CN109840874A - A kind of digital watermarking authentication method and device - Google Patents
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Abstract
The invention discloses a kind of digital watermarking authentication method and devices, comprising: generates the carrier image of insertion watermark information image, comprising: according to watermark information image, generates digital hologram；Using initial carrier image as the amplitude of the input object light function of lens front focal plane, using digital hologram as the output object light function of back focal plane, foundation includes the constraining equation of initial carrier image, digital hologram, phase function, it is calculated using Fractional Fourier transform and solves the phase function for meeting constraining equation, according to the phase function for meeting constraining equation, the carrier image of insertion watermark information image is obtained；Further include the extraction password determined for extracting digital hologram, according to initial carrier image and extracts password, extract digital hologram, be based on digital hologram, rebuild watermark information image.The present invention provides a kind of digital watermarking authentication methods and device with good anti-print performance.
Description
Technical Field
The present invention relates to the field of information security technologies, and in particular, to a digital watermark authentication method and apparatus.
Background
The digital watermarking technology is to directly embed watermark information into carrier information or indirectly express the watermark information, so that the use value of the carrier information is not influenced, and the watermark information is not easy to be ascertained and modified again. The digital watermarking technology is applied to the field of multimedia information security research. At present, in the printing field, after image carrier information embedded with watermark information is printed and scanned, the watermark information is lost. In recent years, the information optical holographic technology has a wide application prospect in the fields of information hiding and digital watermarking due to the advantages of multi-dimension, high capacity, high design freedom, high robustness, difficult tearing, natural parallelism, difficult cracking and the like.
Disclosure of Invention
In view of the above, the present invention is directed to a digital watermark authentication method and apparatus, which have good anti-printing performance.
Based on the above purpose, the present invention provides a digital watermark authentication method, which includes:
generating a carrier image embedded with a watermark information image, comprising:
generating a digital hologram according to the watermark information image;
and establishing a constraint condition equation by taking the original carrier image as the amplitude of an input object light function of the front focal plane of the lens and the digital hologram as an output object light function of the rear focal plane:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η)
wherein f (x, y) is an original carrier image, g (ξ) is the digital hologram, phi (x, y) is a phase function to be solved and meeting the constraint condition equation, and j is a unit imaginary number;
calculating and solving a phase function meeting the constraint condition equation by using fractional Fourier transform;
obtaining a carrier image I (x, y) of the embedded watermark information image according to the phase function meeting the constraint condition equation:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)]
wherein, phi (x, y)(n)To satisfy the phase function of the constraint equation.
Optionally, the method further includes:
determining an extraction password for extracting the digital hologram, comprising:
and performing singular value decomposition on the phase function meeting the constraint condition equation to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm to obtain an encryption processing result D ', and taking the D' as the extracted password.
Optionally, the method further includes:
extracting the digital hologram according to the original carrier image and the extraction password, comprising:
decrypting the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;
reconstructing to obtain the phase function meeting the constraint condition equation by using the singular value matrix D and the two unitary matrices U and V;
calculating the digital hologram g (ξ) by using the original carrier image and a phase function satisfying a constraint condition equation:
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}
optionally, the method further includes:
reconstructing the watermark information image based on the digital hologram,
wherein IFn denotes the inverse fresnel diffraction integral transformation, O (x, y) denotes the reconstructed watermark information image, O (ξ) denotes the light field distribution of the watermark information image on the observation plane, x and y denote the coordinates of the pixel points of O (x, y) on the object plane, ξ denotes the coordinates of the pixel points of O (ξ) on the observation plane, z denotes the distance between the object plane and the observation plane, λ denotes the wavelength of light, and k denotes 2 pi/λ denotes the wave number.
