CN113284036B - Vector map reversible watermarking algorithm based on virtual grid interval mapping - Google Patents

Vector map reversible watermarking algorithm based on virtual grid interval mapping Download PDF

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CN113284036B
CN113284036B CN202110662301.0A CN202110662301A CN113284036B CN 113284036 B CN113284036 B CN 113284036B CN 202110662301 A CN202110662301 A CN 202110662301A CN 113284036 B CN113284036 B CN 113284036B
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CN113284036A (en
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奚旭
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Suzhou University of Science and Technology
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Abstract

The invention discloses a vector map reversible watermarking algorithm based on virtual grid interval mapping, which comprises watermarking embedding and watermarking extraction, wherein the watermarking embedding comprises the steps of forming a virtual grid, determining the step length of the virtual grid according to the data precision and tolerance of a vector map, obtaining an interval to be embedded with a watermark by taking the maximum value of a layer space domain as the maximum value of an interval boundary range, and embedding the watermark in the virtual grid by adopting a watermarking algorithm based on interval state value mapping; the watermark extraction comprises the steps of obtaining the horizontal and vertical most values of a data interval during watermark embedding, equally dividing a coordinate value interval into subintervals to calculate the length, searching a virtual coordinate corresponding to a coordinate point embedded with the watermark through the length, and extracting the watermark by using a watermark algorithm based on interval state value mapping. According to the invention, by using the maximum value and the virtual grid of the layer space domain, the watermark capacity and robustness are improved; safety and data usability are improved by taking data precision and tolerance as constraint conditions, and the method is suitable for two-dimensional vector diagrams.

Description

Vector map reversible watermarking algorithm based on virtual grid interval mapping
Technical Field
The invention relates to the technical field of information security, in particular to a vector map reversible watermarking algorithm based on virtual grid interval mapping.
Background
The vector map is an important national strategic information resource, has the characteristics of high production cost, high positioning accuracy, low redundancy, wide application range and the like, and the safety protection of the vector map not only influences the healthy development of a geographic information market, but also relates to the national safety and national defense construction. With the advent of the big data era, information copying, diffusion and editing become easier, behaviors such as illegal transmission, reverse selling, malicious tampering and the like aiming at a vector map are more frequent, and loss which is difficult to estimate is caused to a data producer or a legal owner. In addition to establishing strict and sophisticated laws and regulations, research improvements on technological means are required as strong support for regulating the geographic information market. Digital watermarking is a technology for embedding a specific digital signal into a digital product to protect the copyright or integrity of the digital product, and the digital watermarking is widely concerned as a leading-edge technology in the field of information security, so that the research on the digital watermarking in a vector map is also concerned more and more.
At present, the research results of vector map watermarking algorithms are rich. However, most of the current mainstream algorithms implement watermark embedding by directly or indirectly modifying coordinate values, so that the embedding of watermark information will certainly disturb coordinate points in a vector map, and most of watermark schemes do not set a precision control measure, and the embedding of watermark information will also cause vector map topological relation errors and geometric form distortion, thereby reducing data fidelity to different degrees and affecting the use value of the watermark-containing vector map. In response to this problem, reversible watermarking techniques are receiving increasing attention. The reversible watermark algorithm can recover original data on the basis of correctly extracting the watermark, and achieves the purposes of copyright protection and content integrity authentication. However, in the current research on reversible watermarks of vector maps, the research focus is mainly on reversibility and watermark capacity, and a reliable error control measure is often lacked to improve the security and invisibility of a watermark scheme. In this case, if there is a large distortion, even if the watermarking algorithm is reversible, it may still be recognized and maliciously destroyed by an illegal party.
Wang [1] A watermarking algorithm based on interval state value mapping, which is provided for a three-dimensional point cloud model, can realize embedding large-capacity watermarking information in a small data volume, but a reasonable coordinate point moving range is not given in the watermarking embedding process, and the precision control of data is ignored, so the algorithm is not suitable for a two-dimensional vector map. In addition, in the watermark algorithm based on the interval state value mapping, the maximum value of the coordinate points of the data is directly taken when the minimum value and the maximum value of the coordinate point state axis are set, that is, the maximum value of the coordinate points in the X axis max And X min Taking x directly at the coordinate point max And x min The two points can not carry watermark information, although the watermark can realize blind detection, the robustness of conventional data editing is poor; moreover, if data splicing and data deleting operations occur, the maximum value and the minimum value of the carrier data are changed, and the watermark cannot be extracted correctly, so that the use of the watermark algorithm in a two-dimensional vector map is limited.
Reference:
[1]Wang P,Wang C.Reversible data hiding for point-sampled geometry
[J].Journal of information science and engineering,2007,23(6):1889-1900.
disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects in the prior art, and design a vector map reversible watermark algorithm based on virtual grid interval mapping, which is suitable for a two-dimensional vector map and has controllable disturbance degree when embedding a watermark, wherein the algorithm realizes watermark embedding and reversible extraction based on virtual grid interval mapping, so that the reversibility and data recoverability of the watermark algorithm can be ensured, errors can be controlled, the invisibility of the watermark can be improved, the actual application requirement of the vector map is met, and the landing of the digital watermark in vector map copyright protection is promoted.
