CN108537717A - Three-dimensional grid blind watermarking algorithm based on angle modulated - Google Patents
Three-dimensional grid blind watermarking algorithm based on angle modulated Download PDFInfo
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Abstract
The invention discloses a kind of three-dimensional grid blind watermarking algorithm based on angle modulated, specially：The average curvature on all vertex of three-dimensional grid model is calculated, the point that average curvature is respectively less than 0 is placed on as characteristic point in set of characteristic points, and remaining vertex ownership as a reference point refers to point set, and the invariant space is established using with reference to all the points in point set；Then by apex coordinate rectangular co-ordinate and rectangular co-ordinate is converted to spherical coordinate；According to the total bit N of binary watermarking information sequence to be embedded in, three-dimensional grid model is divided into N number of region；To insertion watermark information at each characteristic point in each region, and according to embedded watermark information, adjust the size of characteristic point angle in each region；After the completion of embedded watermark, spherical coordinate reversion is turned into rectangular co-ordinate, obtains the three-dimensional grid model of embedded watermark, then extract watermark information.The present invention solves the problems, such as that transition existing in the prior art relies on topological structure and extraction process and need to relocate.
Description
Technical field
The invention belongs to three-dimensional grid watermarking algorithm technical fields, and in particular to a kind of three-dimensional grid based on angle modulated
Blind watermarking algorithm.
Background technology
With the development of 3-D scanning technology and computer graphics and the raising of computer performance, threedimensional model number
Digital watermark has also successfully attracted the attention of people, and the protection for model copyright has also obtained prodigious attention.
Three-dimensional grid watermarking algorithm is divided into air space algorithm and frequency domain algorithm two major classes according to watermark embedded location, wherein empty
Domain algorithm research must be than wide and deep.In spatial domain watermark algorithm, threedimensional model be itself available for the geometric properties used compared with
Horn of plenty, and analyze and processing means diversification, can construct the more polymorphic type such as statistical nature, more stablize
Other features, also, spatial domain watermark algorithm is relatively simple, executes speed, passes through effective model division method and watermark
Repetition insertion can preferably resist the attack of topological class.Existing spatial domain three-dimensional grid watermarking algorithm is mainly the following：
The first is the three-dimensional grid watermarking project using triangle similar four-tuple algorithm and tetrahedron volume ratio algorithm, but it is excessively
The topological structure for relying on vertex, after by geometric attack, it is easy to can not extract watermark sequence；Second is a kind of modification mould
The method that type is embedded in watermark to the distance on vertex, but reorientation step is needed when extracting watermark, extraction process is relative complex；
The third is the three-dimensional grid watermarking algorithm based on genetic algorithm, it uses surface error function measurement in watermark telescopiny
Surface distortion degree, but the adaptation field of genetic algorithm is not extensive.
Invention content
The object of the present invention is to provide a kind of three-dimensional grid blind watermarking algorithm based on angle modulated, solves the prior art
Present in transition rely on the problem of topological structure and extraction process need to relocate.
