CN109840874A - A kind of digital watermarking authentication method and device - Google Patents

Abstract

The invention discloses a digital watermark authentication method and device, comprising: generating a carrier image embedded with a watermark information image, comprising: generating a digital hologram according to the watermark information image; taking the original carrier image as an input object light function of the front focal plane of a lens Taking the digital hologram as the output object light function of the back focal plane, establish the constraint equation including the original carrier image, digital hologram, and phase function, and use the fractal Fourier transform to calculate and solve the phase function that satisfies the constraint equation. , obtain the carrier image embedded in the watermark information image according to the phase function satisfying the constraint equation; it also includes determining the extraction password for extracting the digital hologram, extracting the digital hologram according to the original carrier image and the extraction password, and based on the digital hologram, Reconstruct the watermark information image. The invention provides a digital watermark authentication method and device with good anti-print performance.

Description

A digital watermark authentication method and device

technical field

The invention relates to the technical field of information security, in particular to a digital watermark authentication method and device.

Background technique

Digital watermarking technology directly embeds the watermark information in the carrier information or expresses it indirectly, which does not affect the use value of the carrier information, and is not easy to be detected and modified again. Digital watermarking technology has been applied in the field of multimedia information security research. At present, in the field of printing, after the image carrier information embedded with the watermark information is printed and scanned, there is a problem that the watermark information is lost. In recent years, information optical holography technology has been applied to information hiding and digital watermarking due to its multi-dimensional, large capacity, high design freedom, high robustness, hard to tear, natural parallelism, and hard to crack. The field has broad application prospects.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a digital watermark authentication method and device, which have good anti-printing performance.

Based on the above purpose, the present invention provides a digital watermark authentication method, comprising:

Generate carrier images with embedded watermark information images, including:

generating a digital hologram according to the watermark information image;

Taking the original carrier image as the amplitude of the input object light function of the front focal plane of the lens, and taking the digital hologram as the output object light function of the back focal plane, the constraint equation is established:

|F ^P {f(x,y)exp[jφ(x,y)]}|=g(ξ,η)

Wherein, f(x, y) is the original carrier image, g(ξ, η) is the digital hologram, φ(x, y) is the phase function to be solved that satisfies the constraint equation, and j is a unit imaginary number ;

Use fractal Fourier transform to calculate and solve the phase function that satisfies the constraint equation;

According to the phase function satisfying the constraint equation, the carrier image I(x, y) of the embedded watermark information image is obtained:

I(x, y)=f(x, y) exp[jφ(x, y) ⁽ⁿ⁾ ]

Wherein, φ(x, y) ⁽ⁿ⁾ is the phase function satisfying the constraint equation.

Optionally, the method further includes:

Determine an extraction password for extracting the digital hologram, including:

Perform singular value decomposition on the phase function satisfying the constraint equation to obtain a singular value matrix D and two unitary matrices U and V, and encrypt the singular value matrix D with a symmetric key based on a symmetric encryption algorithm to obtain an encrypted The result D' is processed, and D' is used as the extraction password.

Optionally, the method further includes:

Extracting the digital hologram according to the original carrier image and the extraction password, including:

Decrypt the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;

Using the singular value matrix D and the two unitary matrices U and V, reconstruct the phase function that satisfies the constraint equation;

Using the original carrier image and the phase function satisfying the constraint equation, the digital hologram g(ξ, η) is obtained by calculation:

g(ξ, η)=F ^p {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}

Optionally, the method further includes:

reconstructing the watermark information image based on the digital hologram,

Among them, IFn represents the inverse Fresnel diffraction integral transform, O(x, y) is the reconstructed watermark information image, O(ξ, η) is the light field distribution of the watermark information image on the observation plane, x and y are respectively The coordinates of the pixels of O(x, y) on the object plane, ξ, η are the coordinates of the pixels of O(ξ, η) on the observation plane, z is the distance between the object plane and the observation plane, λ is the light The wavelength of , k=2π/λ is the wave number.

