CN108470318A - The three-dimensional grid doubly time series model method positioned based on grouping strategy and neighborhood relationships - Google Patents
The three-dimensional grid doubly time series model method positioned based on grouping strategy and neighborhood relationships Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T1/00—General purpose image data processing
- G06T1/0021—Image watermarking
- G06T1/005—Robust watermarking, e.g. average attack or collusion attack resistant
- G06T1/0071—Robust watermarking, e.g. average attack or collusion attack resistant using multiple or alternating watermarks
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T1/00—General purpose image data processing
- G06T1/0021—Image watermarking
- G06T1/0042—Fragile watermarking, e.g. so as to detect tampering
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2201/00—General purpose image data processing
- G06T2201/005—Image watermarking
- G06T2201/0601—Image watermarking whereby calibration information is embedded in the watermark, e.g. a grid, a scale, a list of transformations
Abstract
The invention discloses a kind of three-dimensional grid doubly time series model methods positioned based on grouping strategy and neighborhood relationships.The present invention has the function that carry out copyright protection and content authentication to threedimensional model by being first embedded in robust watermarking and rear embedded fragile watermark.Robust watermarking is grouped to be embedded in watermark information using the distribution character opposite vertexes on threedimensional model vertex, and fragile watermark is then embedded in watermark by adjusting the geometrical relationship between model vertices and a ring neighborhood.Wherein, method carries out doubly time series model coupling processing using double-goal optimal model, to solve the problems, such as that robust watermarking and fragile watermark interfere with each other.The method of the present invention extraction watermark does not need original mesh, and robust watermarking is not interfere with each other with fragile watermark.Meanwhile robust watermarking can resist common attack, attack includes that geometric transformation, noise, vertex are reordered, simplify and segmented, and fragile watermark has the function of tampering location.
Description
Technical field
The present invention relates to a kind of three-dimensional grid doubly time series model methods positioned based on grouping strategy and Domain relation.
Background technology
Digital watermark technology is a kind of is widely recognized as and effective copyright protection strategy.By development for many years, number
Digital watermark is quite ripe, can be applied in the scene of various needs.The basic principle of digital watermarking is to utilize data
Redundancy, the embedded watermark information in original carrier data (such as audio, video, image, threedimensional model).Watermark is believed
Breath can be with meaningful copyright information, such as picture, the trade mark of company and the name etc. of author；It can also be meaningless letter
It ceases, such as the character string or number generated at random.Watermark information is hidden in carrier data, will not destroy initial carrier
Visual effect.The difficulty that water mark method is cracked in the case where watermark telescopiny is unknown is larger, so the peace of digital watermarking
Full property is guaranteed.When people need copyright authentication, watermark extracting side corresponding with watermark telescopiny can be passed through
Method extracts watermark, to achieve the purpose that content authentication, copyright protection.
Compared with traditional digital watermark technology such as image, audio and video, the research of threedimensional model digital watermarking is opposite
It is less.The appearance of this present situation be caused by the topological structure of threedimensional model and the irregular sampling of model data, and
For threedimensional model attack pattern it is complicated and changeable be also a main factor.Relative to image, the expression side of threedimensional model
Method is complex.Image is equivalent to two-dimensional matrix, element value of the pixel value in image as the matrix.This means that it is all this
A little pixels all have intrinsic sequence in the picture, such as can establish a sequence by row scanning or column scan.This
Sequence is commonly used in synchronization watermarking bit (know the position of watermark and be embedded in what order).However, for often constituting
The grid elements of watermark bit carrier, there is no an intrinsic sequences that is simple and stablizing.Vertex in three-dimensional grid file and
Dough sheet sequence is not fixed, and the appearance of model after operating that reorders to model progress vertex does not change, therefore three-dimensional grid
Vertex or putting in order for dough sheet can not be as the foundations of embedded watermark in file.In addition to this, due to threedimensional model
What vertex was unevenly distributed, lack the frequency-domain transform method of an effective three-dimensional grid model.
