CN108765253B - Vector geographic space data digital watermarking method based on DFT coefficient combination - Google Patents

Abstract

The invention discloses a vector geospatial data digital watermarking method based on DFT coefficient combination, which comprises the following steps: generating watermark information; establishing a watermark carrier model based on a DFT coefficient combination polynomial by taking a map as an object; taking the map objects as a unit, and modulating watermark information into each map object based on the established watermark carrier model; and extracting watermark information for verification. The invention modulates the watermark information in each DFT coefficient forming the polynomial by using a classical quantization index modulation method based on the DFT coefficient combination polynomial of the geometric object feature point set, thereby distributing the watermark strength to a plurality of coefficients, effectively improving the invisibility of the watermark and realizing the high fidelity of the data under the condition of not reducing the algorithm robustness.

Description

Vector geographic space data digital watermarking method based on DFT coefficient combination

Technical Field

The invention relates to a watermarking method, in particular to a vector geographic space data digital watermarking method based on DFT coefficient combination.

Background

Vector geospatial data digital watermarking technology has attracted the interest of many scholars at home and abroad as a preferred solution to the problem of spatial data copyright protection.

The vector geospatial data robust watermarking algorithm is mainly divided into the following categories according to the embedded position of the watermark: (1) the watermark information is hidden in the vertex coordinates. Modifying the least significant bit of the vertex coordinates to embed the watermark or compounding the watermark bit behind the vertex coordinate bit; to resist compression or simplifying attacks, watermark information is embedded in feature points of the geometric figure. (2) The watermark information is hidden in the transform coefficients. Watermark information is embedded in the amplitude or phase of the fourier transform (DFT). Or embedding watermark information in the wavelet transform coefficients. (3) The watermark information is hidden in the constant function. The constant function under a certain watermark attack is constructed, the constant function is modified by utilizing the invariance of the watermark attack possessed by the constant function, and the constant function is used for calculating the vertex coordinates to embed watermark information. (4) The watermark information is hidden in the distribution pattern of the vertices. This type of watermark model shifts vertices within a local neighborhood to align them into a predetermined distribution pattern to imply the embedding of watermark information. (5) The watermark information is hidden in the statistical variables of the data vertices. Watermark information is embedded by modifying the statistical properties of the statistical variables of the point set. (6) The watermark information is modulated in graphic parameters such as the angle of the geometric object.

The above watermark models can be divided into two broad categories: a spatial domain watermarking algorithm and a transform domain watermarking algorithm. Generally, transform domain algorithms are more robust than spatial domain algorithms, which is also the main direction of the current watermark algorithm research. In the transform domain algorithm, DFT has invariance characteristics on geometric figure translation, rotation, scaling and the like, so that the watermark algorithm based on DFT has natural advantages in resisting geometric attack.

However, the existing DFT domain algorithm directly embeds the watermark into the amplitude coefficient after DFT transform, which has a large influence on the original data and causes a large error.

Disclosure of Invention

In order to solve the technical problem, the invention provides a vector geospatial data digital watermarking method based on DFT coefficient combination.

The technical scheme for solving the problems is as follows: a vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following steps:

1) generating watermark information;

2) establishing a watermark carrier model based on a DFT coefficient combination polynomial by taking a map as an object;

3) taking the map objects as a unit, and modulating watermark information into each map object based on the established watermark carrier model;

4) and extracting watermark information.

The vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following specific steps of step 1): reading an original binary watermark image, and scrambling the watermark image by using Logistic chaotic transformation; the scrambled watermark image is then transformed into a one-dimensional sequence w_j0,1| j ═ 1,2, …, M }, where M is the watermark length.

The vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following specific steps in step 2):

2-1) extracting a feature point set: selecting all curves in the map object, and extracting the Tett from each curve by adopting a Douglas-Puck algorithmFeature point set, the extracted feature point set is the feature point v in v, v_k＝(x_k,y_k) K is 1,2, …, N, N is the total number of the characteristic points;

2-2) Fourier transform of v_kX in (2)_kAnd y_kThe combination is expressed as a complex sequence a_k:

a_k＝x_k+iy_k

For a complex number sequence a_kPerforming discrete Fourier transform on the formed set a to obtain a discrete Fourier coefficient set A, wherein the elements in the set A are A_l，l∈[1,N]；

2-3) establishing a watermark carrier model: the coefficients in A are operated as follows, starting from the first coefficient of A, every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b coefficient group is A_(b-1)n+hWhere h is 1,2, … N, b denotes the serial number of the coefficient group, b is 1,2 … s, s is TRUNC (N/N), TRUNC () denotes a truncation rounding function, and coefficients in the b-th coefficient group are formed into a polynomial of the following formula:

then C is the watermark carrier model, beta_hAre watermark carrier model parameters.

In the above DFT coefficient combination-based vector geospatial data digital watermarking method, in the step 2-1), the curve feature point extraction process is as follows:

(a) selecting a curve Q in a map object₁Will curve Q₁Head and tail nodes v₁，v_NAs initial feature points and are respectively denoted as v₁＝(x₁,y₁)，v_N＝(x_N,y_N) At v is₁，v_NBetween them is connected with a line segment S₁；

(b) Determine the curve Q₁From each point between the head and tail nodes to the line segment S₁To find the distance S from the line segment₁The farthest point, the point furthest from the line segment S₁A distance of d₁If d is₁If the distance is larger than the given threshold value, the point with the farthest distance is marked as a new characteristic point v₂；

(c) Curve Q₁The head node and the tail node are respectively connected with the newly generated characteristic points v₂Virtual connection to form a new line segment S₂And S₃With new feature points v₂Is a boundary curve Q₁Divided into two curves Q₂And Q₃Wherein Q is₂The head and tail nodes of v₁,v₂，Q₃The head and tail nodes of v₂,v_NAssume the AND line segment S₂Corresponding curve is Q₂And line segment S₃Corresponding curve is Q₃Repeating the operation of the step (b) for each new line segment to obtain a new feature point, namely for the line segment S₂To find a curve Q₂From each point between the head and tail nodes to the line segment S₂To find the distance S from the line segment₂The farthest point, if the farthest point reaches the line segment S₂If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point; for line segment S₃To find a curve Q₃From each point between the head and tail nodes to the line segment S₃To find the distance S from the line segment₃The farthest point, if the farthest point reaches the line segment S₃If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point;

(d) repeating the operation of step (c) for each newly generated feature point; and obtaining a curve feature point set v through the feature point extraction process.

In the above DFT coefficient combination-based vector geospatial data digital watermarking method, in the step 2-2), the discrete fourier coefficients obtained by performing discrete fourier transform on the set a include an amplitude coefficient and a phase coefficient.

The vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following specific steps of step 3):

3-1) calculating a watermark carrier quantization value Q (C) according to the embedded watermark bit information and a classical quantization index modulation model; the calculation formula is as follows:

in the above formula, round is the nearest integer function, Δ is the quantization step,% is the remainder operation sign, f is the intermediate temporary variable, w_jThe watermark bit information to be embedded is watermark information generated in the step 1), and the value is 1 or 0;

3-2) calculating the watermark carrier change amount of the b coefficient group: c_e＝Q(C)-C；

3-3) calculating the change amount of the b coefficient group DFT coefficient value: delta A_(b-1)n+h＝C_e/(nβ_h)；

3-4) modifying coefficient values of the b coefficient group DFT: a'_(b-1)n+h＝A_(b-1)n+h+ΔA_(b-1)n+h；

3-5) repeating the step 3-2) -the step 3-4), and modifying the DFT coefficient values of all the coefficient groups to obtain a set A';

3-6) performing inverse discrete Fourier transform on A ' to obtain feature points v ' in the feature point set v ', v ' embedded with the watermark '_k＝(x′_k,y′_k),k＝1,2,…,N；

And 3-7) modifying the feature point coordinates according to v' to obtain vector data embedded with the watermark.

The vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following specific steps in the step 4):

4-1) extracting characteristic points v ' in the characteristic point set v ', v ' of the map object curve by adopting a Douglas-Pock algorithm_k＝(x″_k,y″_k),k＝1,2,…,N；

4-2) mixing v ″)_kX in (1)_kAnd y ″)_kThe combination is represented as a complex sequence a ″_k:

a″_k＝x″_k+iy″_k；

4-3) pairs consisting of a plurality of sequences a ″)_kPerforming discrete Fourier transform on the formed set a 'to obtain a discrete Fourier coefficient set A';

4-4) in A ', the amplitude coefficient and the phase coefficient are respectively operated as follows, starting from the first coefficient of A', every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b-th coefficient group is A ″_(b-1)n+hWhere h is 1,2, … N, b denotes the serial number of the coefficient group, b is 1,2 … s, s is TRUNC (N/N), TRUNC () denotes a truncation rounding function, and coefficients in the b-th coefficient group are formed into a polynomial of the following formula:

4-5) based on the quantization index modulation model, extracting watermark bits according to the quantization interval where C' is located, wherein the calculation method comprises the following steps:

in the above formula, ω "is the extracted watermark bit,/is the division to take the integer arithmetic sign, Δ is the quantization step length,% is the remainder arithmetic sign;

4-6) performing dimension-increasing processing and reverse scrambling on the extracted one-dimensional watermark sequence to obtain a final watermark image.

In the above vector geospatial data digital watermarking method based on DFT coefficient combination, after the step 4), a step of performing watermark image verification on the extracted watermark image by adopting a method of artificial visual judgment is further included.

The invention has the beneficial effects that: firstly, generating watermark information; then, establishing a watermark carrier model based on a DFT coefficient combination polynomial by taking a map as a unit; then, taking the map objects as a unit, and modulating watermark information into each map object based on the established watermark carrier model; and finally, extracting watermark information for verification. The invention modulates the watermark information in each DFT coefficient forming the polynomial by using a classical quantization index modulation method based on the DFT coefficient combination polynomial of the geometric object feature point set, thereby distributing the watermark strength to a plurality of coefficients, effectively improving the invisibility of the watermark and realizing the high fidelity of the data under the condition of not reducing the algorithm robustness.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The invention is further described below with reference to the drawings and examples.

As shown in fig. 1, a vector geospatial data digital watermarking method based on DFT coefficient combination includes:

1) watermark information is generated. The method comprises the following specific steps: reading an original binary watermark image, and scrambling the watermark image by using Logistic chaotic transformation; then the scrambled watermark image is transformed into a one-dimensional sequence w_j0,1| j ═ 1,2, …, M }, where M is the watermark length.

2) And establishing a watermark carrier model based on a DFT coefficient combination polynomial by taking the map as a unit. The method comprises the following specific steps:

2-1) extracting a feature point set: selecting all curves in the map object, and extracting a feature point set for each curve by adopting a Douglas-Pock algorithm, wherein the extracted feature point set is the feature point v in v and v_k＝(x_k,y_k) K is 1,2, …, and N is the total number of the characteristic points.

The curve characteristic point extraction process is as follows:

(a) selecting a curve Q in a map object₁Will curve Q₁Head and tail nodes v₁，v_NAs initial feature points and are respectively denoted as v₁＝(x₁,y₁)，v_N＝(x_N,y_N) At v is₁，v_NBetween them is connected with a line segment S₁；

(b) Determine the curve Q₁From each point between the head and tail nodes to the line segment S₁To find the distance S from the line segment₁The farthest point, the point furthest from the line segment S₁A distance of d₁If d is₁If the distance is larger than the given threshold value, the point with the farthest distance is marked as a new characteristic point v₂；