Optionally, the method for calculating and solving the phase function satisfying the constraint equation by using fractal Fourier transform includes:

Taking the original carrier image as the amplitude of the input object light function, calculate the intermediate output object light function Q ⁽ⁿ⁾ (ξ, η), and the amplitude of Q ⁽ⁿ⁾ (ξ, η) is |Q ⁽ⁿ⁾ (ξ, η, η)|, the intermediate phase function of the observation plane is φ(ξ, η) ⁽ⁿ⁾ ,

Q ⁽ⁿ⁾ (ξ, η)=|Q ⁽ⁿ⁾ ((ξ, η)|exp[jφ(ξ, η) ⁽ⁿ⁾ ]=F ^P {f(x, y))exp[jφ(x , y) ^(n-1) ]}(8)

Taking the digital holographic image as the amplitude of the output object light function, and taking the intermediate phase function φ(ξ, η) ⁽ⁿ⁾ of the observation plane as the phase function, perform inverse fractal Fourier transform to obtain the middle of the object plane. Phase function φ(x, y) ⁽ⁿ⁾ ,

T ⁽ⁿ⁾ (x, y)=|T ⁽ⁿ⁾ (x, y)|exp[jφ(x, y) ⁽ⁿ⁾ ]=IF ^P {g(ξ, η)exp[jφ(ξ, η ) ⁽ⁿ⁾ ]} (9)

Calculate the amplitude |Q ⁽ⁿ⁾ (ξ,η)| of the intermediate output object light function and the root mean square error MSE of the digital hologram:

Wherein, N _x and N _y are the number of pixels in the x and y directions of the digital hologram/original carrier image, respectively, 1≤i≤N _x , 1≤k≤N _y ;

According to the root mean square error, it is judged whether the root mean square error is smaller than a preset error threshold, if so, the intermediate phase function φ(x, y) ⁽ⁿ⁾ satisfies the constraint equation, if not, according to Formulas (8)-(10), recalculate the intermediate phase function, and determine whether the intermediate phase function satisfies the constraint condition equation.

The embodiment of the present invention also provides a digital watermark authentication device, including:

An image embedding module for generating a carrier image embedded with a watermark information image, and the image embedding module includes:

a digital hologram generation module, configured to generate a digital hologram according to the watermark information image;

An image synthesis module, configured to process and generate the carrier image embedded in the watermark information image according to the digital hologram and the original carrier image, including:

Taking the original carrier image as the amplitude of the input object light function of the front focal plane of the lens, and taking the digital hologram as the output object light function of the back focal plane, the constraint equation is established:

|F ^P {f(x,y)exp[jφ(x,y)]}|=g(ξ,η)

Wherein, f(x, y) is the original carrier image, g(ξ, η) is the digital hologram, φ(x, y) is the phase function to be solved that satisfies the constraint equation, and j is a unit imaginary number ;

Use fractal Fourier transform to calculate and solve the phase function that satisfies the constraint equation;

According to the phase function satisfying the constraint equation, the carrier image I(x, y) of the embedded watermark information image is obtained:

I(x, y)=f(x, y) exp[jφ(x, y) ⁽ⁿ⁾ ]

Wherein, φ(x, y) ⁽ⁿ⁾ is the phase function satisfying the constraint equation.

Optionally, the device further includes:

Password determination module: used to determine the extraction password for extracting the digital hologram, including:

Perform singular value decomposition on the phase function satisfying the constraint equation to obtain a singular value matrix D and two unitary matrices U and V, and encrypt the singular value matrix D with a symmetric key based on a symmetric encryption algorithm to obtain an encrypted The result D' is processed, and D' is used as the extraction password.