Threedimensional model digital watermarking requires watermark to have the transparency as image watermark, and threedimensional model is to watermark
Transparency requirement is more stringent, and watermark does not need only to have the visual transparency, it is also necessary to have the functional transparency.Such as
For the model of a part, the precise requirements of specification size are very high, small change can all influence by this zero
The quality of the equipment of part assembling, geometric modification must be in the margins of tolerance of future assembly；Or some threedimensional models have design
On limitation, such as the symmetry of model must be retained.
Invention content
The purpose of the present invention is to provide a kind of three-dimensional grid doubly time series models positioned based on grouping strategy and Domain relation
Method.
The three-dimensional grid model water mark method of the present invention embedded robust watermarking and fragile water simultaneously in three-dimensional grid model
Print, and doubly time series model coupling processing is carried out using double-goal optimal model, it is interfered with each other to solve robust watermarking and fragile watermark
The problem of, reach the double effects of copyright protection and content authentication.
The method of the present invention comprises the concrete steps that：
Step (1) is grouped threedimensional model vertex：
Threedimensional model is transformed into spherical coordinate system from cartesian coordinate system, utilizes the distance pair of model vertices to model center
Vertex is grouped.Even group-division is carried out to model vertices as packet count according to embedded watermark length, each vertex is fallen on
In corresponding group.
Step (2) obtains the vertex quantity in each group, adjusts the quantitative relation of two adjacent groups inner vertex to be embedded in robust
Watermark.In order to reduce the influence to model-based vision effect, as possible vertex of the modification close to group boundary.
Step (3) carries out doubly time series model coupling processing using double-goal optimal model.
If the point changed after threedimensional model insertion robust watermarking is Coupling point, the point that do not changed is non-coupled point.
Pursue two targets：One be three-dimensional grid model deformation it is as small as possible, the other is the insertion of fragile watermark is for robust
The influence of watermark is as small as possible.The small vertex of frontier distance is chosen by double-goal optimal model to be embedded in fragile watermark.
Step (4) carries out piecemeal to fragile watermark, is 128 per block length.Continuous 5 are often encountered in watermark information
" 1 " is just inserted into one " 0 " below, md5 encryption is carried out to each watermark block respectively, in each watermark block and cipher-text information head
It is inserted into mark of the character string " 01111110 " as watermark block and ciphertext BOB(beginning of block).
Three coordinate components of step (5) vertex v (x, y, z) play the role of different in watermark telescopiny：X-component is used
Whether there is embedded watermark in mark vertex v (x, y, z), y-component is for being embedded in watermark information, and z-component is for being embedded in cipher-text information.
It can be embedded in vertex v (x, y, z) by double-goal optimal model selection, obtain a ring neighborhood vertex of vertex v (x, y, z), and right
One ring neighborhood vertex is ranked up.The equal difference on vertex and minimum vertex after the sequence of a ring neighborhood vertex in a ring neighborhood is calculated,
And change the geometrical relationship on vertex and a ring neighborhood by adjusting the coordinate components of respective vertices, to embedded fragile watermark.
The embedded watermark of step (6) extraction is with the following method：
The central point O coordinates of step 6.1. computation models first, then calculate each vertex viTo the distance ρ of model center Oi,
Pass through maximum radius ρmaxWith least radius ρminIt determines the range each organized and model vertices is grouped.
Step 6.2. each two groups since second group form two tuples, compare the vertex of two groups in two tuples
Number.Previous group more than the latter group vertex number, then the watermark information extracted is " 1 ", conversely, the watermark information of extraction is
“0”.It traverses two all tuples and obtains complete robust watermarking.
The equal difference on step 6.3. computation models vertex and one ring neighborhood passes through apex coordinate component x and equal difference
Quantitative relation judges whether the vertex has embedded watermark, if the vertex is embedded vertex, fragile watermark is extracted using y-component,
Cipher-text information is extracted using z-component.