The technical solution adopted in the present invention is the three-dimensional grid blind watermarking algorithm based on angle modulated, specifically according to
Lower step carries out：
Step 1, embedded watermark information
Step 1.1, the average curvature on all vertex of three-dimensional grid model is calculated first, and will according to the value of average curvature
Vertex partition is characterized a little and reference point, is individually placed to：Set of characteristic points SfWith reference point set SrIn, wherein set of characteristic points
SfIn vertex be average curvature be respectively less than 0 point, the corresponding remaining vertex of model is all belonged to reference to point set Sr,
And using with reference to point set SrIn all reference points establish the invariant space；
Step 1.2, by the rectangular co-ordinate for the invariant space that all apex coordinate steps 1.1 are established in three-dimensional grid model
It is expressed as vi=(xi,yi,zi), i indicates i-th of vertex, and is spherical coordinate by the coordinate transformation of all the points newly indicated
Step 1.3, according to the total bit N of binary watermarking information sequence to be embedded in, three-dimensional grid model is divided into N number of area
Domain；
Step 1.4, it gives at each characteristic point in each region and is embedded in watermark information, and according to the watermark information to be embedded in,
It is sequentially adjusted in the θ of the corresponding spherical coordinate of characteristic point in each regioniThe size of angle；
Step 1.5, after the completion of embedded watermark, by the spherical coordinate reversion of all the points turn to rectangular co-ordinate to get to by
The three-dimensional grid model of embedded watermark；
Step 2, watermark information is extracted
Step 2.1, according to the step 1.1-1.3 during embedded watermark information, the three-dimensional after embedded watermark information is obtained
The set of characteristic points of grid model and N number of subregion, the spherical coordinate of characteristic point in set of characteristic points
Step 2.2, in each sub-regions, watermark information is extracted according to formula (9)；
Wherein, θ "iIt is the θ " in the spherical coordinate corresponding to embedded watermark three-dimensional grid model ith feature pointiAngle；w′n
It is the watermark information of n-th of extracted region, n=1.2.3....N, d=(2 π/N), the watermark information number of each extracted region
It is identical with the number of the provincial characteristics point, therefore each region can extract multiple w 'nIf multiple w 'nMiddle watermark information value ' 1 ' is
Majority, then final w 'n=1, if multiple w 'nMiddle watermark information value ' 0 ' is majority, then final w 'n=0；
Step 2.3, such as step 2.2 is executed successively to N number of subregion of embedded watermark three-dimensional grid model, is extracted
Watermark information sequence b ', b '=(w1′、w2′、w3′、、、wN′)。
It is of the invention to be further characterized in that,
The coordinate transformation of all the points is that spherical coordinate conversion formula (1) is in step 1.2：
Wherein, (xc, yc, zc) be three-dimensional grid model center of gravity, (xi, yi, zi) indicate model i-th of vertex, and
ρi∈[0,+∞),θi∈ [0,2 π) and
When carrying out region division in step 1.3, according to the rule rotated clockwise on the section of three-dimensional grid model, draw
Subangle, the equal angular range in each region is 2 π/N.
In embedded watermark bit information, the watermark information embedded by the same all characteristic points divided in region is identical,
For the same position in watermark information sequence, the number of region insertion watermark information and feature points phase in the area is fallen
Together.
First in watermark information sequence is corresponding in turn to for watermark information to N and is embedded into subregional first to N
A region.
The θ of the corresponding spherical coordinate of characteristic point in each region is adjusted in step 1.4iThe adjusting method of the size of angle
For：Assuming that θ 'iIt is the θ of characteristic point corresponding vertexiBy modulated angle, that is, it is exactly i-th of vertex insertion watermark bit information
Angle afterwards, then
Wherein, Δ is embedded step-length, and initial value is Δ=(1/8) × d, and d=(2 π/N), α are Dynamic genes, 0 ＜ α ＜ 4,
wnWhen the insertion watermark information in=1 n-th of region of expression is 1, wnWhen the insertion watermark information in=0 n-th of region of expression is 0.
As embedded watermark information wnWhen=1, the size of adjustment Dynamic gene α makes θ 'iMeet (n- (1/2)) × d≤θ 'i＜
n×d；
As embedded watermark information wnWhen=0, the size of adjustment Dynamic gene α makes θ 'iMeet (n-1) × d≤θ 'i＜ (n-
(1/2))×d。
The formula (6) that spherical coordinate is reversed to rectangular co-ordinate in step 1.5 is：
Wherein, (x 'i,y′i,z′i) indicate i-th of vertex rectangular co-ordinate of three-dimensional grid model after embedded watermark.
The beneficial effects of the invention are as follows：
(1) the present invention is based on the three-dimensional grid blind watermarking algorithms of angle modulated in watermark telescopiny, only selection modification
The angle value on vertex is embedded in watermark, and ensures that radial distance and zenith angle are constant, this makes model maximally reduce mistake
True degree；And the present invention is the operation that the vertex based on grid model carries out, not strong to the topological structure dependence of grid.It is carrying
Original threedimensional model is not needed yet during water intaking print, realizes the operation of watermarking blind extraction；Due to being built using reference point
The coordinate information of the vertical invariant space, reference point is constant in embedded watermarking process, is with the invariant space still when extracting watermark
With reference to conversion spherical coordinate solves the problems, such as extraction watermark reorientation.