In order to solve the technical problems, the invention provides a vector map reversible watermarking algorithm based on virtual grid interval mapping, which comprises watermark embedding and watermark extraction,
the watermark embedding comprises the following steps:
step A1: two adjacent virtual coordinates are created for two data vertexes in the horizontal and vertical directions in which the watermark needs to be embedded to form a virtual grid,
step A2: the step size of the virtual grid is determined by the data accuracy of the vector map and the requirements of tolerance control,
step A3: combining the step size of the virtual grid, taking the maximum value and the minimum value of the layer space domain as the maximum value and the minimum value of the interval boundary range to obtain an interval to be embedded with the watermark,
step A4: embedding watermarks in the virtual grid intervals x and y by adopting a watermark algorithm based on interval state value mapping;
the watermark extraction comprises the following steps:
step B1: obtaining the transverse maximum X of the whole data interval when the watermark is embedded max Minimum value X min And a longitudinal maximum Y max Minimum value Y min ，
Step B2: dividing the whole data coordinate value interval into multiple sub-intervals, and passing through X min 、X max Calculating the length l of each subinterval by the number of the sum subspaces t ；
Step B3: by length l t Finding virtual coordinates corresponding to the coordinate points where the watermark is embedded,
step B4: and extracting the watermark by using a watermark algorithm based on interval state value mapping.
Further, the specific process of step a2 is as follows:
step (ii) ofA2.1: when watermark information is embedded into the abscissa X and the ordinate Y of a coordinate point at the same time, the maximum change amount of the coordinate point on the abscissa and the ordinate is l t The Euclidean space distance variation of coordinate points before and after watermark embedding is as follows:
Figure BDA0003115582550000031
step A2.2: definition of l t And l e The range of (A):
Figure BDA0003115582550000041
wherein R is the resolution of the data, and T is the tolerance value of the data;
step A2.3: combining step A2.1 with step A2.2 to obtain D x The range of (A) is as follows:
Figure BDA0003115582550000042
on the basis, a larger value meeting the requirements of precision and tolerance is adopted as D x The value of (A) is as follows:
Figure BDA0003115582550000043
Figure BDA0003115582550000044
step A2.4: d is obtained by adopting the same principle as the step A2.1 to the step A2.3 y The value of (A) is as follows:
Figure BDA0003115582550000045
further, the specific process of step a3 is as follows:
step A3.1: array X ═ X composed of data points abscissa X i |i∈[1，n]The coordinate values in the array are n, x i Is the most initial coordinate value before embedding watermark into the coordinate point(ii) a Find out the maximum X in X max And minimum value X min The searching method comprises the following steps:
Figure BDA0003115582550000046
wherein x max Is the maximum value in the array X, X min Is the minimum value in the array X, X min And X max The values of all the layers are the maximum values of the spatial domain in the layers;
step A3.2: definition of L X (X min ，X，X max ) To comprise X min X and X max Section L, section L X Is equally divided into D x (D x Not less than 2) sub-intervals, length l of each sub-interval t ＝(X max -X min )/D x ；
Step A3.3: coordinate point X to be embedded with watermark information is X i |i∈[1，D x ]Each x in i Calculating to obtain x i Two virtual coordinate values adjacent to each other on the left and right sides
Figure BDA0003115582550000047
And
Figure BDA0003115582550000048
step A3.4: definition of
Figure BDA0003115582550000051
Is x i At L x The interval sequence number in (2) is,
Figure BDA0003115582550000052
the calculation formula of (2) is as follows:
Figure BDA0003115582550000053
step A3.5: according to
Figure BDA0003115582550000054
Finding x i Adjacent virtual coordinates of
Figure BDA0003115582550000055
And
Figure BDA0003115582550000056
Figure BDA0003115582550000057
x i and its adjacent coordinate value form transverse interval in which the watermark is to be embedded
Figure BDA0003115582550000058
Step A3.6: obtaining a longitudinal interval of the ordinate Y to be embedded with the watermark by adopting the same principle as the step A3.1 to the step A3.6
Figure BDA0003115582550000059
Further, the specific process of step a3.6 is:
step A3.6.1: array Y ═ Y composed of data point ordinates Y i |i∈[1，n]N coordinate values in the array; finding out the maximum value Y of Y max And minimum value Y min The searching method comprises the following steps:
Figure BDA00031155825500000510
wherein y is max Is the maximum value in the array Y, Y min Is the minimum value in the array Y, Y min And Y max The values of all the layers are the maximum values of the spatial domain in the layers;
step A3.6.2: definition of L Y (Y min ，Y，Y max ) To contain Y min Y and Y max Section L, section L Y Is equally divided into D y (D y Not less than 2) sub-intervals, length l of each sub-interval t ＝(Y max -Y min )/D y ；
Step A3.6.3: seat for embedding watermark informationPunctuation Y ═ Y i |i∈[1，D y ]Each of y i Calculating to obtain y i Two virtual coordinate values adjacent up and down
Figure BDA00031155825500000511
And
Figure BDA00031155825500000512
step A3.6.4:
Figure BDA00031155825500000513
is y i At L y The interval sequence number in (2) is,
Figure BDA00031155825500000514
the calculation formula of (2) is as follows:
Figure BDA00031155825500000515
step A3.6.5: according to
Figure BDA00031155825500000516
Outgrowth y i Adjacent virtual coordinates of
Figure BDA00031155825500000517
And
Figure BDA00031155825500000518
Figure BDA0003115582550000061
y i and its adjacent coordinate value form longitudinal interval in which the watermark is to be embedded
Figure BDA0003115582550000062
Further, the specific process of step a4 is as follows:
step A4.1: selecting a coordinate point set to be embedded with watermark information, arranging coordinate points on a coordinate axis for sequencing, and generating a new sequence;
step A4.2: classifying the ordered coordinate point sequences according to intervals, so that the transverse interval Qx and the longitudinal interval Qy both comprise three adjacent coordinate points;
step A4.3: the watermark is embedded in the intervals Qx and Qy through mapping of the state values of the x and y intervals.