Obtained watermark information w and cipher-text information p is identified according to " 01111110 " and is carried out piecemeal by step 6.4., to every piece
Watermark information carries out md5 encryption and obtains new cipher-text information p'.If p！=p' illustrates that the watermark block is tampered, if instead p
=p' then illustrates that the watermark block is not tampered with, and " 0 " added when removing embedded obtains fragile watermark.
The present invention has the beneficial effect that：
The method of the present invention extraction watermark does not need original mesh, and robust watermarking is not interfere with each other with fragile watermark.Meanwhile
Robust watermarking can resist common attack, and attack includes that geometric transformation, noise, vertex are reordered, simplify and segmented, and fragile watermark has
There is tampering location function.
Description of the drawings
Fig. 1 doubly time series models couple schematic diagram
Fig. 2 doubly time series model algorithm overall procedures
Fig. 3 robust watermarkings are embedded in flow
Fig. 4 fragile watermarks are embedded in flow
Fig. 5 robust watermarkings extract flow
The flow of Fig. 6 fragile watermarks extraction.
Specific implementation mode
The invention will be further described with reference to the accompanying drawings and examples.
As shown in figures 1 to 6, the three-dimensional grid doubly time series model method positioned based on grouping strategy and Domain relation, specific steps
It is as follows：
Step (1) is grouped threedimensional model vertex：
Threedimensional model is transformed into spherical coordinate system from cartesian coordinate system, utilizes the distance pair of model vertices to model center
Vertex is grouped.According to embedded watermark length even group-division, each vertex is fallen in corresponding group.
Enable (xi,yi,zi) represent with N number of vertex quantity threedimensional model i-th of vertex cartesian coordinate.It calculates
Center (the x of threedimensional modelc,yc,zc), obtain main shaft v using principle component analysis.If the origin of spherical coordinate system
Pass through center (xc,yc,zc) on straight line along the directions main shaft v, as shown in formula (1).
It is obtained by exhaustive search, the number of vertices distribution after grouping in each group can be made as uniform as possible, met
The requirement of formula (2).
[tmin,tmax] range of the t that will be considered is defined, this range will meet origin (xc,yc,zc) three
In dimension module boundary, abs (x) represents the absolute value of x, | Bk| expression group BkThe number of inner vertex.
With spherical coordinate (ρi,φi,θi) indicate vertex (xi,yi,zi), and 1≤i≤N, ρi∈ [0 ,+∞), φi∈[0,
π] and θi∈[0,2π).Model is corresponded to radial coordinate P={ ρi:1≤i≤N } vertex be divided into K group B={ Bk:1≤k≤
K }, BKIt is the subset of P, as shown in formula (3).
Bk={ ρi:ρmin+(k-1)·Δρ≤ρi＜ ρmin+k·Δρ} (3)
ρminAnd ρmaxIt is the minimum value and maximum value of P, and
Δρ=(ρmax-ρmin)/K (4)
ΔρIt is each group of range size, sets ρmax∈BK。
Step (2) obtains the vertex quantity in each group, adjusts the quantitative relation of two adjacent groups inner vertex to be embedded in robust
Watermark.As shown in figure 3, in order to reduce the influence to model-based vision effect, modification is close to the vertex of group inner boundary as possible.
After the completion of opposite vertexes grouping, from second group B2Start, adjacent group is divided into binary group (B2,B3), (B4,
B5) ..., (Bk-2,Bk-1), it embeds watermark data into each embeddable two tuple.Meet formula (5) then two tuples be can
Embedded.