(c) Curve Q₁The head node and the tail node are respectively connected with the newly generated characteristic points v₂Virtual connection to form a new line segment S₂And S₃With new feature points v₂Is a boundary curve Q₁Divided into two curves Q₂And Q₃Wherein Q is₂The head and tail nodes of v₁,v₂，Q₃The head and tail nodes of v₂,v_NAssume the AND line segment S₂Corresponding curve is Q₂And line segment S₃Corresponding curve is Q₃Repeating the operation of the step (b) for each new line segment to obtain a new feature point, namely for the line segment S₂To find a curve Q₂From each point between the head and tail nodes to the line segment S₂To find the distance S from the line segment₂The farthest point, if the farthest point reaches the line segment S₂If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point; for line segment S₃To find a curve Q₃From each point between the head and tail nodes to the line segment S₃To find the distance S from the line segment₃The farthest point, if the farthest point reaches the line segment S₃If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point;

(d) repeating the operation of step (c) for each newly generated feature point; and obtaining a curve feature point set v through the feature point extraction process.

2-2) mixing v_kX in (2)_kAnd y_kThe combination is expressed as a complex sequence a_k:

a_k＝x_k+iy_k

For a plurality of sequences a_kThe formed set a is subjected to discrete Fourier transform to obtain discrete Fourier amplitude coefficients and phase coefficients, the number of the amplitude coefficients and the number of the phase coefficients are the same and are N, and the amplitude coefficients and the phase coefficients are operated in the subsequent steps in the same way, so that the amplitude coefficients are only taken as an example to form a coefficient set A, and the set is formed by setting the amplitude coefficientsThe element in A is A_l，l∈[1,N]；

2-3) establishing a watermark carrier model: the coefficients in A are operated as follows, starting from the first coefficient of A, every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b coefficient group is A_(b-1)n+hWhere h is 1,2, … N, b denotes the number of the coefficient group, b is 1,2 … s, s is TRUNC (N/N), TRUNC () denotes a truncate rounding function, and if N/N is not an integer, the remaining coefficients after the rounding are not operated; and forming coefficients in the b-th coefficient group into a polynomial of the following formula:

c is the watermark carrier model; beta is a_hThe parameters of the watermark carrier model are determined during algorithm implementation, and the watermark carrier model which can obtain the coefficient set formed by the phase coefficients in the same way is the same as C.

3) And modulating the watermark information into each map object based on the established watermark carrier model by taking the map object as a unit. The method comprises the following specific steps:

3-1) calculating a watermark carrier quantization value Q (C) according to the embedded watermark bit information and a classical quantization index modulation model; the calculation formula is as follows:

in the above formula, round is the nearest integer function, Δ is the quantization step,% is the remainder operation sign, f is the intermediate temporary variable, w_jThe watermark bit information to be embedded is watermark information generated in the step 1), and the value is 1 or 0;

3-2) calculating the watermark carrier change amount of the b coefficient group: c_e＝Q(C)-C；

3-3) calculating the change amount of the b coefficient group DFT coefficient value: delta A_(b-1)n+h＝C_e/(nβ_h)；

3-4) modifying coefficient values of the b-th coefficient group DFT:

A′_(b-1)n+h＝A_(b-1)n+h+ΔA_(b-1)n+h；

3-5) repeating the step 3-2) -the step 3-4), modifying the DFT coefficient values of all the coefficient groups to obtain a set A ', wherein the amplitude coefficient and the phase coefficient are modified simultaneously in the process of modulating the watermark information, so that the amplitude coefficient and the phase coefficient are included in the obtained set A';

3-6) performing inverse discrete Fourier transform on A ' to obtain feature points v ' in the feature point set v ', v ' embedded with the watermark '_k＝(x′_k,y′_k),k＝1,2,…,N；

And 3-7) modifying the feature point coordinates according to v' to obtain vector data embedded with the watermark.

4) Extracting watermark information; the method comprises the following specific steps:

4-1) extracting a characteristic point set v' of a map object curve by using a Douglas-Pock algorithm by taking the map object as a unit_k＝(x″_k,″_k) K is 1,2, …, N; the specific steps are the same as the steps of extracting the curve feature point set v in the step S121;

4-2) mixing v ″)_kX in (1)_kAnd y ″)_kThe combination is represented as a complex sequence a ″_k:

a″_k＝x″_k+iy″_k；

4-3) pairs consisting of a plurality of sequences a ″)_kPerforming discrete Fourier transform on the formed set a 'to obtain a discrete Fourier coefficient set A';