Further, the specific process of the step a4.2 is as follows:
step A4.2.1: definition of x left X and x right Is based on three coordinates in the X-axis ordering sequence and satisfies X left ≤x≤x right X is to be left And x right The interval between the two is equally divided into m subintervals, and x is the initial abscissa value of the coordinate point; the subinterval sequence number of the position of the x coordinate is the interval state value s;
step A4.2.2: defining Qx as containing three coordinate values X in the sequence based on X-axis left X and x right In the total state interval, Qx ═ x left ，x，x right ) (ii) a Definition of x center Is the midpoint of the interval Q, x center ＝(x left +x right ) 2; setting the number m of the intervals to 2 c+1 C is the number of watermark bits and c is greater than or equal to 0, then Qx is equally divided into 2 c+1 A sub-interval;
step A4.2.3: using the same principle as in steps A4.2.1 to A4.2.2, the longitudinal section Qy (y) is obtained bottom ，y，y top )。
Further, the specific process of the step a4.3 is as follows:
step A4.3.1: defining w as the initial watermark to be carried by x, and satisfying that w is more than or equal to 0 and less than or equal to 2 c (ii) a Defining r as the coefficient of x in the interval Q and satisfying
Figure BDA0003115582550000071
Step A4.3.2: in the embedding process of the watermark, x needing to be embedded with the watermark is in a coefficient r of an interval Qx, and the calculation formula is as follows:
Figure BDA0003115582550000072
the coordinate value of the coordinate point x after the watermark is embedded is recorded as x ', the interval state value of x' in Qx is recorded as s ', and the calculation formula of s' is as follows: s' ═ 2 c ×r+w；
Step A4.3.3: moving x to the s 'th interval, obtaining the value of x' embedded with the watermark:
Figure BDA0003115582550000073
Figure BDA0003115582550000074
wherein
Figure BDA0003115582550000075
Step A4.3.4: embedding the watermark into the section Qy by mapping the y-section state value using the same principle as in steps A4.3.1 to A4.3.3, thereby completing embedding of w.
Further, the specific process of step B2 is as follows: equally dividing the interval of the abscissa value of the whole data into D x (D x Not less than 2) sub-intervals, the calculation formula of the length of each sub-interval is l t ＝(X max -X min )/D x 。
Further, the length l is passed in the step B3 t Finding virtual coordinates x 'corresponding to coordinate points embedded with watermarks' i The specific method comprises the following steps:
step B3.1: by passing
Figure BDA0003115582550000076
To obtain x' i Left and right virtual coordinate points of
Figure BDA0003115582550000077
And
Figure BDA0003115582550000078
by passing
Figure BDA0003115582550000079
To give y' i Upper and lower two virtual coordinate points of (2)
Figure BDA00031155825500000710
And
Figure BDA00031155825500000711
step B3.2: x' i And the left and right virtual coordinate values form a transverse interval in which the watermark is to be embedded
Figure BDA00031155825500000712
y′ i And the upper and lower virtual coordinate values form a longitudinal interval in which the watermark is to be embedded
Figure BDA0003115582550000081
Further, it is characterized in that: the specific process of the step B4 is as follows:
step B4.1: equal spacing of the sub-intervals of interval Qx
Figure BDA0003115582550000082
And satisfy
Figure BDA0003115582550000083
Subinterval spacing l by x' and Qx s Calculating the interval state value s 'of x' in Qx, wherein the calculation formula is as follows:
s′＝[(x′-x left )/l s ]＝[(x′-x left )/(x right -x left )/2 c+1 ]；
step B4.2: and recovering the watermark value w ' carried by the watermark x ' according to the interval state value s ', wherein the calculation formula is as follows:
w′＝s′-r×2 c ；
combination formula
Figure BDA0003115582550000084
And
Figure BDA0003115582550000085
Figure BDA0003115582550000086
recovering to obtain an original x;
step B4.3: the watermark value w 'carried by the recovered watermark y' and the original y are recovered in the same principle.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the vector map reversible watermarking algorithm based on virtual grid interval mapping takes the maximum value and the minimum value of the layer spatial domain as the maximum value and the minimum value of an interval boundary range, and performs spatial positioning on a coordinate point embedded with a watermark through a virtual grid, so that the watermark capacity and algorithm robustness are improved; the size of the virtual grid is limited by taking the data precision and tolerance as constraint conditions, so that the offset range of a coordinate point during watermark embedding is limited, the disturbance caused by watermark embedding is controlled within an allowable range, the security of a watermark algorithm and the usability of data are improved, and the method is suitable for a two-dimensional vector diagram.
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In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of the entire X coordinate interval and the virtual coordinate of X in the present invention.
Fig. 3 is a schematic diagram of the positions of coordinate points in a virtual coordinate (grid) in the present invention.
FIG. 4 is a diagram illustrating the state values of x intervals in m equal intervals according to the present invention.
FIG. 5 is a diagram illustrating the interval state values of x in Qx in the present invention.
FIG. 6 is a schematic diagram illustrating the setting rule of r value in the present invention.