|Bk|+|Bk+1|+|Bk+2|≥nthr(nthr≥1) (5)
nthrIt is an integer thresholds of setting, its effect is balance robustness and the transparency.It may be noted that B1And BK
It is not involved in embedded watermark, it means that the two endpoint (ρ projected on main shaftminAnd ρmax) will not be moved in telescopiny
It is dynamic, increase the robustness in extraction process.If K is odd number, also need to exclude a group, the group excluded in the present invention
It is Bk-2。
By increasing or reducing triple (Bk,Bk+1,Bk+2) number on vertex in each group comes to two tuple (Bk,
Bk+1) in embedded watermark bit wi.More specifically, in order to be embedded in wi=0, by vertex from BkAnd Bk+2Move Bk+1In, and it is full
Sufficient formula (6)：
|Bk+1|-|Bk|≥nthr (6)
Vertex is moved to Bk+1Mode there are two types of, one is from BkMiddle mobile nleftA element, according to formula (7)：
Another way is from Bk+2Middle mobile nrightA element, according to formula (8)：
Spherical coordinates is finally transformed into cartesian coordinate, obtains the threedimensional model of embedded robust watermarking.
Step (3) carries out doubly time series model coupling processing using double-goal optimal model.
If the point changed after threedimensional model insertion robust watermarking is Coupling point, the point that do not changed is non-coupled point.
Pursue two targets：One be three-dimensional grid model deformation it is as small as possible, the other is the insertion of fragile watermark
Influence for robust watermarking is as small as possible.The small vertex of frontier distance is chosen by double-goal optimal model to be embedded in fragile water
Print.
It is first embedded in robust as shown in figure 4, being followed for pending three-dimensional grid model carrier during concrete application
Then watermark information is embedded in the principle of fragile watermark again on the basis of having been inserted into robust watermarking.Using such doubly time series model
The phenomenon that embedding strategy is coupled there is robust watermarking and fragile watermark, i.e., after embedded fragile watermark information can influence and cover
The robust watermarking information being embedded in, causes robust watermarking information to be seriously damaged.
As shown in Figure 1, according to radius, there are three groupings：Ci-1Group is located at radius section [ρi-2,ρi-1], organize CiPositioned at radius
Section [ρi-1,ρi], organize Ci+1Positioned at radius section [ρi,ρi+1].Three are grouped the robust watermarking information that has been inserted into and are respectively： Due toIt is required that Ci-1The quantity of class mid point is more than CiGroup.So embedded first
Modifying point P when heavy water prints0By it from CiGroup is moved to Ci-1Group, i.e. P in Fig. 10', this model modification is by the embedding of robust watermarking
Caused by entering.In follow-up embedded fragile watermark, if necessary to further modification P0' and change that there are prodigious uncertain
Property, then P after changing0' position may will continue to fall in original grouping Ci-1, it is also possible to it falls in other groupings, such as Fig. 1 institutes
Show CiIn group, the quantity of two class mid points is changed at this time.
In order to further increase Optimization Solution efficiency, embedded fragile watermark vertex is chosen handling this biobjective scheduling problem
When, propose the insertion vertex of the method choice fragile watermark based on frontier distance (Boundary Distance, BD).The master of BD
It is the frontier distance according to point in its grouping to want thought, as shown in Figure 1, point P1Frontier distance be BD=| d1-d2|, BD values are got over
The small center for illustrating the point and more occuping grouping, is less susceptible to cause the robust watermarking information to having been inserted into when changing this
Change, so the Greedy strategy taken is the small point of preferential selection frontier distance.
Step (4) carries out piecemeal to fragile watermark, is 128 per block length.Continuous 5 are often encountered in watermark information
" 1 " character is just being inserted into " 0 " character below, md5 encryption is carried out to each watermark block respectively, in each watermark block and ciphertext
Information header is inserted into mark of the character string " 01111110 " as watermark block and ciphertext BOB(beginning of block).
Three coordinate components of step (5) vertex v (x, y, z) play the role of different in watermark telescopiny：X-component is used
Whether there is embedded watermark in mark vertex v (x, y, z), y-component is for being embedded in watermark information, and z-component is for being embedded in cipher-text information.
It can be embedded in vertex v (x, y, z) by double-goal optimal model selection, obtain a ring neighborhood vertex of vertex v (x, y, z), and right
One ring neighborhood vertex is ranked up.The equal difference on vertex and minimum vertex after the sequence of a ring neighborhood vertex in a ring neighborhood is calculated,
And change the geometrical relationship on vertex and a ring neighborhood by adjusting the coordinate components of respective vertices, to embedded fragile watermark.