Optionally, the method for calculating and solving the phase function satisfying the constraint equation by using the fractional fourier transform includes:
calculating an intermediate output object light function Q by using the original carrier image as the amplitude of the input object light function(n)(ξ，η)，Q(n)(ξ) has an amplitude of | Q(n)(ξ) |, the intermediate phase function of the observation plane is phi (ξ)(n)，
Q(n)(ξ，η)＝|Q(n)((ξ，η)|exp[jφ(ξ，η)(n)]＝FP{f(x，y))exp[jφ(x，y)(n-1)]}(8)
Using the digital holographic image as the amplitude of the output object light function, using the intermediate phase function phi of the observation plane (ξ)(n)For the phase function, inverse fractional Fourier transform is performed to obtain an intermediate phase function phi (x, y) of the object plane(n)，
T(n)(x，y)＝|T(n)(x，y)|exp[jφ(x，y)(n)]＝IFP{g(ξ，η)exp[jφ(ξ，η)(n)]} (9)
Calculating the amplitude | Q of the intermediate output objective function(n)(ξ) | and the root mean square error MSE of the digital hologram:
wherein N isx、NyThe number of pixel points of the digital hologram/original carrier image in the x direction and the y direction respectively, i is more than or equal to 1 and is more than or equal to Nx，1≤k≤Ny；
Judging whether the root mean square error is smaller than a preset error threshold value or not according to the root mean square error, if so, judging the intermediate phase function phi (x, y)(n)And if not, recalculating the intermediate phase function according to the formulas (8) to (10), and judging whether the intermediate phase function meets the constraint condition equation.
An embodiment of the present invention further provides a digital watermark authentication apparatus, including:
an image embedding module for generating a carrier image in which a watermark information image is embedded, the image embedding module comprising:
the digital hologram generating module is used for generating a digital hologram according to the watermark information image;
the image synthesis module is used for processing and generating the carrier image embedded with the watermark information image according to the digital hologram and the original carrier image, and comprises:
and establishing a constraint condition equation by taking the original carrier image as the amplitude of an input object light function of the front focal plane of the lens and the digital hologram as an output object light function of the rear focal plane:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η)
wherein f (x, y) is an original carrier image, g (ξ) is the digital hologram, phi (x, y) is a phase function to be solved and meeting the constraint condition equation, and j is a unit imaginary number;
calculating and solving a phase function meeting the constraint condition equation by using fractional Fourier transform;
obtaining a carrier image I (x, y) of the embedded watermark information image according to the phase function meeting the constraint condition equation:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)]
wherein, phi (x, y)(n)To satisfy the phase function of the constraint equation.
Optionally, the apparatus further comprises:
a password determination module: for determining an extraction password for extracting the digital hologram, comprising:
and performing singular value decomposition on the phase function meeting the constraint condition equation to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm to obtain an encryption processing result D ', and taking the D' as the extracted password.
Optionally, the apparatus further comprises:
the image extraction module is used for extracting the digital hologram according to the original carrier image and the extraction password, and comprises:
decrypting the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;
reconstructing to obtain the phase function meeting the constraint condition equation by using the singular value matrix D and the two unitary matrices U and V;
calculating the digital hologram g (ξ) by using the original carrier image and a phase function satisfying a constraint condition equation:
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}
optionally, the apparatus further comprises:
the watermark reconstruction module is used for reconstructing a watermark information image based on the extracted digital hologram, and comprises:
wherein IFn denotes the inverse fresnel diffraction integral transformation, O (x, y) denotes the reconstructed watermark information image, O (ξ) denotes the light field distribution of the watermark information image on the observation plane, x and y denote the coordinates of the pixel points of O (x, y) on the object plane, ξ denotes the coordinates of the pixel points of O (ξ) on the observation plane, z denotes the distance between the object plane and the observation plane, λ denotes the wavelength of light, and k denotes 2 pi/λ denotes the wave number.
