is S × Q individual; In the embodiment of the present invention, by protected for the watermark after scramble image array $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right]$ With 0,1 stochastic matrix $\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right]$ Corresponding element is multiplied, namely $\left[\begin{array}{ccc}1& 2& 4\\ 7& 6& 9\\ 5& 3& 8\end{array}\right]\·*\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 7& 0& 9\\ 0& 3& 0\end{array}\right];$

Read non-zero element in matrix Z and by its assignment in matrix E=(e _{s, q}) _{s × Q}, read cipher key matrix F=(f _{s, q}) _{s × Q}, utilize the element of the relevant position of matrix E to deduct the element of matrix F relevant position, namely obtain the watermarking images information P2=(p after scramble ² _{s, q}) _{s × Q}, in the embodiment of the present invention, the matrix after being multiplied $\left[\begin{array}{ccc}1& 0& 0\\ 7& 0& 9\\ 0& 3& 0\end{array}\right]$ Extracting non-zero element by row is $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right];$

Step 3-5, by the extraction matrix that obtains and cipher key matrix, namely the 4th key subtracts each other, and obtains the watermarking images picture element matrix after scramble;

In the embodiment of the present invention, by matrix $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right]$ With matrix $\left[\begin{array}{cc}-4& -3\\ 0& 8\end{array}\right]$ Namely corresponding element subtracts each other $\left[\begin{array}{cc}1& 3\\ 7& 9\end{array}\right]\·-\left[\begin{array}{cc}-4& -3\\ 0& 8\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right],$ Matrix $\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right]$ Be the watermarking images matrix of scramble.

Step 3-6, the watermarking images picture element matrix after scramble is carried out being inverted unrest, namely obtain watermarking images picture element matrix;

In the embodiment of the present invention, by the watermarking images picture element matrix P after the scramble of acquisition ₂=(p _{2s, q}) _{s × Q}carry out reverse scramble and obtain matrix P ₁=(p _{1s, q}) _{s × Q}, in the embodiment of the present invention, the scramble watermarking images matrix obtained is $\left[\begin{array}{cc}5& 6\\ 7& 1\end{array}\right],$ Be inverted is disorderly matrix $\left[\begin{array}{cc}1& 7\\ 6& 5\end{array}\right].$

Matrix P ₁what represent is the watermarking images picture element matrix of real fractional fourier transform, reads the coefficient alpha of real fractional fourier transform, beta, i.e. the first key, by matrix P ₁carry out reverse real fractional fourier transform and namely obtain watermarking images information P=(p _{s, q}) _{s × Q}.

Step 3-7, carry out real fraction Fourier inverse transformation to acquisition watermarking images picture element matrix, obtain the time-domain value of a pixel, the matrix after conversion is original watermark image picture element matrix, completes the extraction to embed watermark image.

The leaching process of so far watermark terminates, the legitimacy of watermarking images and provable copyright owner, and the watermarking images extracted in the embodiment of the present invention as shown in Figure 7.

Test carrying out attacks containing the protected image of watermark with multiple common attack pattern respectively below, Binding experiment data and experimental result and accompanying drawing illustrate the superiority of present embodiment:

As schemed shown in (a) in Fig. 8, the white Gaussian noise protected image containing watermark being carried out to 0.003 (variance) is attacked, extract watermarking images, the NC value extracting watermark is: 0.9980, shown in figure (b), the white Gaussian noise protected image containing watermark being carried out to 0.006 (variance) is attacked, extract the NC value of watermarking images: 0.9890, shown in figure (c), the white Gaussian noise protected image containing watermark being carried out to 0.009 (variance) is attacked, extract the NC value of watermarking images: 0.9947, shown in figure (d), the white Gaussian noise protected image containing watermark being carried out to 0.03 (variance) is attacked, extract the NC value of watermarking images: 0.9858, illustrate that contain the protected image of watermark has superperformance under white Gaussian noise is attacked thus.

As schemed shown in (a) in Fig. 9; the salt-pepper noise attack that noise intensity is 0.03 is being subject to containing the protected image of watermark; the watermarking images NC value extracted: 0.9915; shown in figure (b); be subject to the salt-pepper noise attack that noise intensity is 0.05, the watermarking images NC value of extraction: 0.9951, shown in figure (c); be subject to the salt-pepper noise attack that noise intensity is 0.08, the watermarking images NC value of extraction: 0.9962.Illustrate that the protected image containing watermark has good resistivity for salt-pepper noise attack.

As schemed shown in (a) in Figure 10, containing the protected image of watermark when JPEG quality factor are the JPEG compression attack of 90, the watermarking images NC value extracted: 0.9985, shown in figure (b), when JPEG quality factor are 60, the watermarking images NC value extracted: 0.9999, shown in figure (c), when JPEG quality factor are 30, the watermarking images NC value extracted: 0.9983, shown in figure (d), when JPEG quality factor are 10, the watermarking images NC value extracted: 0.9997, shown in figure (e), when JPEG quality factor are 5, the watermarking images NC value extracted: 0.9976.Illustrate that containing the protected image of watermark shows when being subject to JPEG compression attack well.