Optionally, the device further includes:

An image extraction module for extracting the digital hologram according to the original carrier image and the extraction password, including:

Decrypt the extracted password by using the symmetric key based on the symmetric encryption algorithm to generate the singular value matrix D;

Using the singular value matrix D and the two unitary matrices U and V, reconstruct the phase function that satisfies the constraint equation;

Using the original carrier image and the phase function satisfying the constraint equation, the digital hologram g(ξ, η) is obtained by calculation:

g(ξ, η)=F ^p {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}

Optionally, the device further includes:

The watermark reconstruction module is used to reconstruct the watermark information image based on the extracted digital hologram, including:

Among them, IFn represents the inverse Fresnel diffraction integral transform, O(x, y) is the reconstructed watermark information image, O(ξ, η) is the light field distribution of the watermark information image on the observation plane, x and y are respectively The coordinates of the pixels of O(x, y) on the object plane, ξ, η are the coordinates of the pixels of O(ξ, η) on the observation plane, z is the distance between the object plane and the observation plane, λ is the light The wavelength of , k=2π/λ is the wave number.

Optionally, the method for calculating and solving the phase function satisfying the constraint equation by using fractal Fourier transform includes:

Taking the original carrier image as the amplitude of the input object light function, calculate the intermediate output object light function Q ⁽ⁿ⁾ (ξ, η), and the amplitude of Q ⁽ⁿ⁾ (ξ, η) is |Q ⁽ⁿ⁾ (ξ, η, η)|, the intermediate phase function of the observation plane is φ(ξ, η) ⁽ⁿ⁾ ,

Q ⁽ⁿ⁾ (ξ, η)=|Q ⁽ⁿ⁾ ((ξ, η)|exp[jφ(ξ, η) ⁽ⁿ⁾ ]=F ^P {f(x, y))exp[jφ(x , y) ^(n-1) ]} (8)

Taking the digital holographic image as the amplitude of the output object light function, and taking the intermediate phase function φ(ξ, η) ⁽ⁿ⁾ of the observation plane as the phase function, perform inverse fractal Fourier transform to obtain the middle of the object plane. Phase function φ(x, y) ⁽ⁿ⁾ ,

T ⁽ⁿ⁾ (x, y)=|T ⁽ⁿ⁾ (x, y)|exp[jφ(x, y) ⁽ⁿ⁾ ]=IF ^P {g(ξ, η)exp[jφ(ξ, η ) ⁽ⁿ⁾ ]} (9)

Calculate the amplitude |Q ⁽ⁿ⁾ (ξ,η)| of the intermediate output object light function and the root mean square error MSE of the digital hologram:

Wherein, N _x and N _y are the number of pixels in the x and y directions of the digital hologram/original carrier image, respectively, 1≤i≤N _x , 1≤k≤N _y ;

According to the root mean square error, it is judged whether the root mean square error is smaller than a preset error threshold, if so, the intermediate phase function φ(x, y) ⁽ⁿ⁾ satisfies the constraint equation, if not, according to Formulas (8)-(10), recalculate the intermediate phase function, and determine whether the intermediate phase function satisfies the constraint condition equation.

As can be seen from the above, the digital watermark authentication method and device provided by the present invention have the following advantages:

1) According to the method and the device of the present invention, the watermark information image can be recovered only by having the original carrier image and the phase function information satisfying the constraint conditions at the same time; because the reconstructed watermark image information is realized based on the original carrier image and the phase function, and the watermark information is embedded. The carrier image of the image is irrelevant. Therefore, the carrier image embedded with the watermark information image will not affect the watermark image information after printing, scanning and copying, so that the carrier image embedded with the watermark information image has strong anti-printing characteristics;

2) According to the method and the device of the present invention, the watermark information image is processed by the holographic watermark technology to generate a digital hologram, which greatly increases the difficulty of cracking. The watermark information image cannot be reconstructed and restored; at the same time, the phase function is encrypted by using a symmetric encryption algorithm (such as the SM4 national secret algorithm), which realizes multiple encryption of the watermark information image and further improves the difficulty of cracking;

3) According to the method and device of the present invention, the information hiding and extraction including multimedia information in the carrier image is realized, the scope of application is greatly expanded, the authenticity, diversity and non-replicability of the watermark information can be ensured, and the authenticity of the watermark information can be realized. Fake valid authentication.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

1 is a schematic flowchart of a method for generating a carrier image embedded in a watermark information image according to an embodiment of the present invention;

2 is a schematic flowchart of a method for reconstructing a watermark information image according to an embodiment of the present invention;

3 is a schematic structural diagram of an apparatus for generating a carrier image embedded in 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 ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are for the purpose of distinguishing two entities with the same name but not the same or non-identical parameters. It can be seen that "first" and "second" It is only for the convenience of expression and should not be construed as a limitation to the embodiments of the present invention, and subsequent embodiments will not describe them one by one.