Fig. 7 is a schematic diagram of embedding a watermark by x through interval mapping in the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
In the description of the present invention, it should be understood that the term "comprises/comprising" is intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to the listed steps or elements but may alternatively include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to fig. 1, a flowchart shows an embodiment of a vector map reversible watermarking algorithm based on virtual grid interval mapping according to the present invention, including watermark embedding and watermark extraction,
the watermark embedding comprises the following steps:
step A1: and creating two adjacent virtual coordinates for two data vertexes in the horizontal and vertical directions in which the watermark needs to be embedded to form a virtual grid.
Step A2: the step size of the virtual grid is determined by the requirements of data precision and tolerance control of the vector map, and is used for controlling the coordinate movement caused when the watermark is embedded within a proper range.
Step A2.1: when watermark information is embedded into the abscissa X and the ordinate Y of a coordinate point at the same time, the maximum variation of the coordinate point on the abscissa and the ordinate is l t The Euclidean space distance variation of the coordinate points before and after watermark embedding is as follows:
Figure BDA0003115582550000101
step A2.2: definition of l t And l e The range of (A):
Figure BDA0003115582550000102
for rendering embedded watermark information inaccessible to mapsAnd (5) degree disturbance.
Wherein R is the resolution of the data, and T is the tolerance value of the data; the values of R and T are set according to the data characteristics. R also represents a data-precision bit in the vector map, and if the data-precision bit is 0.001, the embedding position defined in the present embodiment can be only after 0.001, preferably 0.0011-0.0019. If the distance between two points is less than the tolerance, the two points are automatically merged into one point, so that the topological relation of the data changes. In order not to make this happen, the movable range of the coordinate point is set to be smaller than a tolerance of 0.001 for each scale of 1: 20001: 1000 in the vector map.
Step A2.3: combining step A2.1 with step A2.2 to obtain D x The range of (A) is as follows:
Figure BDA0003115582550000103
on the basis, a larger value meeting the requirements of precision and tolerance is adopted as D x The value of (A) is as follows:
Figure BDA0003115582550000104
Figure BDA0003115582550000105
step A2.4: d is obtained by adopting the same principle as the step A2.1 to the step A2.3 y The value of (A) is as follows:
Figure BDA0003115582550000106
step A3: combining the step size of the virtual grid, taking the maximum value of the layer space domain as the maximum value and the minimum value of the boundary range of the interval to obtain the interval to be embedded with the watermark, wherein the target coordinate point of the embedded watermark needs to be controlled in a reasonable range to ensure the availability of data, and the movable range of the coordinate point is not limited in the watermark algorithm based on the interval state value mapping proposed by Wang.
Step A3.1: array X ═ X composed of data points abscissa X i |i∈[1，n]}, the coordinate values in the array are n, x i The coordinate value is the most initial coordinate value before the watermark is not embedded into the coordinate point; find out the maximum value X in X max And minimum value X min The searching method comprises the following steps:
Figure BDA0003115582550000111
wherein x max Is the maximum value in the array X, X min Is the minimum value in the array X, X min And X max The value of the vector data is the maximum value of the spatial domain in the layer, so that no matter how the data is modified, the coordinate value of the vector data cannot exceed the range, the quantity of the embeddable data points can be increased, the robustness of a watermark embedding algorithm can be improved, and the blind detection can be realized; mixing X min And X max As a key which needs to be input when the watermark is extracted, after the vector map is edited and modified or attacked, noise points outside the range are not processed when the watermark is extracted, so that the robustness of the algorithm can be increased;
step A3.2: definition of L X (X min ，X，X max ) To comprise X min X and X max Section L, section L X Is equally divided into D x (D x Not less than 2) sub-intervals, length of each sub-interval t ＝(X max -X min )/D x ；
Step A3.3: coordinate point X ═ X of watermark information to be embedded i |i∈[1，D x ]Each x in i Calculating to obtain x i Two virtual coordinate values adjacent to each other on the left and right sides
Figure BDA0003115582550000112
And
Figure BDA0003115582550000113
step A3.4: statorYi (Chinese character)
Figure BDA0003115582550000114
Is x i At L x The interval sequence number in (2) is,
Figure BDA0003115582550000115
the calculation formula of (c) is:
Figure BDA0003115582550000116
step A3.5: according to
Figure BDA0003115582550000117
Finding x i Adjacent virtual coordinates of
Figure BDA0003115582550000118
And
Figure BDA0003115582550000119
Figure BDA00031155825500001110
x i and its adjacent coordinate value form transverse interval in which the watermark is to be embedded
Figure BDA00031155825500001111
Fig. 2 is a schematic diagram showing the entire X coordinate interval and the virtual coordinate of X.