Optionally, the method for calculating and solving the phase function satisfying the constraint equation by using the fractional fourier transform includes:
calculating an intermediate output object light function Q by using the original carrier image as the amplitude of the input object light function(n)(ξ，η)，Q(n)(ξ) has an amplitude of | Q(n)(ξ) |, the intermediate phase function of the observation plane is phi (ξ)(n)，
Q(n)(ξ，η)＝|Q(n)((ξ，η)|exp[jφ(ξ，η)(n)]＝FP{f(x，y))exp[jφ(x，y)(n-1)]} (8)
Using the digital holographic image as the amplitude of the output object light function, using the intermediate phase function phi of the observation plane (ξ)(n)For the phase function, inverse fractional Fourier transform is performed to obtain an intermediate phase function phi (x, y) of the object plane(n)，
T(n)(x，y)＝|T(n)(x，y)|exp[jφ(x，y)(n)]＝IFP{g(ξ，η)exp[jφ(ξ，η)(n)]} (9)
Calculating the amplitude | Q of the intermediate output objective function(n)(ξ) | and the root mean square error MSE of the digital hologram:
wherein N isx、NyThe number of pixel points of the digital hologram/original carrier image in the x direction and the y direction respectively, i is more than or equal to 1 and is more than or equal to Nx，1≤k≤Ny；
Judging whether the root mean square error is smaller than a preset error threshold value or not according to the root mean square error, if so, judging the intermediate phase function phi (x, y)(n)Satisfying the constraint condition equation, if not, according to the formulas (8) - (10), recalculating the intermediate phase functionCounting, and judging whether the intermediate phase function meets the constraint condition equation.
As can be seen from the above description, the digital watermark authentication method and apparatus provided by the present invention have the following advantages:
1) according to the method and the device, the watermark information image can be recovered only if the original carrier image and the phase function information meeting the constraint condition are simultaneously provided; because the reconstructed watermark image information is realized based on the original carrier image and the phase function and is irrelevant to the carrier image embedded with the watermark information image, the carrier image embedded with the watermark information image does not influence the watermark image information after being printed, scanned and copied, so that the carrier image embedded with the watermark information image has strong anti-printing property;
2) according to the method and the device, the watermark information image is processed by utilizing the holographic watermark technology to generate the digital hologram, so that the cracking difficulty is greatly increased, and the watermark information image cannot be reconstructed and recovered even if the phase function and the password are obtained under the condition of no holographic manufacturing parameters and methods; meanwhile, a symmetric encryption algorithm (such as SM4 national encryption algorithm) is used for encrypting the phase function, so that multiple encryption of the watermark information image is realized, and the cracking difficulty is further improved;
3) according to the method and the device, the information hiding and extraction of the multimedia information in the carrier image are realized, the application range is greatly expanded, the authenticity, diversity and non-replicability of the watermark information can be ensured, and the effective authentication of the authenticity of the watermark information is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for generating a carrier image embedded with a watermark information image according to an embodiment of the present invention;
fig. 2 is a schematic flowchart of a method for reconstructing a watermark information image according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of an apparatus for generating a carrier image embedded with a watermark information image according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of an apparatus for reconstructing a watermark information image according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
Fig. 1 is a schematic flow chart of a method for generating a carrier image with an embedded watermark information image according to an embodiment of the present invention, and as shown in the drawing, the digital watermark authentication method provided in the embodiment of the present invention includes generating a carrier image with an embedded watermark information image, and the method includes:
s10: generating a digital hologram according to the watermark information image;
the digital hologram is a pattern of interference fringes of object light waves and reference light recorded by a hologram plate. And taking the hidden watermark information image as an object light source, calculating by utilizing Fresnel diffraction integral transformation to obtain object light distribution, and calculating with reference light to form a digital hologram.
Fresnel diffraction integral transform into:
where Fn represents fresnel diffraction integral, O (x, y) and O (ξ) are light wave distribution functions of an object plane and an observation plane, respectively, j is a unit imaginary number, x and y are coordinates of a pixel point of object light (watermark information image) O (x, y) on the object plane, ξ are coordinates (also called spatial frequency domain coordinates) of a pixel point of object light diffracted light O (ξ) on the observation plane, z is a distance between the object plane and the observation plane, λ is a wavelength of light, k is 2 pi/λ is a wave number, and diffraction field distribution of light wave (called fresnel diffraction field) can be calculated by equation (1).