(2) present invention use the vertex of model profound level as watermark be embedded in characteristic point can increase the invisibility of watermark with
Resist geometric attacks；The performance that the lattice simplified attack of resistance of algorithm can be improved in subregion insertion is carried out to model；In same area
Domain is repeatedly embedded in the robustness that same watermark bit can enhance the resistance attacked by noise of algorithm.
(3) insertion that watermark information is realized present invention utilizes the geometrical property of model itself, in selected characteristic point mistake
Then Cheng Zhong selects value and is less than 0 by calculating the average curvature values on vertex to classify to all vertex of grid model
Point as watermark be embedded in point；Point according to the average curvature on vertex less than 0 is located at the principle of the surface higher depth of model, this hair
It is bright that the deeper vertex in this part is selected to be embedded in point as the watermark of three-dimensional grid model and remaining vertex is as a reference point
The invariant space is established to improve the robustness of algorithm, the angle for adjusting characteristic point in model each region according to watermark bit value is big
It is small to be embedded in watermark；Specifically according to the direction rotated clockwise, when embedded watermark bit ' 1 ', corresponding is to increase angle；
When being embedded in watermark bit ' 0 ', reduce the angle value of characteristic point, on the one hand solves model and be embedded in point after by rotation attack without legal
On the one hand the problem of position, also improves the performance that model resists the geometric attacks such as noise, simplification, increases its robustness.
Description of the drawings
Fig. 1 is the flow chart of the three-dimensional grid blind watermarking algorithm the present invention is based on angle modulated；
Fig. 2 is the model cut zone schematic diagram of the three-dimensional grid blind watermarking algorithm the present invention is based on angle modulated；
Fig. 3 is the original mould of three-dimensional grid blind watermarking algorithm embodiment ant three-dimensional grid the present invention is based on angle modulated
Type；
Fig. 4 is the original mould of three-dimensional grid blind watermarking algorithm embodiment ant grid illumination the present invention is based on angle modulated
Type；
Fig. 5 is the three-dimensional grid blind watermarking algorithm embodiment horse three-dimensional grid archetype the present invention is based on angle modulated；
Fig. 6 is the three-dimensional grid blind watermarking algorithm embodiment horse grid illumination archetype the present invention is based on angle modulated；
Fig. 7 is the original mould of three-dimensional grid blind watermarking algorithm embodiment leopard three-dimensional grid the present invention is based on angle modulated
Type；
Fig. 8 is three-dimensional grid blind watermarking algorithm embodiment leopard grid illumination archetype of the invention based on angle modulated；
Fig. 9 is the three-dimensional grid blind watermarking algorithm embodiment pig three-dimensional grid archetype the present invention is based on angle modulated；
Figure 10 is the three-dimensional grid blind watermarking algorithm embodiment pig grid illumination archetype the present invention is based on angle modulated；
Figure 11 is three be embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment ant of angle modulated after watermark
Tie up grid model；
Figure 12 is that the light after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment ant of angle modulated
According to model；
Figure 13 is that the three-dimensional after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment horse of angle modulated
Grid model；
Figure 14 is that the illumination after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment horse of angle modulated
Model；
Figure 15 is three be embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment leopard of angle modulated after watermark
Tie up grid model；
Figure 16 is that the light after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment leopard of angle modulated
According to model；
Figure 17 is that the three-dimensional after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment pig of angle modulated
Grid model；
Figure 18 is that the illumination after watermark is embedded in the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment pig of angle modulated
Model；
Figure 19 is that the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment ants of angle modulated to be attacked by simplified
Three-dimensional grid model after 15%；
Figure 20 is that the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment ants of angle modulated to be attacked by simplified
Illumination model after 15%；
Figure 21 is that the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment pigs of angle modulated by simplified attack 15%
Three-dimensional grid model afterwards；
Figure 22 is that the present invention is based on the three-dimensional grid blind watermarking algorithm embodiment pigs of angle modulated by simplified attack 15%
Illumination model afterwards.