Step A3.6: obtaining a longitudinal interval of the ordinate Y to be embedded with the watermark by adopting the same principle as the step A3.1 to the step A3.6
Figure BDA0003115582550000121
Step A3.6.1: array Y ═ Y composed of data point ordinates Y i |i∈[1，n]N coordinate values in the array; finding out the maximum value Y of Y max And minimum value Y min The searching method comprises the following steps:
Figure BDA0003115582550000122
wherein y is max Is the maximum value in the array Y, Y min Is the minimum value in the array Y, Y min And Y max The values of all the layers adopt the maximum value of a spatial domain in the layer; will Y min And Y max As a key to be input when extracting the watermark;
step A3.6.2: definition of L Y (Y min ，Y，Yma x ) To contain Y min Y and Y max Section L, section L Y Is equally divided into D y (D y Not less than 2) sub-intervals, length of each sub-interval t ＝(Y max -Y min )/D y ；
Step A3.6.3: coordinate point Y to be embedded with watermark information is { Y ═ Y i |i∈[1，D y ]Each of y i Calculating to obtain y i Two virtual coordinate values adjacent up and down
Figure BDA0003115582550000123
And
Figure BDA0003115582550000124
step A3.6.4:
Figure BDA0003115582550000125
is y i At L y The interval sequence number in (2) is,
Figure BDA0003115582550000126
the calculation formula of (2) is as follows:
Figure BDA0003115582550000127
step A3.6.5: according to
Figure BDA0003115582550000128
Finding y i Adjacent virtual coordinates of
Figure BDA0003115582550000129
And
Figure BDA00031155825500001210
Figure BDA00031155825500001211
y i and its adjacent coordinate value form longitudinal interval in which the watermark is to be embedded
Figure BDA00031155825500001212
The x and y coordinates of such a coordinate point can both construct two coordinates of length l t Section Q of x And Q y The virtual grid is shown in figure 3.
Step A4: embedding watermarks in the virtual grid intervals x and y by adopting a watermark algorithm based on interval state value mapping; the coordinate change value is controlled by setting the length and the width of the grid, and the watermark information is hidden. Watermark algorithm based on interval state value mapping at given x left And x right On the premise of (3), the watermark embedding and extraction of the coordinate point x can be realized, the data is recovered after extraction, and the one-to-one mapping of the coordinate value watermark embedding and extraction is realized. Constructing fixed x by using interval state value mapping-based watermarking algorithm left And x right Embedding and extracting the watermark; and on this basis limit the size of the virtual grid by using the data accuracy and tolerance as constraints (i.e. control x) left And x right The difference value of (b) to limit the shift range of the coordinate point (i.e. to control the change amount of x within a certain range) when the watermark is embedded, thereby ensuring that the disturbance caused by the watermark embedding is controlled within an allowable range.
Step A4.1: and selecting a coordinate point set to be embedded with watermark information, arranging coordinate points on a coordinate axis for sequencing, and generating a new sequence.
Step A4.2: and classifying the ordered coordinate point sequences according to the intervals, so that the horizontal interval Qx and the vertical interval Qy both comprise three adjacent coordinate points.
Step A4.2.1: definition of x left X and x right Is based on three coordinates in the X-axis ordering sequence and satisfies X left ≤x≤x right X is to left And x right The interval between the two is equally divided into m subintervals, and x is the initial abscissa value of the coordinate point; the sub-interval serial number of the position of the x coordinate is an interval state value s, namely the initial state value of the coordinate point of the watermark to be embedded; the interval state value of x is 3 as shown in fig. 4.
Step A4.2.2: as shown in FIG. 5, Qx is defined as including three coordinate values X in the sequence ordered based on the X-axis left X and xr ight The total state interval, i.e. Qx ═ x left ，x，x right ) (ii) a Definition of x center At the midpoint of the interval Q, i.e. x center ＝(x left +x right ) 2; setting the number m of the intervals to 2 c+1 C is the number of watermark bits and c is greater than or equal to 0, then Qx is equally divided into 2 c+1 And (4) sub-intervals.
Step A4.2.3: using the same principle as in steps A4.2.1 to A4.2.2, the vertical section Qy (y) is obtained bottom ，y，y top )。
Step A4.3: the watermark is embedded in the intervals Qx and Qy through mapping of the state values of the x and y intervals.
Step A4.3.1: defining w as the initial watermark to be carried by x, and satisfying that w is more than or equal to 0 and less than or equal to 2 c (ii) a Defining r as a coefficient of x in the interval Q and satisfying
Figure BDA0003115582550000141
Fig. 6 shows a rule for setting the r value.
Step A4.3.2: in the embedding process of the watermark, x which needs to be embedded with the watermark is in the coefficient r of the interval Qx, and the calculation formula is as follows:
Figure BDA0003115582550000142
the coordinate value of the coordinate point x embedded with the watermark is recorded as x ', the interval state value of x' in Qx is recorded as s ', and s' is also recordedThat is, the sequence number of the subinterval where x 'should fall in Qx, i.e., the state value of the coordinate point after embedding the watermark, the calculation formula of s' is: s' ═ 2 c X r + w, because the value of w is (0 ≦ w ≦ 2 c ) Within the range, and r takes a value of 0 or 1, so that s 'takes a value within a range of (0. ltoreq. s' < 2) c+1 ) Nor does x' exceed the range of Qx.
Step A4.3.3: moving x to the s 'th interval, obtaining the value of x' embedded with the watermark:
Figure BDA0003115582550000143
Figure BDA0003115582550000144
wherein
Figure BDA0003115582550000145
Calculation formula of combination k
Figure BDA0003115582550000146
To obtain
Figure BDA0003115582550000147
X 'will lie within the sub-interval s' as shown in fig. 7.
Step A4.3.4: and embedding the watermark into the interval Qy by mapping the state value of the y interval by adopting the same principle as the steps A4.3.1 to A4.3.3 to complete the embedding of w, wherein each coordinate value can be embedded with a w value, namely c bits can be obtained, and each coordinate point can be embedded with 2c bits. The values of x and y are mapped to the intervals Qx and Qy where the watermark w is positioned after the watermark is embedded; because 0. ltoreq. w.ltoreq.2 c So that the value of x will still be in the interval x left ，x right ) The values of middle and y are still in the interval y bottom ，y top ) In the section Qx and Qy, x and y at any position in the section Qx and Qy do not exceed the range of Qx and Qy by this mapping method. The interval state value based on the coordinates is mapped, the coordinates can be subjected to watermark embedding in mathematical principle, the watermarks can be accurately extracted, data can be recovered, and the number of the data is realizedAccording to one-to-one mapping of the coordinate values of the points.