The object light distribution of the watermark information image on the observation plane is calculated by utilizing Fresnel diffraction integral transformation, and the object light distribution is as follows:
wherein, O0(x, y) is the amplitude of the object light, ψ (x, y) is the phase function of the object light at the object plane (when the watermark information is an image ψ (x, y) ═ 0), O (ξ) is the object light diffraction field distribution of the object light at the observation plane,is a function of the phase of the object light in the observation plane.
The reference light (parallel light) was chosen as:
R(ξ，η)＝R0exp[2πjαξ](3)
wherein R (ξ) is the light distribution of the reference light in the observation plane, R0For reference light amplitude, α is for parallel light transmissionThe direction of the broadcast.
Superposing the object light and the reference light of the observation plane to obtain the intensity distribution of the digital hologram as follows:
H(ξ，η)＝|R(ξ，η)|2+|O(ξ，η)|2+R*(ξ，η)O(ξ，η)+R(ξ，η)O*(ξ，η) (4)
wherein, R (ξ) and O (ξ) are the optical field distributions of the object light O (x, y) and the reference light on the observation plane, respectively, and the superscript denotes the complex conjugate number.
Recording:
g (ξ) is a real number, i.e., g (ξ) ═ g (ξ) |, and g (ξ) is the distribution of the light intensity (interference fringes) of the object light and the reference light in the observation plane, which is called a digital hologram.
In the embodiment of the invention, the watermark information image is an image generated according to multimedia information, the multimedia information comprises characters, audio, images and the like, and if the multimedia information is the characters or the audio, the multimedia information is processed to generate a corresponding watermark information image.
According to a fractal Fourier transform:
wherein, x and y are respectively coordinates of pixel points of an image M (x, y), M (ξ) is called fractional Fourier spectrum of M (x, y), ξ is respectively space frequency domain coordinates (or coordinates of observation plane pixels) of the fractional Fourier spectrum M (ξ), pi is circumferential ratio, phi is pi p/2, and p is order of fractional Fourier transform.
The specific method for embedding the digital hologram into the original carrier image and generating the carrier image embedded with the watermark information image is as follows:
s11: the amplitude of an input object light function taking an original carrier image as a front focal plane of a lens and an output object light function taking a digital hologram as a rear focal plane are used for establishing the following constraint condition equation:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η) (7)
where f (x, y) is the original carrier image, g (ξ) is the digital hologram, and φ (x, y) is the phase function to be solved that satisfies the constraint.
S12: solving a phase function phi (x, y) satisfying the constraint condition by utilizing fractional Fourier transform calculation;
the specific process is as follows:
s120: calculating intermediate output object light function Q by using original carrier image f (x, y) as amplitude of input object light function(n)(ξ，η)：
Q(n)(ξ，η)＝|Q(n)((ξ，η)|exp[jφ(ξ，η)(n)]＝FP{f(x，y))exp[jφ(x，y)(n-1)]} (8)
Wherein n is the number of iterations. Obtaining an intermediate output objective optical function Q through the calculation of the formula (8)(n)(ξ) having an amplitude of | Q(n)(ξ) |, the intermediate phase function of the corresponding observation plane is phi (ξ)(n)。
For the first iteration, n is 1, and a two-dimensional random function is used to generate an initial phase function phi (x, y)(n)Obtaining an intermediate output objective function Q(1)(ξ，η)。
Intermediate phase function phi (ξ) calculated by formula (8) using digital hologram g (ξ) as the amplitude of the output object light function(n)For the phase function, inverse fractal Fourier transform calculation is carried out to obtain:
T(n)(x，y)＝|T(n)(x，y)|exp[jφ(x，y)(n)]＝IFP{g(ξ，η)exp[jφ(ξ，η)(n)]} (9)
wherein, IFPExpressing fractional dimension inverse Fourier transform, taking p in the formula (6) as-p to obtain an intermediate phase function phi (x, y) of the object plane through the calculation of the formula (9)(n)。
S121: calculating amplitude | Q of intermediate output objective function(n)Root mean square error MSE of (ξ) | and digital hologram | g (ξ) |:
wherein N isx、NyRespectively the number of the pixel points of the digital hologram/the original carrier image (the number of the pixel points of the two images is the same) in the x direction and the y direction, i is more than or equal to 1 and less than or equal to Nx，1≤k≤Ny。
S122: according to the root mean square error obtained by calculation, judging the currently calculated intermediate phase function phi (x, y)(n)Whether the constraint condition is met or not, if so, the currently calculated intermediate phase function phi (x, y)(n)And (4) determining the phase function which is in accordance with the constraint condition equation shown in the formula (7), if the constraint condition is not satisfied, executing steps S1110-S1112, recalculating the determined intermediate phase function, and judging whether the constraint condition is satisfied.