4-4) in A ', the amplitude coefficient and the phase coefficient are respectively operated as follows, starting from the first coefficient of A', every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b-th coefficient group is A ″_(b-1)n+hWhere h is 1,2, … n, b denotes the number of the coefficient group, b is 1,2 … s, s＝TRUNC(N/n)，

TRUNC () represents a truncate integer function, forming the coefficients in the b-th coefficient group into a polynomial of the following formula:

4-5) based on the quantization index modulation model, extracting watermark bits according to the quantization interval where C' is located; the calculation method is as follows:

in the above formula, ω "is the extracted watermark bit,/is the division to take the integer arithmetic sign, Δ is the quantization step size,% is the remainder arithmetic sign.

4-6) performing dimension-increasing processing and reverse scrambling on the extracted one-dimensional watermark sequence to obtain a final watermark image.

5) And verifying the watermark image.

And (4) carrying out watermark image verification on the extracted watermark image by adopting a manual visual judgment method.

Claims (6)

1. A vector geographic space data digital watermarking method based on DFT coefficient combination comprises the following steps:

1) generating watermark information;

2) establishing a watermark carrier model based on a DFT coefficient combination polynomial by taking a map as an object;

the step 2) comprises the following specific steps:

2-1) extracting a feature point set: selecting all curves in the map object, and extracting a feature point set for each curve by adopting a Douglas-Pock algorithm, wherein the extracted feature point set is the feature point v in v and v_k＝(x_k,y_k) K is 1,2, …, N, N is the total number of the characteristic points;

2-2) Fourier transform of v_kX in (2)_kAnd y_kThe combination is expressed as a complex sequence a_k:

a_k＝x_k+iy_k

For a plurality of sequences a_kPerforming discrete Fourier transform on the formed set a to obtain a discrete Fourier coefficient set A, wherein the elements in the set A are A_l，l∈[1,N]；

2-3) establishing a watermark carrier model: the coefficients in A are operated as follows, starting from the first coefficient of A, every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b coefficient group is A_(b-1)n+hWhere h is 1,2, … N, b denotes the serial number of the coefficient group, b is 1,2 … s, s is TRUNC (N/N), TRUNC () denotes a truncate integer function, and the coefficients in the b-th coefficient group are configured as a polynomial of the following formula:

then C is the watermark carrier model, beta_hIs watermark carrier model parameter;

3) taking the map objects as a unit, and modulating watermark information into each map object based on the established watermark carrier model;

the step 3) comprises the following specific steps:

3-1) calculating a watermark carrier quantization value Q (C) according to the embedded watermark bit information and a classical quantization index modulation model; the calculation formula is as follows:

in the above formula, round is the nearest integer function, Δ is the quantization step,% is the remainder operation sign, f is the intermediate temporary variable, w_jThe watermark bit information to be embedded is watermark information generated in the step 1), and the value is 1 or 0;

3-2) calculating the watermark carrier change amount of the b coefficient group: c_e＝Q(C)-C；

3-3) calculating the change amount of the coefficient value of the b coefficient group DFT: delta A_(b-1)n+h＝C_e/(nβ_h)；

3-4) modifying coefficient values of the b-th coefficient group DFT:

A′_(b-1)n+h＝A_(b-1)n+h+ΔA_(b-1)n+h；

3-5) repeating the step 3-2) -the step 3-4), and modifying the DFT coefficient values of all the coefficient groups to obtain a set A';

3-6) performing inverse discrete Fourier transform on A ' to obtain feature points v ' in the feature point set v ', v ' embedded with the watermark '_k＝(x′_k,y′_k),k＝1,2,…,N；

3-7) modifying the feature point coordinates according to v' to obtain vector data embedded with the watermark;

4) and extracting watermark information.

2. The vector geospatial data digital watermarking method based on DFT coefficient combination as claimed in claim 1, wherein the step 1) is specifically the steps of: reading an original binary watermark image, and scrambling the watermark image by using Logistic chaotic transformation; the scrambled watermark image is then transformed into a one-dimensional sequence w_j0,1| j ═ 1,2, …, M }, M is the watermark length, w_jAnd generating a value of 0 or 1 according to the scrambled watermark image.