The watermark algorithm based on the interval state value mapping does not provide a reasonable coordinate point moving range in the watermark embedding process, and ignores the precision control of data, so the algorithm is not suitable for a two-dimensional vector map. The invention improves the watermark algorithm based on the interval state value mapping, introduces the idea of embedding the watermark into the two-dimensional vector map, and sets the movable range of the coordinate point in the watermark embedding process, thereby ensuring the usability of the data.
The watermark extraction comprises the following steps:
step B1: obtaining the transverse maximum X of the whole data interval when the watermark is embedded max Minimum value X min And a longitudinal maximum Y max Minimum value Y min In a key space X min 、X max 、Y max 、Y min Watermark extraction is performed, so that the security is enhanced, and the watermark information can be successfully extracted.
Step B2: dividing the whole data coordinate value interval into multiple sub-intervals, and passing through X min 、X max Calculating the length l of each subinterval by the number of the sum subspaces t 。
Equally dividing the interval of the abscissa value of the whole data into D x (D x Not less than 2) sub-intervals, the calculation formula of the length of each sub-interval is l t ＝(X max -X min )/D x . The length of each section may be obtained by equally dividing the longitudinal coordinate value.
Step B3: through length l t And finding a virtual coordinate corresponding to any coordinate point embedded with the watermark is the key of watermark extraction. Because the coordinates of the watermark embedding will not change beyond the virtual grid in which it is located, i.e. the coordinate values are the same as the virtual coordinates before and after the watermark embedding.
Step B3.1: by passing
Figure BDA0003115582550000151
To give x' i Left and right virtual coordinate points of
Figure BDA0003115582550000152
And
Figure BDA0003115582550000153
by passing
Figure BDA0003115582550000154
To give y' i Upper and lower two virtual coordinate points of (2)
Figure BDA0003115582550000155
And
Figure BDA0003115582550000156
step B3.2: x' i And the left and right virtual coordinate values form a transverse interval in which the watermark is to be embedded
Figure BDA0003115582550000157
y′ i And the upper and lower virtual coordinate values form a longitudinal interval in which the watermark is to be embedded
Figure BDA0003115582550000161
Step B4: and (4) extracting the watermark by using a watermark algorithm based on interval state value mapping, and performing copyright verification.
Step B4.1: equal spacing of the sub-intervals of interval Qx
Figure BDA0003115582550000162
And satisfy
Figure BDA0003115582550000163
Subinterval spacing l by x' and Qx s Calculating the interval state value s 'of x' in Qx, wherein the calculation formula is as follows:
s′＝[(x′-x left )/l s ]＝[(x′-x left )/(x right -x left )/2 c+1 ]；
step B4.2: and recovering the watermark value w ' carried by the watermark x ' according to the interval state value s ', wherein the calculation formula is as follows:
w′＝s′-r×2 c ：
combination formula
Figure BDA0003115582550000164
And
Figure BDA0003115582550000165
Figure BDA0003115582550000166
recovering to obtain an original x;
step B4.3: the watermark value w 'carried by the recovered watermark y' and the original y are recovered in the same principle.
In the watermark algorithm based on interval state value mapping, the most value of the coordinate point of the data is directly taken when the minimum value and the maximum value of the coordinate point state axis are set, namely X in the X axis max And X min Taking x of coordinate points directly max And x min The two points can not carry watermark information, and although the watermark can realize blind detection, the robustness of conventional data editing is poor; in addition, if data splicing and data deletion operations occur, the maximum value and the minimum value of the carrier data are changed, and the watermark cannot be extracted correctly, so that the use of the watermark algorithm in a two-dimensional vector map is limited. The invention improves the method, and the maximum value of the spatial domain of the image layer is taken as X max And X min And as a key to enable full blind detection.
Compared with the prior art, the technical scheme of the invention has the following advantages:
(1) on the basis of a watermark algorithm based on interval state value mapping, the maximum value and the minimum value of an interval boundary range are used as the maximum value and the minimum value of an image layer space domain, coordinate points embedded with watermarks are spatially positioned through a virtual grid, a key is generated, operations such as data reordering, data splicing and vertex increasing can be completely resisted, and watermark capacity and robustness of the algorithm are improved.
(2) The range of the virtual grid is the movable range of the coordinate points when the watermarks are embedded, and the step size of the virtual grid is determined according to the requirements of data accuracy and tolerance control of the vector map, so that the moving range of the coordinate points is limited, disturbance caused by watermark embedding is controlled within a reasonable range, and the safety of a watermark algorithm and the usability of data are improved.
(3) Under the reversible watermark algorithm based on the virtual grid, the watermark embedding can be realized by moving the x coordinate, the watermark embedding can also be realized by moving the y coordinate, and the moving range of the y coordinate can be based on the same limiting rule, so that the reversible watermark algorithm based on the virtual grid is suitable for a two-dimensional vector diagram.