Specific implementation mode
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention is based on the three-dimensional grid blind watermarking algorithms of angle modulated, specifically follow the steps below：
Step 1, embedded watermark information, as shown in Figure 1,
Step 1.1, the average curvature on all vertex of three-dimensional grid model is calculated first, and will according to the value of average curvature
Vertex partition is characterized a little and reference point, is individually placed to：Set of characteristic points SfWith reference point set SrIn, wherein set of characteristic points
SfIn vertex be average curvature be respectively less than 0 point, the corresponding remaining vertex of model is all belonged to reference to point set Sr,
And using with reference to point set SrIn all reference points establish the invariant space；
Step 1.2, by the rectangular co-ordinate for the invariant space that all apex coordinate steps 1.1 are established in three-dimensional grid model
It is expressed as vi=(xi,yi,zi), i indicates i-th of vertex, and is spherical coordinate by the coordinate transformation of all the points newly indicatedConversion formula (1) is：
Wherein, (xc, yc, zc) be three-dimensional grid model center of gravity, (xi, yi, zi) indicate model i-th of vertex, and
ρi∈[0,+∞),θi∈ [0,2 π) and
As shown in Fig. 2, step 1.3, according to the total bit N of binary watermarking information sequence to be embedded in, by three-dimensional grid model
It is divided into N number of region；When dividing region, according to the rule rotated clockwise on the section of three-dimensional grid model, angle is divided,
The equal angular range in each region is 2 π/N；θ in n-th of region of model in characteristic point spherical coordinateiMeet：
Rn={ θn,i|(n-1)×(2π/N)≤θi＜ n × (2 π/N) } (2)
Wherein, N is the sum (n in model division domain<=N), RnIt is n-th of region of model, θn,iIt is in n-th of region
θ in all characteristic point spherical coordinatesiThe angular range at place；
Step 1.4, it gives at each characteristic point in each region and is embedded in watermark information, in embedded watermark bit information, together
The watermark information embedded by all characteristic points in stroke subregion is identical, is the same position in watermark information sequence, an area
The number of domain insertion watermark information is identical as feature points in the area are fallen；First in watermark information sequence is to N
Watermark information, which is corresponding in turn to, is embedded into institute subregional first to n-th region.And it according to the watermark information to be embedded in, adjusts successively
The θ of the corresponding spherical coordinate of characteristic point in whole each regioniThe size of angle；
Adjust the θ of the corresponding spherical coordinate of characteristic point in each regioniThe adjusting method of the size of angle is：Assuming that θ 'iIt is
The θ of characteristic point corresponding vertexiBy modulated angle, that is, it is exactly the angle after i-th of vertex insertion watermark bit information, then
Wherein, Δ is embedded step-length, and initial value is Δ=(1/8) × d, and d=(2 π/N), α are Dynamic genes, 0 ＜ α ＜ 4,
wnWhen the insertion watermark information in=1 n-th of region of expression is 1, wnWhen the insertion watermark information in=0 n-th of region of expression is 0；
As embedded watermark information wnWhen=1, the size of adjustment Dynamic gene α makes θ 'iMeet (n- (1/2)) × d≤θ 'i＜
n×d；
As embedded watermark information wnWhen=0, the size of adjustment Dynamic gene α makes θ 'iMeet (n-1) × d≤θ 'i＜ (n-
(1/2))×d。
Step 1.5, after the completion of embedded watermark, by the spherical coordinate reversion of all the points turn to rectangular co-ordinate to get to by
The three-dimensional grid model of embedded watermark；The formula (6) that spherical coordinate is reversed to rectangular co-ordinate is：
Wherein, (x 'i,y′i, z 'i) indicate i-th of vertex rectangular co-ordinate of three-dimensional grid model after embedded watermark；
Step 2, watermark information is extracted
Step 2.2, in each sub-regions, watermark information is extracted according to formula (9)；
Wherein, θ "iIt is the θ " in the spherical coordinate corresponding to embedded watermark three-dimensional grid model ith feature pointiAngle；w′n
It is the watermark information of n-th of extracted region, n=1.2.3....N, d=(2 π/N), the watermark information number of each extracted region