In the embodiment of the invention, if the root mean square error MSE is smaller than the set error threshold, the current calculated intermediate phase function phi (x, y) is determined(n)The constraint condition shown in the formula (7) is met, and the value of the error threshold is 0.05.
S13: and obtaining the carrier image embedded with the watermark information image according to the phase function meeting the constraint condition.
According to the determined phase function phi (x, y) satisfying the constraint condition equation shown in the formula (7)(n)And obtaining a complex wavefront function I (x, y) of the image with the hidden watermark information as follows:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)](11)
a complex wavefront function I (x, y) shown in formula (11) is a carrier image embedded with a watermark information image, the carrier image embedded with the digital hologram I (x, y) includes all information of an original carrier image and a digital hologram, the amplitude of the carrier image is an original carrier image f (x, y), and as shown in formula (12), a fractional fourier transform of the complex wavefront function I (x, y) is a digital hologram g (ξ):
|FP{f(x，y)exp[jφ(x，y)(n)]}|＝g(ξ，η) (12)
fig. 2 is a schematic flow chart of a method for reconstructing a watermark information image according to an embodiment of the present invention, as shown in the figure, the digital watermark authentication method provided in the embodiment of the present invention includes extracting watermark image information, and the method includes:
s20: determining an extraction password for extracting the digital hologram;
based on a phase function phi (x, y) meeting a constraint(n)And generating an extraction password for extracting the digital hologram. The method specifically comprises the following steps:
the phase function phi (x, y) to be qualified(n)And performing singular value decomposition to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm, and taking an encryption processing result D' as an extraction password for extracting the digital hologram.
S21: extracting a digital hologram according to the original carrier image and the extraction password;
according to the original carrier image and the extraction password D', the method for extracting the digital hologram comprises the following steps:
s210: decrypting the extracted password D' by using a symmetric key based on a symmetric encryption algorithm to generate a singular value matrix D;
s211: reconstructing by using a singular value matrix D and two unitary matrices U and V to obtain a phase function phi (x, y)(n)；
S212: using the original carrier image f (x, y) and the phase function phi(n)(x, y), computing the digital hologram g (ξ):
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}
s22: and reconstructing the watermark information image based on the digital hologram.
Reconstructing a watermark information image by utilizing holographic inverse transformation, specifically:
multiplying the reference light (called the reproduction light) by the digital hologram g (ξ) yields:
wherein, is constant, in the formula (15), if neglectedDoes not affect the optical field distribution O (ξ) O of object light on the observation plane*(ξ) is a conjugate image of O (ξ), and when the original object plane is selected as a diffraction (imaging) plane, that is, the Fresnel diffraction integral inverse transformation is performed, a reconstructed watermark information image O (x, y) of the digital hologram is obtained, wherein R in the formula (15) is2(ξ，η)O*The inverse transformation of (ξ) generates a background field distribution with a distribution close to uniform distribution by the Fresnel diffraction integral of the original object plane, and the quality of the reconstructed watermark information image is not affected basically, therefore, the inverse transformation of the Fresnel diffraction integral is carried out on O (ξ), and the following results are obtained:
here, IFn denotes the inverse fresnel diffraction integral transform, and O (x, y) is the reconstructed watermark information image. Wherein, selecting reference light in different directions can reconstruct to obtain different watermark image information, and selecting reference light as R*(ξ) the reconstructed watermark information image is O*(ξ，η)
Fig. 3 is a schematic structural diagram of an apparatus for generating a carrier image embedded with a watermark information image according to an embodiment of the present invention. As shown in the drawings, the digital watermark authentication apparatus provided in the embodiment of the present invention includes:
the image embedding module is used for generating a carrier image embedded with the watermark information image;
the image embedding module includes:
the digital hologram generating module is used for generating a digital hologram according to the watermark information image;
the object light distribution of the watermark information image on the observation plane is calculated by utilizing Fresnel diffraction integral transformation, and the object light distribution is as follows:
wherein, O0(x, y) is the amplitude of the object light, ψ (x, y) is the phase function of the object light at the object plane, O (ξ) is the object light diffraction field distribution of the object light at the observation plane,is a function of the phase of the object light in the observation plane.