1 is a schematic flowchart of a method for generating a carrier image embedded in a watermark information image according to an embodiment of the present invention. As shown in the figure, a digital watermark authentication method provided by an embodiment of the present invention includes generating a carrier image embedded in a watermark information image, and the method includes:

S10: generate a digital hologram according to the watermark information image;

The digital hologram is the interference fringe pattern of the object light wave and the reference light recorded by the holographic plate. The hidden watermark information image is used as the crop light source to calculate the object light distribution by Fresnel diffraction integral transformation, and then calculate with the reference light to form a digital hologram.

The Fresnel diffraction integral transforms into:

Among them, Fn represents the Fresnel diffraction integral, O(x, y) and O(ξ, η) are the light wave distribution functions of the object plane and the observation plane, respectively; j is the unit imaginary number, and x and y are the object light (watermark information), respectively. image) O(x, y) coordinates of the pixel points on the object plane, ξ, η are the coordinates of the object light diffracted light O(ξ, η) on the observation plane pixel points (also called spatial frequency domain coordinates); z is The distance between the object plane and the observation plane; λ is the wavelength of light; k=2π/λ is the wave number. The diffraction field distribution of the light wave (called the Fresnel diffraction field) can be calculated using the formula (1).

Using the Fresnel diffraction integral transform to calculate the object light distribution of the watermark information image in the observation plane is:

Among them, O ₀ (x, y) is the amplitude of the object light, ψ(x, y) is the phase function of the object light in the object plane (if the watermark information is an image, ψ(x, y)=0), O(ξ , η) is the object light diffraction field distribution of the object light in the observation plane, is the phase function of the object light in the observation plane.

Select the reference light (parallel light) as:

R(ξ, η)=R ₀ exp[2πjαξ] (3)

Among them, R(ξ, η) is the light distribution of the reference light in the observation plane, R ₀ is the amplitude of the reference light, and α is the propagation direction of the parallel light.

By superimposing the object light on the observation plane and the reference light, the intensity distribution of the digital hologram is obtained as:

H(ξ, η)=|R(ξ, η)| ² +|O(ξ, η)| ² +R ^* (ξ, η)O(ξ, η)+R(ξ, η)O ^* ( ξ, η) (4)

Among them, R(ξ, η) and O(ξ, η) are the light field distributions of the object light O(x, y) and the reference light on the observation plane, respectively, and the superscript * indicates the complex conjugate number.

Record:

g(ξ, η) is a real number, that is, g(ξ, η)=|g(ξ, η)|, then g(ξ, η) is the light intensity (interference fringe) distribution of the object light and the reference light in the observation plane , known as a digital hologram.

In the embodiment of the present invention, the watermark information image is an image generated according to multimedia information, and the multimedia information includes text, audio, images, etc. If the multimedia information is text or audio, the multimedia information is processed to generate a corresponding watermark information image.

According to the fractal Fourier transform:

Among them, x and y are the coordinates of the pixel points of the image m(x, y) respectively, M(ξ, η) is called the fractal Fourier spectrum of m(x, y), ξ, η are the fractal Fourier spectrum, respectively The spatial frequency domain coordinates of the Liye spectrum M(ξ, η) (or the coordinates of the observation plane pixels); π is the pi, φ=πp/2, and p is the order of the fractal Fourier transform.