It is identical with the number of the provincial characteristics point, therefore each region can extract multiple w 'nIf multiple w 'nMiddle watermark information value ' 1 ' is
Majority, then final w 'n=1, if multiple w 'nMiddle watermark information value ' 0 ' is majority, then final w 'n=0；If the 8th region has 9
Characteristic point can then extract 9 w ' altogether8, it is assumed that w '8It is value ' 1 ' to have 7 watermark informations, then it is assumed that w '8=1；
Step 2.3, such as step 2.2 is executed successively to N number of subregion of embedded watermark three-dimensional grid model, is extracted
Watermark information sequence b ', b '=(w1′、w2′、w3′、、、wN′)。
Embodiment
The present embodiment selects four three-dimensional grid models.It is respectively embodiment ant, horse, leopard, pig as shown in figs. 3-10
Archetype figure is as experimental subjects, wherein ant model is made of 10206 vertex and 19680 faces；Horse model by
32315 vertex and 66752 face compositions；Leopard model is made of 20676 vertex and 40258 faces；Pig model is by 36817
A vertex and 62589 face compositions, are embedded in, embedded watermarking process is as follows using 32 watermarks：
Step 1.1, it is directed to three-dimensional grid model, calculates the average curvature on all vertex of three-dimensional grid model first, and
And vertex partition is two according to the value of average curvature and is gathered：Set of characteristic points and refer to point set.
Step 1.2, all apex coordinates in model are indicated with the rectangular co-ordinate of the newly-established invariant space, and by new table
The coordinate transformation for all the points shown is spherical coordinate；
Step 1.3, embedded region is divided.It is 32 according to the watermark information sequence total bit to be embedded in, by three-dimensional grid mould
Type is divided into 32 regions, as shown in Fig. 2, dividing angle, Mei Gequ according to the rule rotated clockwise on the section of model
The angular range in domain is consistent, and should be noted that all characteristic points in the same ready-portioned region will the embedded same water
Information bit is printed, embedded number is identical as feature points in one's respective area are fallen；
Step 1.4, according to the watermark information to be embedded in, it is sequentially adjusted in the angular dimension of characteristic point in each region, to reach
To the purpose of embedded watermark；
Step 1.5, after the completion of embedded watermark, the reversion of existing spherical coordinate is turned into rectangular co-ordinate, so far threedimensional model
Watermark telescopiny complete, describe entire algorithmic procedure in a flow diagram in figure 1.And if Figure 11-18 is respectively to implement
Three-dimensional model diagram after example ant, horse, leopard, pig insertion watermark.
It is whether feasible to verify water mark method of the present invention, illustrate in terms of two, watermark is on the one hand embedded in by archetype
Front and back invisibility considers, the invisibility of watermarking algorithm, computational methods such as following formula are evaluated using the equal value difference in root side (RMSE)
(7)：
Wherein, θoriginal,iAnd θtest,iThe angle value of model corresponding vertex respectively after archetype, embedded watermark, N
For watermark bit number；On the other hand, similar to original watermark progress by the watermark extracted from the threedimensional model attacked
Value calculates to verify, its similitude is verified using correlation coefficient value (Corr) in the present invention, such as formula (8)：When Corr values are got over
Close to 1, illustrate that three-dimensional grid model watermarking algorithm robustness is better.
Wherein, m and m ' is respectively the mean value of embedded watermark information sequence b and the watermark information sequence b ' extracted；
Wherein, b=(w1、w2、、、wN), b '=(w1′、w2′、w3′、、、wN′)。
1. invisibility is tested
After watermark insertion, model and archetype error after algorithm insertion watermark it can be seen from model contrast schematic diagram
Smaller, visual quality is interference-free.The experimental results showed that the watermarking algorithm is smaller on model-based vision influence, after embedded watermark
Three-dimensional grid model is almost the same with archetype, human eye can not differentiate difference between the two, hence it is demonstrated that watermark have compared with
Good invisibility.