3. The vector geospatial data digital watermarking method based on DFT coefficient combination as claimed in claim 2, wherein in the step 2-1), the curve feature point extraction process is as follows:

(a) selecting a curve Q in a map object₁Will curve Q₁Head and tail nodes v₁，v_NAs initial feature points and are respectively denoted as v₁＝(x₁,y₁)，v_N＝(X_N,y_N) At v is₁，v_NA line segment S is connected between the two₁；

(b) Determine the curve Q₁From each point between the head and tail nodes to the line segment S₁To find the distance S from the line segment₁The farthest point, recording the farthest point to the line segment S₁A distance of d₁If d is₁If the distance is larger than the given threshold value, the point with the farthest distance is marked as a new characteristic point v₂；

(c) Curve Q₁The head node and the tail node are respectively connected with the newly generated characteristic points v₂Virtual connection to form a new line segment S₂And S₃With new feature points v₂Is a boundary curve Q₁Divided into two curves Q₂And Q₃Wherein Q is₂The head and tail nodes of v₁,v₂，Q₃The head and tail nodes of v₂,v_NAssume the AND line segment S₂Corresponding curve is Q₂And line segment S₃Corresponding curve is Q₃Repeating the operation of the step (b) for each new line segment to obtain a new feature point, namely for the line segment S₂To find a curve Q₂From each point between the head and tail nodes to the line segment S₂To find the distance S from the line segment₂The farthest point, if the farthest point reaches the line segment S₂If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point; for line segment S₃To find a curve Q₃From each point between the head and tail nodes to the line segment S₃To find the distance S from the line segment₃The farthest point, if the farthest point reaches the line segment S₃If the distance is greater than a given threshold value, the point with the farthest distance is marked as a new characteristic point;

(d) repeating the operation of step (c) for each newly generated feature point; and obtaining a curve feature point set v through the feature point extraction process.

4. The vector geospatial data digital watermarking method based on DFT coefficient combination as claimed in claim 2, wherein in the step 2-2), the discrete Fourier coefficients obtained by performing discrete Fourier transform on the set a comprise amplitude coefficients and phase coefficients.

5. The vector geospatial data digital watermarking method based on DFT coefficient combination as claimed in claim 4, wherein the step 4) is specifically the steps of:

4-1) extracting characteristic points v ' in the characteristic point set v ', v ' of the map object curve by adopting a Douglas-Pock algorithm_k″＝(x_k″,y_k″),k＝1,2,…,N；

4-2) mixing v_k"of x_kAnd y_k"combination is expressed as a complex sequence a_k″:

a_k″＝x_k″+iy_k″；

4-3) pairs of complex sequences a_kPerforming discrete Fourier transform on the formed set a to obtain a discrete Fourier coefficient set A';

4-4) in A ', the amplitude coefficient and the phase coefficient are respectively operated as follows, starting from the first coefficient of A', every adjacent n coefficients form a coefficient group in sequence, and the coefficient in the b-th coefficient group is A ″_(b-1)n+hWhere h is 1,2, … N, b denotes the serial number of the coefficient group, b is 1,2 … s, s is TRUNC (N/N), TRUNC () denotes a truncation rounding function, and coefficients in the b-th coefficient group are formed into a polynomial of the following formula:

4-5) based on the quantization index modulation model, extracting watermark bits according to the quantization interval where C' is located, wherein the calculation method comprises the following steps:

in the above formula, ω "is the extracted watermark bit,/is the division to take the integer arithmetic sign, Δ is the quantization step length,% is the remainder arithmetic sign;

4-6) performing dimension-increasing processing and reverse scrambling on the extracted one-dimensional watermark sequence to obtain a final watermark image.

6. The vector geospatial data digital watermarking method based on DFT coefficient combination as claimed in claim 5, further comprising a step of performing watermark image verification by adopting a method of artificial visual judgment on the extracted watermark image after the step 4).

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