g (ξ) is a real number, i.e., g (ξ) ═ g (ξ) |, and g (ξ) is the distribution of the light intensity (interference fringes) of the object light and the reference light in the observation plane, which is called a digital hologram.
And the image synthesis module is used for processing and generating the carrier image embedded with the watermark information image according to the digital hologram and the original carrier image.
The amplitude of an input object light function taking an original carrier image as a front focal plane of a lens and an output object light function taking a digital hologram as a rear focal plane are used for establishing the following constraint condition equation:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η) (7)
where f (x, y) is the original carrier image, g (ξ) is the digital hologram, and φ (x, y) is the phase function to be solved.
According to the steps S1110-S1112, the phase function phi (x, y) meeting the constraint condition is calculated and solved by utilizing the fractional Fourier transform;
obtaining a carrier image I (x, y) of the embedded watermark information image according to the phase function meeting the constraint condition:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)](11)
the carrier image I (x, y) embedded with the watermark information image contains all information of the original carrier image and the digital hologram, the amplitude of the carrier image is the original carrier image f (x, y), as shown in formula (14), the fractional fourier transform of the carrier image I (x, y) is the digital hologram g (ξ), the digital hologram contains all information of the watermark information image,
|FP{f(x，y)exp[jφ(x，y)(n)]}|＝g(ξ，η) (12)
fig. 4 is a schematic structural diagram of an apparatus for reconstructing a watermark information image according to an embodiment of the present invention, and as shown in the drawing, the digital watermark authentication apparatus further includes:
and the watermark extraction module is used for extracting the watermark information image.
The watermark extraction module comprises:
a password determination module: for determining an extraction password for extracting the digital hologram;
the phase function phi (x, y) to be qualified(n)And performing singular value decomposition to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm, and taking an encryption processing result D' as an extraction password for extracting the digital hologram.
The image extraction module is used for extracting the digital hologram according to the original carrier image and the extracted password;
decrypting the extracted password D' by using a symmetric key based on a symmetric encryption algorithm to generate a singular value matrix D; reconstructing by using a singular value matrix D and two unitary matrices U and V to obtain a phase function phi (x, y)(n)(ii) a Using the original carrier image f (x, y) and the phase function phi(n)(x, y), computing the digital hologram g (ξ):
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}
and the watermark reconstruction module is used for reconstructing a watermark information image based on the extracted digital hologram.
Reconstructing the watermark information image by utilizing holographic inverse transformation,
here, IFn denotes the inverse fresnel diffraction integral transform, and O (x, y) is the reconstructed watermark information image.
The apparatus of the foregoing embodiment is used to implement the corresponding method in the foregoing embodiment, and has the beneficial effects of the corresponding method embodiment, which are not described herein again.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
In addition, well known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown within the provided figures for simplicity of illustration and discussion, and so as not to obscure the invention. Furthermore, devices may be shown in block diagram form in order to avoid obscuring the invention, and also in view of the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform within which the present invention is to be implemented (i.e., specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the invention, it should be apparent to one skilled in the art that the invention can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative instead of restrictive.