(4) In the aspect of data recovery of the reversible watermark, the watermark-containing data can still be recovered and extracted after the data is attacked, the situation that error recovery is carried out on points without watermark information can be avoided, and the capacity of the watermark and the robustness of the algorithm are enhanced.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Various other modifications and alterations will occur to those skilled in the art upon reading the foregoing description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the scope of the invention.

Claims (8)

1. A vector map reversible watermarking algorithm based on virtual grid interval mapping is characterized in that: including the embedding and extraction of the watermark,
the watermark embedding comprises the following steps:
step A1: two adjacent virtual coordinates are created for two data vertexes in the horizontal and vertical directions in which the watermark needs to be embedded to form a virtual grid,
step A2: determining the step size of the virtual grid according to the data precision and tolerance control requirements of the vector map, which specifically comprises the following steps:
step A2.1: when watermark information is embedded into the abscissa X and the ordinate Y of a coordinate point at the same time, the maximum variation of the coordinate point on the abscissa and the ordinate is l t1 The Euclidean space distance variation of coordinate points before and after watermark embedding is as follows:
Figure FDA0003688534130000011
step A2.2: definition of l t1 And l e In the following range:
Figure FDA0003688534130000012
wherein R is the resolution of the data, and T is the tolerance value of the data;
step A2.3: combining step A2.1 with step A2.2 to obtain D x The range of (A) is as follows:
Figure FDA0003688534130000013
on the basis, a larger value meeting the requirements of precision and tolerance is adopted as D x The value of (A) is as follows:
Figure FDA0003688534130000014
Figure FDA0003688534130000015
step A2.4: d is obtained by adopting the same principle as the step A2.1 to the step A2.3 y The value of (A) is as follows:
Figure FDA0003688534130000021
step A3: combining the step size of the virtual grid, and taking the maximum value and the minimum value of the layer spatial domain as the maximum value and the minimum value of the interval boundary range to obtain an interval to be embedded with the watermark, specifically comprising:
step A3.1: array X ═ X composed of data points abscissa X i |i∈[1，n]}, the coordinate values in the array are n, x i As a coordinate pointThe most initial coordinate value before embedding the watermark; find out the maximum value X in X max And minimum value X min The searching method comprises the following steps:
Figure FDA0003688534130000022
wherein x max Is the maximum value in the array X, X min Is the minimum value in the array X, X min And X max The values of all the layers are the maximum values of the spatial domain in the layers;
step A3.2: definition of L X (X min ，X，X max ) To comprise X min X and X max Section L, section L X Is equally divided into D x Sub-interval, wherein D x Not less than 2, length of each subinterval l t ＝(X max -X min )/D x ；
Step A3.3: coordinate point X to be embedded with watermark information is X i |i∈[1，D x ]Each of x in (b) } i Calculating to obtain x i Two virtual coordinate values adjacent to each other on the left and right sides
Figure FDA0003688534130000023
And
Figure FDA0003688534130000024
step A3.4: definition of
Figure FDA0003688534130000025
Is x i At L x The interval sequence number in (1) is,
Figure FDA0003688534130000026
the calculation formula of (2) is as follows:
Figure FDA0003688534130000027
step A3.5: according to
Figure FDA0003688534130000028
Finding x i Adjacent virtual coordinates of
Figure FDA0003688534130000029
And
Figure FDA00036885341300000210
Figure FDA00036885341300000211
x i and its adjacent coordinate value form transverse interval in which the watermark is to be embedded
Figure FDA00036885341300000212
Step A3.6: obtaining a longitudinal interval of the ordinate Y to be embedded with the watermark by adopting the same principle as the step A3.1 to the step A3.6
Figure FDA00036885341300000213
Step A4: embedding watermarks in the virtual grid intervals x and y by adopting a watermark algorithm based on interval state value mapping;
the watermark extraction comprises the following steps:
step B1: obtaining the transverse maximum X of the whole data interval when the watermark is embedded max Minimum value X min And a longitudinal maximum Y max Minimum value Y min ，
Step B2: dividing the whole data coordinate value interval into multiple sub-intervals, and passing through X min 、X max Calculating the length l of each sub-interval by the number of the subspaces t ；
Step B3: through length l t Finding virtual coordinates corresponding to the coordinate points where the watermark is embedded,
step B4: and extracting the watermark by using a watermark algorithm based on interval state value mapping.
2. The vector map reversible watermarking algorithm based on virtual grid interval mapping as claimed in claim 1, wherein: the specific process of the step A3.6 is as follows:
step A3.6.1: array Y ═ Y composed of data point ordinates Y i |i∈[1，n]N coordinate values in the array; find out the maximum value Y in Y max And minimum value Y min The searching method comprises the following steps:
Figure FDA0003688534130000031
wherein y is max Is the maximum value in the array Y, Y min Is the minimum value in the array Y, Y min And Y max The values of all the layers are the maximum values of the spatial domain in the layers;
step A3.6.2: definition of L Y (Y min ，Y，Y max ) To contain Y min Y and Y max Section L, section L Y Is equally divided into D y Sub-interval, wherein D y Not less than 2, length of each subinterval l t ＝(Y max -Y min )/D y ；
Step A3.6.3: coordinate point Y to be embedded with watermark information is { Y ═ Y i |i∈[1，D y ]Each of y i Calculating to obtain y i Two adjacent virtual coordinate values
Figure FDA0003688534130000032
And
Figure FDA0003688534130000033
step A3.6.4:
Figure FDA0003688534130000034
is y i At L y The interval sequence number in (2) is,
Figure FDA0003688534130000035
the calculation formula of (2) is as follows:
Figure FDA0003688534130000036
step A3.6.5: according to
Figure FDA0003688534130000041
Finding y i Adjacent virtual coordinates of
Figure FDA0003688534130000042
And
Figure FDA0003688534130000043
Figure FDA0003688534130000044
y i and its adjacent coordinate value form longitudinal interval in which the watermark is to be embedded
Figure FDA0003688534130000045
3. The vector map reversible watermarking algorithm based on virtual grid interval mapping of claim 1, wherein: the specific process of the step A4 is as follows:
step A4.1: selecting a coordinate point set to be embedded with watermark information, arranging coordinate points on a coordinate axis for sequencing, and generating a new sequence;
step A4.2: classifying the ordered coordinate point sequences according to intervals, so that the transverse interval Qx and the longitudinal interval Qy both comprise three adjacent coordinate points;
step A4.3: the watermark is embedded in the intervals Qx and Qy through mapping of the state values of the x and y intervals.