2. robustness is tested
Table 1 is the three-dimensional grid model of four embedded watermark informations by related between archetype when various attacks
The comparable situation of coefficient value Corr coefficients；
Table 1
(1) plus white noise is attacked
Noise amplitude size used in inventive algorithm is respectively 0.05%, 0.01% and 0.02%.Noise amplitude is got over
Greatly, correlation coefficient value is smaller, and model is more distorted, and the present invention is directed to as can be seen from Table 1 plus white noise has preferable Shandong
Stick.
(2) lattice simplified attack
Model simplification attack is not arbitrary, and intensity should limit within limits, and the determination principle of range is：
Premised on not reducing or damage the application of model-based vision quality, damage model, therefore, watermark extracting should centainly attacked
It is carried out under hit intensity.It is to simplify 5%, 10% and 15% that inventive algorithm used, which simplifies value respectively,.Simplify result such as 1 institute of table
Show, from experimental result as can be seen that inventive algorithm has good anti-simplified attack performance, figure in limited simplified range
19-22 is respectively that ant is attacked by the three-dimensional grid model after attacking 15% and illumination model and pig is simplified by simplified
Three-dimensional grid model after 15% and illumination model.
(3) model rotation attack
Apex coordinate is likely to occur variation when model is rotated, thus influences the integrality of watermark extracting.And this hair
This defect is supplied by establishing the invariant space in bright：The invariant space is established to ensure spy using the vertex with reference to point set
Sign point can determine coordinate position in new coordinate space.Our preference patterns are revolved around X-coordinate axle during the experiment
Turn, the angle of rotation is 10 °, 20 ° and 30 ° respectively, and experimental result is presented in table 1, and inventive algorithm known to analysis result exists
There is the robustness of preferable watermark under different rotation angles.
(4) shearing attack
In shearing attack experiment, since watermark is only embedded in watermark at characteristic point, and characteristic point changes in inventive algorithm
Everywhere for discrete incorporation model, shear only the watermark bit that can be lost embedded by shearing part to model, can not break completely
Bad watermark still can extract relatively complete watermark from remaining model, but compare and white noise be added to attack, is lattice simplified
For attack and rotation attack, the performance that this algorithm is directed to shearing attack is also greatly improved space.It can by data in table 1
Know, shearing part is smaller, and effect is better.
Algorithm pair proposed by the invention plus white noise attack, lattice simplified attack, model rotation attack and shearing attack
There is stronger robustness, is especially adding white noise, lattice simplified and model rotation test part effect best.In shearing experiment
In counted and the difference of shearing part due to archetype, caused experimental result also differs, and model points get over multi-model
Experimental result is better, and shearing attack result is more preferable below 10%, and robustness is stronger.
Claims (8)
1. the three-dimensional grid blind watermarking algorithm based on angle modulated, which is characterized in that specifically follow the steps below：
Step 1, embedded watermark information
Step 1.1, the average curvature on three-dimensional grid model all vertex is calculated first, and according to the value of average curvature by vertex
It is divided into characteristic point and reference point, is individually placed to：Set of characteristic points SfWith reference point set SrIn, wherein set of characteristic points SfIn
Vertex be average curvature be respectively less than 0 point, the corresponding remaining vertex of model is all belonged to reference to point set Sr, and make
With with reference to point set SrIn all reference points establish the invariant space；
Step 1.2, the rectangular co-ordinate for the invariant space that all apex coordinates are established with step 1.1 in three-dimensional grid model is expressed as vi
=(xi,yi,zi), i indicates i-th of vertex, and is spherical coordinate by the coordinate transformation of all the points newly indicated
Step 1.3, according to the total bit N of binary watermarking information sequence b to be embedded in, three-dimensional grid model is divided into N number of region；
Step 1.4, it gives at each characteristic point in each region and is embedded in watermark information, and according to the watermark information to be embedded in, successively