While the present invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic ram (dram)) may use the discussed embodiments.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A digital watermark authentication method, comprising:
generating a carrier image embedded with a watermark information image, comprising:
generating a digital hologram according to the watermark information image;
and establishing a constraint condition equation by taking the original carrier image as the amplitude of an input object light function of the front focal plane of the lens and the digital hologram as an output object light function of the rear focal plane:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η)
wherein f (x, y) is an original carrier image, g (ξ) is the digital hologram, phi (x, y) is a phase function to be solved and meeting the constraint condition equation, and j is a unit imaginary number;
calculating and solving a phase function meeting the constraint condition equation by using fractional Fourier transform;
obtaining a carrier image I (x, y) of the embedded watermark information image according to the phase function meeting the constraint condition equation:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)]
wherein, phi (x, y)(n)To satisfy the phase function of the constraint equation.
2. The method of claim 1, further comprising:
determining an extraction password for extracting the digital hologram, comprising:
and performing singular value decomposition on the phase function meeting the constraint condition equation to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm to obtain an encryption processing result D ', and taking the D' as the extracted password.
3. The method of claim 2, further comprising:
extracting the digital hologram according to the original carrier image and the extraction password, comprising:
decrypting the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;
reconstructing to obtain the phase function meeting the constraint condition equation by using the singular value matrix D and the two unitary matrices U and V;
calculating the digital hologram g (ξ) by using the original carrier image and a phase function satisfying a constraint condition equation:
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}。
4. the method of claim 3, further comprising:
reconstructing the watermark information image based on the digital hologram,
wherein IFn denotes the inverse fresnel diffraction integral transformation, O (x, y) denotes the reconstructed watermark information image, O (ξ) denotes the light field distribution of the watermark information image on the observation plane, x and y denote the coordinates of the pixel points of O (x, y) on the object plane, ξ denotes the coordinates of the pixel points of O (ξ) on the observation plane, z denotes the distance between the object plane and the observation plane, λ denotes the wavelength of light, and k denotes 2 pi/λ denotes the wave number.
5. The method of claim 1, wherein the method of solving the phase function satisfying the constraint equations using a fractional Fourier transform computation comprises:
calculating an intermediate output object light function Q by using the original carrier image as the amplitude of the input object light function(n)(ξ，η)，Q(n)(ξ) has an amplitude of | Q(n)(ξ) |, the intermediate phase function of the observation plane is phi (ξ)(n)，
Q(n)(ξ，η)＝|Q(n)((ξ，η)|exp[jφ(ξ，η)(n)]＝FP{f(x，y))exp[jφ(x，y)(n-1)]} (8)
Using the digital holographic image as the amplitude of the output object light function, using the intermediate phase function phi of the observation plane (ξ)(n)For the phase function, inverse fractional Fourier transform is performed to obtain an intermediate phase function phi (x, y) of the object plane(n)，
T(n)(x，y)＝|T(n)(x，y)|exp[jφ(x，y)(n)]＝IFP{g(ξ，η)exp[jφ(ξ，η)(n)]} (9)
Calculating the amplitude | Q of the intermediate output objective function(n)(ξ) | and the root mean square error MSE of the digital hologram:
wherein N isx、NyThe number of pixel points of the digital hologram/original carrier image in the x direction and the y direction respectively, i is more than or equal to 1 and is more than or equal to Nx，1≤k≤Ny；
Judging whether the root mean square error is smaller than a preset error threshold value or not according to the root mean square error, if so, judging the intermediate phase function phi (x, y)(n)And if not, recalculating the intermediate phase function according to the formulas (8) to (10), and judging whether the intermediate phase function meets the constraint condition equation.