If threedimensional model is expressed as M (V, F), wherein V is the set on all vertex of model M, and F indicates all the three of model M
The geometry of edged surface piece, the i.e. topological structure of representative model.If watermark information is W=(w1,w2,...,wn), vertex is embedded in watermark
It is front and back to be denoted as v (x, y, z) and v (x', y', z') respectively.Specific process is as follows：
Step 5.1. is first ranked up the vertex of threedimensional model：It first sorts according to the size of x, if the size phase of x
Deng, then the size for pressing y sorts, and so on；By piecemeal to watermark information and encryption, 136 W can be obtainedr' and phase
With the P of lengthr'.Then, (wi,pi) be not embedded into the y and z of model vertices coordinate components as a binary composition.
Step 5.2. is by i-th of vertex viVertex in (x, y, z) ring neighborhood is ranked up：First according to the big float of x
Sequence sorts if x's is equal in magnitude by the size of y, and so on；Obtain vertex viThe one ring neighborhood vertex sequence of (x, y, z)
Arrange vj(j=1,2 ...), vjIndicate viVertex in one ring neighborhood, the vertex for coming sequence foremost are v1, while v1It is also one
Minimum vertex in ring neighborhood is labeled as vm(xm,ym,zm).DefinitionIt is vertex viVertex in one ring neighborhood with
Minimum vertex v after the sequence of one ring neighborhood vertexm(xm,ym,zm) equal difference, as shown in formula (9)：
Wherein, N (v) indicates vertex viThe set on vertex in (x, y, z) ring neighborhood, | N (v) | it indicates to push up in a ring neighborhood
The quantity of point.
Step 5.3. sets a parameter lambda, for vertex vi(x, y, z) remembers SixAnd dixValue such as formula (10) shown in：
Then the relationship of formula (11) is obtained：
Wherein QixIt is quotient's then value after rounding still further below of two floating numbers, RixBoth it is after complementation as a result, here
Illustratively, because of RixIt is the remainder of two floating numbers, can be calculated by formula (12)：
Rix=dix-Qix·Six (12)
By the BD distances on each vertex of the seismic responses calculated of doubly time series model coupling processing, need to ensure each of selection
The one ring neighborhood on embedded vertex is independent from each other, that is to say, that the point on a ring neighborhood on each embedded vertex does not weigh mutually
It is folded.One marker bit is arranged to all vertex of the threedimensional model after sequence.The purpose on this embedded vertex of selection is in order to anti-
Only previously embedded fragile watermark information is impacted in embedded fragile watermark.Finally selection simultaneously meet Optimized model with
The one mutually independent vertex of ring neighborhood is that fragile watermark is embedded in vertex.
Assuming that selection is in vertex viWatermark information is embedded in (x, y, z), then QixValue need the requirement for meeting odd number, if
QixIt is even number, then changes di'x=dix+Six.If vertex vi(x, y, z) is not selected embedded vertex, then QixValue it is necessary
It is even number, if QixIt is odd number, similarly changes di'x=dix+Six, as shown in formula (13)：
Wherein η=Qix%2, dix=| x |, therefore can be by adjusting vertex viThe x coordinate component of (x, y, z) is embedding to mark
Enter vertex, shown in adjustment mode such as formula (14)：
Set Siy,Siz,diy,dizValue such as formula (15)：
Then formula (16) is obtained：
Wherein QiyAnd QizIt is quotient's then value after rounding still further below of two floating numbers, RiyAnd RizAfter both being complementation
As a result.