The specific method of embedding the digital hologram into the original carrier image and generating the carrier image embedded with the watermark information image is as follows:

S11: Taking the original carrier image as the amplitude of the input object light function of the front focal plane of the lens, and taking the digital hologram as the output object light function of the back focal plane, establish the following constraint equation:

|F ^P {f(x,y)exp[jφ(x,y)]}|=g(ξ,η) (7)

Among them, f(x, y) is the original carrier image, g(ξ, η) is the digital hologram, and φ(x, y) is the phase function to be solved that satisfies the constraints.

S12: Use the fractal Fourier transform to calculate and solve the phase function φ(x, y) that satisfies the constraint condition;

The specific process is:

S120: Taking the original carrier image f(x, y) as the amplitude of the input object light function, calculate the intermediate output object light function Q ⁽ⁿ⁾ (ξ, η):

Q ⁽ⁿ⁾ (ξ, η)=|Q ⁽ⁿ⁾ ((ξ, η)|exp[jφ(ξ, η) ⁽ⁿ⁾ ]=F ^P {f(x, y))exp[jφ(x , y) ^(n-1) ]} (8)

where n is the number of iterations. After the calculation of formula (8), the intermediate output object optical function Q ⁽ⁿ⁾ (ξ, η) is obtained, its amplitude is |Q ⁽ⁿ⁾ (ξ, η)|, and the corresponding intermediate phase function of the observation plane is φ( ξ, η) ⁽ⁿ⁾ .

In the first iteration, n=1, the initial phase function φ(x, y) ⁽ⁿ⁾ is generated by a two-dimensional random function, and the intermediate output object light function Q ⁽¹⁾ (ξ, η) is obtained.

Taking the digital holographic image g(ξ, η) as the amplitude of the output object light function, and the intermediate phase function φ(ξ, η) ⁽ⁿ⁾ calculated by formula (8) as the phase function, perform the inverse fractal Fourier transform Calculated:

T ⁽ⁿ⁾ (x, y)=|T ⁽ⁿ⁾ (x, y)|exp[jφ(x, y) ⁽ⁿ⁾ ]=IF ^P {g(ξ, η)exp[jφ(ξ, η ) ⁽ⁿ⁾ ]} (9)

Among them, IF ^P represents the inverse fractal Fourier transform, and it is only necessary to take -p from p in formula (6) to obtain the intermediate phase function of the object plane through the calculation of formula (9) as φ(x, y) ⁽ⁿ⁾ .

S121: Calculate the root mean square error MSE of the amplitude |Q ⁽ⁿ⁾ (ξ, η)| of the intermediate output object light function and the digital hologram |g(ξ, η)|:

Wherein, N _x and N _y are respectively the number of pixels in the x and y directions of the digital hologram/original carrier image (the number of pixels in the two images is the same), _1≤i≤Nx , 1≤k≤ N _y .

S122: According to the calculated root mean square error, determine whether the currently calculated intermediate phase function φ(x, y) ⁽ⁿ⁾ conforms to the constraints, and if it conforms to the constraints, the currently calculated intermediate phase function φ(x , y) ⁽ⁿ⁾ is determined as a phase function that complies with the constraint equation shown in formula (7). If it does not meet the constraint, steps S1110-S1112 are performed to recalculate and determine the intermediate phase function, and determine whether it satisfies the constraint.

In the embodiment of the present invention, if the root mean square error MSE is less than the set error threshold, it is determined that the currently calculated intermediate phase function φ(x, y) ⁽ⁿ⁾ complies with the constraints shown in formula (7), and the error threshold The value is 0.05.

S13: Obtain a carrier image embedded in the watermark information image according to the phase function satisfying the constraint condition.