6. A digital watermark authentication apparatus, comprising:
an image embedding module for generating a carrier image in which a watermark information image is embedded, the image embedding module comprising:
the digital hologram generating module is used for generating a digital hologram according to the watermark information image;
the image synthesis module is used for processing and generating the carrier image embedded with the watermark information image according to the digital hologram and the original carrier image, and comprises:
and establishing a constraint condition equation by taking the original carrier image as the amplitude of an input object light function of the front focal plane of the lens and the digital hologram as an output object light function of the rear focal plane:
|FP{f(x，y)exp[jφ(x，y)]}|＝g(ξ，η)
wherein f (x, y) is an original carrier image, g (ξ) is the digital hologram, phi (x, y) is a phase function to be solved and meeting the constraint condition equation, and j is a unit imaginary number;
calculating and solving a phase function meeting the constraint condition equation by using fractional Fourier transform;
obtaining a carrier image I (x, y) of the embedded watermark information image according to the phase function meeting the constraint condition equation:
I(x，y)＝f(x，y)exp[jφ(x，y)(n)]
wherein, phi (x, y)(n)To satisfy the phase function of the constraint equation.
7. The apparatus of claim 6, further comprising:
a password determination module: for determining an extraction password for extracting the digital hologram, comprising:
and performing singular value decomposition on the phase function meeting the constraint condition equation to obtain a singular value matrix D and two unitary matrices U and V, encrypting the singular value matrix D by using a symmetric key based on a symmetric encryption algorithm to obtain an encryption processing result D ', and taking the D' as the extracted password.
8. The apparatus of claim 7, further comprising:
the image extraction module is used for extracting the digital hologram according to the original carrier image and the extraction password, and comprises:
decrypting the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;
reconstructing to obtain the phase function meeting the constraint condition equation by using the singular value matrix D and the two unitary matrices U and V;
calculating the digital hologram g (ξ) by using the original carrier image and a phase function satisfying a constraint condition equation:
g(ξ，η)＝Fp{f(x，y)exp[jφ(x，y)(n)]}。
9. the apparatus of claim 8, further comprising:
the watermark reconstruction module is used for reconstructing a watermark information image based on the extracted digital hologram, and comprises:
wherein IFn denotes the inverse fresnel diffraction integral transformation, O (x, y) denotes the reconstructed watermark information image, O (ξ) denotes the light field distribution of the watermark information image on the observation plane, x and y denote the coordinates of the pixel points of O (x, y) on the object plane, ξ denotes the coordinates of the pixel points of O (ξ) on the observation plane, z denotes the distance between the object plane and the observation plane, λ denotes the wavelength of light, and k denotes 2 pi/λ denotes the wave number.
10. The apparatus of claim 6,
the method for solving the phase function which meets the constraint condition equation by utilizing the fractional Fourier transform calculation comprises the following steps:
calculating an intermediate output object light function Q by using the original carrier image as the amplitude of the input object light function(n)(ξ，η)，Q(n)(ξ) has an amplitude of | Q(n)(ξ) |, the intermediate phase function of the observation plane is phi (ξ)(n)，
Q(n)(ξ，η)＝|Q(n)((ξ，η)|exp[jφ(ξ，η)(n)]＝FP{f(x，y))exp[jφ(x，y)(n-1)]} (8)
Using the digital holographic image as the amplitude of the output object light function, using the intermediate phase function phi of the observation plane (ξ)(n)For the phase function, inverse fractional Fourier transform is performed to obtain an intermediate phase function phi (x, y) of the object plane(n)，
T(n)(x，y)＝|T(n)(x，y)|exp[jφ(x，y)(n)]＝IFP{g(ξ，η)exp[jφ(ξ，η)(n)]} (9)
Calculating the amplitude | Q of the intermediate output objective function(n)(ξ) | and the root mean square error MSE of the digital hologram:
wherein N isx、NyThe number of pixel points of the digital hologram/original carrier image in the x direction and the y direction respectively, i is more than or equal to 1 and is more than or equal to Nx，1≤k≤Ny；
Judging whether the root mean square error is smaller than a preset error threshold value or not according to the root mean square error, if so, judging the intermediate phase function phi (x, y)(n)And if not, recalculating the intermediate phase function according to the formulas (8) to (10), and judging whether the intermediate phase function meets the constraint condition equation.
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