4. The vector map reversible watermarking algorithm based on virtual grid interval mapping of claim 3, wherein: the specific process of the step A4.2 is as follows:
step A4.2.1: definition of x left X and x right Is based on three coordinates in the X-axis ordering sequence and satisfies X left ≤x≤x right X is to be left And x right The interval between the two is equally divided into m sub-intervals, and x is an initial abscissa value of the coordinate point; the sub-interval sequence number of the position of the x coordinate is the interval state value s;
step A4.2.2: defining Qx as containing three coordinate values X in the ordered sequence based on the X axis left X and x right In the total state interval, Qx ═ x left ,x,x right ) (ii) a Definition of x center Is the midpoint of the interval Q, x cneter ＝(x left +x right ) 2; let the number m of intervals equal to 2 c+1 C is the number of watermark bits and c is greater than or equal to 0, then Qx is equally divided into 2 c+1 A sub-interval;
step A4.2.3: using the same principle as in steps A4.2.1 to A4.2.2, the longitudinal section Qy (y) is obtained bottom ，y，y top )。
5. The vector map reversible watermarking algorithm based on virtual grid interval mapping as claimed in claim 3, wherein: the specific process of the step A4.3 is as follows:
step A4.3.1: defining w as the initial watermark to be carried by x, and satisfying that w is more than or equal to 0 and less than or equal to 2 c (ii) a Defining r as a coefficient of x in the interval Q and satisfying
Figure FDA0003688534130000051
Step A4.3.2: in the embedding process of the watermark, x needing to be embedded with the watermark is in a coefficient r of an interval Qx, and the calculation formula is as follows:
Figure FDA0003688534130000052
the coordinate value of the coordinate point x after embedding the watermark is recorded as x ', the interval state value of x' in Qx is recorded as s ', and the calculation formula of s' is as follows: s' ═ 2 c ×r+w；
Step A4.3.3: moving x to the s 'th interval, obtaining the value of x' embedded with the watermark:
Figure FDA0003688534130000053
Figure FDA0003688534130000054
wherein
Figure FDA0003688534130000055
Step A4.3.4: embedding the watermark into the section Qy by mapping the y section state value by using the same principle as in steps A4.3.1 to A4.3.3, thereby completing the embedding of w.
6. The vector map reversible watermarking algorithm based on virtual grid interval mapping as claimed in claim 1, wherein: the specific process of the step B2 is as follows: equally dividing the interval of the abscissa value of the whole data into D x Sub-interval, wherein D x Not less than 2, the calculation formula of the length of each subinterval is l t ＝(X max -X min )/D x 。
7. The vector map reversible watermarking algorithm based on virtual grid interval mapping as claimed in claim 1, wherein: the step B3 is carried out by the length l t Finding virtual coordinates x 'corresponding to coordinate points embedded with watermarks' i The specific method comprises the following steps:
step B3.1: by passing
Figure FDA0003688534130000056
To obtain x' i Left and right virtual coordinate points of
Figure FDA0003688534130000061
And
Figure FDA0003688534130000062
by passing
Figure FDA0003688534130000063
To give y' i Upper and lower two virtual coordinate points of
Figure FDA0003688534130000064
And
Figure FDA0003688534130000065
step B3.2: x' i And the left and right virtual coordinate values form a transverse interval in which the watermark is to be embedded
Figure FDA0003688534130000066
y′ i And the upper and lower virtual coordinate values form a longitudinal interval in which the watermark is to be embedded
Figure FDA0003688534130000067
8. The vector map reversible watermarking algorithm based on virtual grid interval mapping according to any one of claims 1 to 7, wherein: the specific process of the step B4 is as follows:
step B4.1: equal spacing of sub-intervals of interval Qx
Figure FDA0003688534130000068
And satisfy
Figure FDA0003688534130000069
Subinterval spacing l by x' and Qx s Calculating the interval state value s 'of x' in Qx, wherein the calculation formula is as follows:
s′＝[(x′-x left )/l s ]＝[(x′-x left )/(x right -x left )/2 c+1 ]；
step B4.2: and recovering the watermark value w ' carried by the watermark x ' according to the interval state value s ', wherein the calculation formula is as follows:
w′＝s′-r×2 c ；
combination formula
Figure FDA00036885341300000610
And
Figure FDA00036885341300000611
Figure FDA00036885341300000612
recovering to obtain an original x;
step B4.3: the watermark value w 'carried by the recovered watermark y' and the original y are recovered in the same principle.
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