According to the determined phase function φ(x, y) ⁽ⁿ⁾ that satisfies the constraint equation shown in formula (7), the complex wavefront function I(x, y) of the image with hidden watermark information is obtained as:

I(x, y)=f(x, y) exp[jφ(x, y) ⁽ⁿ⁾ ] (11)

The complex wavefront function I(x, y) shown in formula (11) is the carrier image embedded with the watermark information image, and the carrier image I(x, y) embedded in the digital hologram contains the original carrier image and the digital hologram. , whose amplitude is the original carrier image f(x, y), as shown in formula (12), the fractional Fourier transform of the complex wavefront function I(x, y) is the digital hologram g(ξ, η) :

|F ^P {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}|=g(ξ, η) (12)

2 is a schematic flowchart of a method for reconstructing a watermark information image according to an embodiment of the present invention. As shown in the figure, a digital watermark authentication method provided by an embodiment of the present invention includes extracting watermark image information, and the method includes:

S20: determine the extraction password for extracting the digital hologram;

Based on the constrained phase function φ(x, y) ⁽ⁿ⁾ , an extraction cipher for extracting the digital hologram is generated. Specifically include:

Perform singular value decomposition on the phase function φ(x, y) ⁽ⁿ⁾ that meets the constraints, and obtain the singular value matrix D and two unitary matrices U and V. Based on the symmetric encryption algorithm, the singular value matrix D is processed by the symmetric key. For encryption, the encryption processing result D' is used as the extraction password for extracting the digital hologram.

S21: Extract the 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 of extracting the digital hologram is:

S210: Decrypt the extraction password D` with a symmetric key based on a symmetric encryption algorithm, and generate a singular value matrix D;

S211: utilize singular value matrix D and two unitary matrices U and V to reconstruct to obtain phase function φ(x, y) ⁽ⁿ⁾ ;

S212: Using the original carrier image f(x, y) and the phase function φ ⁽ⁿ⁾ (x, y), calculate the digital hologram g(ξ, η):

g(ξ, η)=F ^p {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}

S22: Based on the digital hologram, reconstruct the watermark information image.

Use the holographic inverse transform to reconstruct the watermark information image, specifically:

Multiplying the reference light (called the reproduced light) by the digital hologram g(ξ, η) gives:

in, is a constant, in formula (15), if ignored It will not affect the light field distribution O(ξ, η) of the object light on the observation plane. O ^* (ξ, η) is the conjugate image of O(ξ, η). If the original object plane is selected as the diffraction (imaging) plane, that is, the inverse Fresnel diffraction integral transformation is performed, the reconstructed watermark information of the digital hologram can be obtained. The image O(x, y); it should be noted that the inverse transformation of R ² (ξ, η)O ^* (ξ, η) in Eq. (15) results in a Fresnel diffraction integral of the original object plane with a distribution close to uniform The background field distribution of , basically does not affect the quality of the reconstructed watermark information image. Therefore, by performing the inverse Fresnel diffraction integral transformation on O(ξ, η), we get:

Among them, IFn represents the Fresnel diffraction integral inverse transform, and O(x, y) is the reconstructed watermark information image. Among them, selecting reference light in different directions can reconstruct different watermark image information. If the reference light is selected as R ^* (ξ, η), 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 in a watermark information image according to an embodiment of the present invention. As shown in the figure, the digital watermark authentication device provided by the embodiment of the present invention includes:

Image embedding module, used to generate a carrier image embedded with watermark information image;

The image embedding module includes:

The digital hologram generation module is used to generate a digital hologram according to the watermark information image;

Using the Fresnel diffraction integral transform to calculate the object light distribution of the watermark information image in the observation plane is:

Among them, O ₀ (x, y) is the amplitude of the object light, ψ(x, y) is the phase function of the object light in the object plane, O(ξ, η) is the object light diffraction field distribution of the object light in the observation plane, is the phase function of the object light in the observation plane.

g(ξ, η) is a real number, that is, g(ξ, η)=|g(ξ, η)|, then g(ξ, η) is the light intensity (interference fringe) distribution of the object light and the reference light in the observation plane , known as a digital hologram.

The image synthesis module is used to process and generate the carrier image embedded with the watermark information image according to the digital hologram and the original carrier image.

Taking the original carrier image as the amplitude of the input object light function of the front focal plane of the lens, and taking the digital hologram as the output object light function of the back focal plane, the following constraint equations are established:

|F ^P {f(x,y)exp[jφ(x,y)]}|=g(ξ,η) (7)

Among them, f(x, y) is the original carrier image, g(ξ, η) is the digital hologram, and φ(x, y) is the phase function to be obtained.