As schemed shown in (a) in Figure 11; containing the protected image of watermark when being subject to standard deviation and being the Gassian low-pass filter attack of 0.5; the watermarking images NC value extracted: 0.9973; shown in figure (b); when standard deviation is 0.7, the watermarking images NC value of extraction: 0.9896, shown in figure (c); when standard deviation is 0.9, the watermarking images NC value of extraction: 0.9984..Illustrate that containing the protected image of watermark also shows good robustness when being subject to Gassian low-pass filter attack.

From above experimental data, the present embodiment all has good resistivity to various attacks, has good robustness.And realize easily, easy.The present embodiment has certain superiority feasibility as can be seen here.

Carry out noise to the protected image containing watermark, compression, shearing waits various attacks test Lu Bangxing, and experimental result is as shown in table 1:

Table 1: multiple common attack experimental results

As can be seen from experimental result, to various common attack mode, this algorithm can ensure that the watermark NC value extracted is more than 0.9, even most NC values, higher than 0.95, has good robustness.

Claims (2)

1. the image zero watermarking based on real fractional Fourier transform embeds and an extracting method, it is characterized in that: comprise the following steps:

Step 1, watermarking images is embedded in protected image, specific as follows:

Step 1-1, watermarking images is carried out matrixing process, namely the picture element matrix of this watermarking images is obtained, the line number of this matrix is the line number of watermarking images pixel, and this matrix column number is the columns of watermarking images pixel, and this entry of a matrix element is the pixel value of pixel;

Step 1-2, real fractional fourier transform is carried out to the watermarking images after matrixing process, obtain the frequency domain value of each pixel, and then obtain the watermarking images picture element matrix after conversion, and record real fractional fourier transform exponent number as the first key;

Step 1-3, element in the watermarking images picture element matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 1-4, protected image is carried out matrixing process, namely the picture element matrix of this protected image is obtained, the line number of this matrix is the line number of protected image slices vegetarian refreshments, and this matrix column number is the columns of protected image slices vegetarian refreshments, and this entry of a matrix element is the pixel value of pixel;

Step 1-5, real fractional fourier transform is carried out to the protected image after matrixing process, obtain the frequency domain value of each pixel, and then obtain the protected image pixel matrix after conversion, and record real fractional fourier transform exponent number as the second key;

Step 1-6, element in the protected image pixel matrix after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 1-7, structure 0,1 stochastic matrix, the line number of this matrix is identical with protection image pixel matrix with columns, and in this matrix, the number of 1 is identical with element number in the picture element matrix of watermarking images, and records this 0,1 stochastic matrix as the 3rd key;

Step 1-8, by the protected image pixel matrix and 0 after scramble, 1 stochastic matrix corresponding element is multiplied, and obtains a new matrix, then presses leu from top to bottom time by the non-zero element extraction in this matrix out, obtains and extracts matrix;

Step 1-9, with obtain extraction matrix deduct the watermarking images picture element matrix after scramble, obtain cipher key matrix, using this matrix as the 4th key;

Step 1-10, complete zero watermarking telescopiny;

Step 2, preserve the first key, the second key, the 3rd key, the 4th key and protected image;

Step 3, the first key according to storing, the second key, the 3rd key, the 4th key and protected image, carry out watermark extracting, specific as follows:

Step 3-1, the protected image of embed watermark is carried out matrixing process, namely the picture element matrix of the protected image of this embed watermark is obtained, the line number of this matrix is the line number of the protected image slices vegetarian refreshments of embed watermark, this matrix column number is the columns of the protected image slices vegetarian refreshments of embed watermark, and this entry of a matrix element is the pixel value of pixel;

Step 3-2, according to the second key stored, real fractional fourier transform is carried out to the protected image of the embed watermark after matrixing process, obtains the frequency domain value of each pixel, and then obtain the protected image pixel matrix of embed watermark after conversion;

Step 3-3, element in the protected image pixel matrix of the embed watermark after conversion is carried out disorder processing, eliminate the relevance between each element in matrix;

Step 3-4, by conversion after the protected image pixel matrix of embed watermark and 0 of storage, 1 stochastic matrix, namely the 3rd double secret key answers element multiplication, obtains a new matrix, press leu more from top to bottom secondary by the non-zero element extraction in this matrix out, obtain and extract matrix;

Step 3-5, by the extraction matrix that obtains and cipher key matrix, namely the 4th key subtracts each other, and obtains the watermarking images picture element matrix after scramble;

Step 3-6, the watermarking images picture element matrix after scramble is carried out being inverted unrest, namely obtain watermarking images picture element matrix;

Step 3-7, according to preserve the first key, to obtain watermarking images picture element matrix carry out real fraction Fourier inverse transformation, obtain the time-domain value of each pixel, the matrix after conversion is original watermark image picture element matrix, completes the extraction to embed watermark image.

2. the image zero watermarking based on real fractional Fourier transform according to claim 1 embeds and extracting method, it is characterized in that, step 1-3, disorder processing described in step 1-6 and step 3-3, by the first row element in matrix and last column element switch, second row element and row element switch second from the bottom, by that analogy, complete the scramble of matrix rows element, again by first row element in matrix and last column element switch, secondary series element and column element switch second from the bottom, by that analogy, complete the scramble of each column element of matrix.