Adjust the θ of the corresponding spherical coordinate of characteristic point in each regioniThe size of angle；
Step 1.5, after the completion of embedded watermark, the spherical coordinate reversion of all the points is turned into rectangular co-ordinate to get to being already embedded in
The three-dimensional grid model of watermark；
Step 2, watermark information is extracted
Step 2.1, according to the step 1.1-1.3 during embedded watermark information, the three-dimensional grid after embedded watermark information is obtained
The set of characteristic points of model and N number of subregion, the spherical coordinate of characteristic point in set of characteristic points
Step 2.2, in each sub-regions, watermark information is extracted according to formula (9)；
Wherein, θ "iIt is the θ " in the spherical coordinate corresponding to embedded watermark three-dimensional grid model ith feature pointiAngle；w′nIt is
The watermark information of n extracted region, n=1.2.3....N, d=(2 π/N), the watermark information number of each extracted region and should
The number of provincial characteristics point is identical, therefore each region can extract multiple w 'nIf multiple w 'nMiddle watermark information value ' 1 ' is majority,
Then final w 'n=1, if multiple w 'nMiddle watermark information value ' 0 ' is majority, then final w 'n=0；
Step 2.3, N number of subregion of embedded watermark three-dimensional grid model is executed successively such as step 2.2, the water extracted
Print information sequence b ', b '=(w1′、w2′、w3′、、、wN′)。
2. the three-dimensional grid blind watermarking algorithm according to claim 1 based on angle modulated, which is characterized in that the step
The coordinate transformation of all the points is that spherical coordinate conversion formula (1) is in 1.2：
Wherein, (xc, yc, zc) be three-dimensional grid model center of gravity, (xi, yi, zi) indicate i-th of vertex of model, and ρi∈
[0,+∞),θi∈ [0,2 π) and
3. the three-dimensional grid blind watermarking algorithm according to claim 1 based on angle modulated, which is characterized in that the step
When carrying out region division in 1.3, according to the rule rotated clockwise on the section of three-dimensional grid model, angle is divided, each
The equal angular range in region is 2 π/N.
4. the three-dimensional grid blind watermarking algorithm according to claim 3 based on angle modulated, which is characterized in that in embedded water
When printing bit information, the watermark information embedded by the same all characteristic points divided in region is identical, is in watermark information sequence
Same position, the number of region insertion watermark information is identical as feature points in the area are fallen.
5. the three-dimensional grid blind watermarking algorithm according to claim 4 based on angle modulated, which is characterized in that the watermark
First to N watermark informations in information sequence, which are corresponding in turn to, is embedded into institute subregional first to n-th region.
6. the three-dimensional grid blind watermarking algorithm according to claim 5 based on angle modulated, which is characterized in that the step
The θ of the corresponding spherical coordinate of characteristic point in each region is adjusted in 1.4iThe adjusting method of the size of angle is：Assuming that θ 'iIt is special
The θ of sign point corresponding vertexiBy modulated angle, that is, it is exactly the angle after i-th of vertex insertion watermark bit information, then
Wherein, Δ is embedded step-length, and initial value is Δ=(1/8) × d, and d=(2 π/N), α are Dynamic gene, 0 ＜ α ＜ 4, wn=1
When indicating that the insertion watermark information in n-th of region is 1, wnWhen the insertion watermark information in=0 n-th of region of expression is 0, n=1,
2,3....., N, b=(w1、w2、、、wN)。
7. the three-dimensional grid blind watermarking algorithm according to claim 6 based on angle modulated, which is characterized in that when embedded water
Official seal ceases wnWhen=1, the size of adjustment Dynamic gene α makes the θ 'iMeet (n- (1/2)) × d≤θ 'i＜ n × d；
As embedded watermark information wnWhen=0, the size of adjustment Dynamic gene α makes the θ 'iMeet (n-1) × d≤θ 'i＜ (n-
(1/2))×d。
8. the three-dimensional grid blind watermarking algorithm according to claim 1 based on angle modulated, which is characterized in that the step
The formula (6) that spherical coordinate is reversed to rectangular co-ordinate in 1.5 is：
Wherein, (x 'i,y′i,z′i) indicate i-th of vertex rectangular co-ordinate of three-dimensional grid model after embedded watermark.
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