According to steps S1110-S1112, use the fractal Fourier transform to calculate and solve the phase function φ(x, y) that satisfies the above constraints;

According to the phase function satisfying the constraints, the carrier image I(x, y) of the embedded watermark information image is obtained:

I(x, y)=f(x, y) exp[jφ(x, y) ⁽ⁿ⁾ ] (11)

The carrier image I(x, y) embedded in the watermark information image contains all the information of the original carrier image and the digital hologram, and its amplitude is the original carrier image f(x, y), as shown in formula (14), the carrier image I The fractional Fourier transform of (x, y) is the digital hologram g(ξ, η), and the digital hologram contains all the information of the watermark information image,

|F ^P {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}|=g(ξ, η) (12)

4 is a schematic structural diagram of an apparatus for reconstructing a watermark information image according to an embodiment of the present invention. As shown in the figure, the digital watermark authentication apparatus further includes:

The watermark extraction module is used to extract the watermark information image.

The watermark extraction module includes:

Password determination module: used to determine the extraction password for extracting the digital hologram;

Perform singular value decomposition on the phase function φ(x, y) ⁽ⁿ⁾ that meets the constraints, and obtain the singular value matrix D and two unitary matrices U and V. Based on the symmetric encryption algorithm, the singular value matrix D is processed by the symmetric key. For encryption, the encryption processing result D' is used as the extraction password for extracting the digital hologram.

The image extraction module is used to extract the digital hologram according to the original carrier image and the extraction password;

Utilize symmetric key to extract password D ` to decrypt based on symmetric encryption algorithm, generate singular value matrix D; Utilize singular value matrix D and two unitary matrices U and V reconstruction to obtain phase function φ(x, y) ⁽ⁿ⁾ ; Using the original carrier image f(x, y) and the phase function φ ⁽ⁿ⁾ (x, y), calculate the digital hologram g(ξ, η):

g(ξ, η)=F ^p {f(x, y)exp[jφ(x, y) ⁽ⁿ⁾ ]}

The watermark reconstruction module is used to reconstruct the watermark information image based on the extracted digital hologram.

Using the holographic inverse transform to reconstruct the watermark information image,

Among them, IFn represents the Fresnel diffraction integral inverse transform, and O(x, y) is the reconstructed watermark information image.

The apparatuses in the foregoing embodiments are used to implement the corresponding methods in the foregoing embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

Those of ordinary skill in the art should understand that the discussion of any of the above embodiments is only exemplary, and is not intended to imply that the scope of the present disclosure (including the claims) is limited to these examples; under the spirit of the present invention, the above embodiments or There may also be combinations between technical features in different embodiments, steps may be carried out 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.

Additionally, well known power/ground connections to integrated circuit (IC) chips and other components may or may not be shown in the figures provided in order to simplify illustration and discussion, and in order not to obscure the present invention. . Furthermore, devices may be shown in block diagram form in order to avoid obscuring the present invention, and this also takes into account the fact that the details regarding the implementation of these block diagram devices are highly dependent on the platform on which the invention will be implemented (i.e. , these details should be fully within the understanding of those skilled in the art). Where specific details (eg, circuits) are set forth to describe exemplary embodiments of the invention, it will be apparent to those skilled in the art that these specific details may be used without or with changes The present invention is carried out below. Accordingly, these descriptions are to be considered illustrative rather than restrictive.

Although the present invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations to these embodiments will be apparent to those of ordinary skill in the art from the foregoing description. For example, other memory architectures (eg, dynamic RAM (DRAM)) may use the discussed embodiments.

Embodiments of the present invention are intended to cover all such alternatives, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present 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:

|F^P{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)＝F^p{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⁾]＝F^P{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⁾]＝IF^P{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 is_x、N_yThe 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 N_x，1≤k≤N_y；

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:

|F^P{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)＝F^p{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⁾]＝F^P{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⁾]＝IF^P{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 is_x、N_yThe 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 N_x，1≤k≤N_y；

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.