Two tuple (wi,pi) it is to be respectively embedded in vertex v as watermark informationiIn the y and z coordinate component of (x, y, z), institute
It is embedded in watermark with coordinate value by adjusting y and z.QiyAnd QizIf being adjusted to even number indicates embedded 0, it is adjusted to odd number table
Show embedded 1.In order to enable Qiy%2=wiAnd Qiz%2=pi, by the value of embedded watermark come jitter modulation distance diyAnd diz.Tool
Gymnastics is made as shown in formula (17) and formula (18)：
Because of diy=| y |, diz=| z |, it is possible to by changing vertex viThe y of (x, y, z) and z coordinate adjust diy
And diz。
As it can be seen in figures 5 and 6, the watermark that step (6) extraction is embedded, specific as follows：
The central point O coordinates of step 6.1. computation models first, then calculate each vertex viTo the distance ρ of model center Oi,
Pass through maximum radius ρmaxWith least radius ρminIt determines the range each organized and model vertices is grouped.
Step 6.2. each two groups since second group form two tuples, compare the vertex of two groups in two tuples
Number.Previous group more than the latter group vertex number, then the watermark information extracted is " 1 ", conversely, the watermark information of extraction is
" 0 " traverses two all tuples and obtains complete robust watermarking.
The equal difference on step 6.3. computation models vertex and one ring neighborhood passes through apex coordinate component x and equal difference
Quantitative relation judges whether the vertex has embedded watermark, if the vertex is embedded vertex, fragile watermark is extracted using y-component,
Cipher-text information is extracted using z-component.
As shown in fig. 6, for vertex vi' (x', y', z'), definitionIt is vertex viVertex in the ring neighborhood of ' one
Minimum vertex v after sorting with a ring neighborhood vertexm(xm,ym,zm) equal difference, as shown in formula (19)：
For the parameter lambda used in telescopiny, note
It can obtain relationship：
For Qi'xValue be odd number vertex, extracted from the y-component on the vertex and w' and extract p' from z-component.For
The parameter lambda used in watermark telescopiny, note：
It can obtain following relationship：
Finally extract watermark information and encryption information：
W'=Qi'y%2, p'=Qi'z%2 (24)
Obtained watermark information w and cipher-text information p is carried out piecemeal by step 6.4. according to " 01111110 ", to every piece of watermark
Information carries out md5 encryption and obtains new cipher-text information p'.If p！=p' illustrates that the watermark block is tampered, if p=p', removes
" 0 " added when embedded obtains fragile watermark.
Claims (6)
1. the three-dimensional grid doubly time series model method positioned based on grouping strategy and neighborhood relationships, it is characterised in that this method it is specific
Step is：
Step (1) is grouped threedimensional model vertex：Threedimensional model is transformed into spherical coordinate system from cartesian coordinate system, is utilized
Model vertices are grouped to model center apart from opposite vertexes；According to embedded watermark length as packet count to model vertices
Even group-division is carried out, each vertex is fallen in corresponding group；
Step (2) obtains the vertex quantity in each group, adjusts the quantitative relation of two adjacent groups inner vertex to be embedded in robust watermarking；
In order to reduce the influence to model-based vision effect, modification is close to the vertex of group inner boundary as possible；
Step (3) carries out doubly time series model coupling processing using double-goal optimal model；
It is Coupling point to define the point changed after threedimensional model insertion robust watermarking, and the point that do not changed is non-coupled point；It chases after
Seek two targets：One be three-dimensional grid model deformation it is as small as possible, the other is the insertion of fragile watermark is for robust water
The influence of print is as small as possible；The small vertex of frontier distance is chosen by double-goal optimal model to be embedded in fragile watermark；
Step (4) carries out piecemeal to fragile watermark, is 128 per block length；It is often encountered in watermark information continuous 5 " 1 "
Character is just being inserted into " 0 " character below, carries out md5 encryption to each watermark block respectively, believes in each watermark block and ciphertext
It ceases head and is inserted into mark of the character string " 01111110 " as watermark block and ciphertext BOB(beginning of block)；
Three coordinate components of step (5) vertex v (x, y, z) play the role of different in watermark telescopiny：X-component is for marking
Know whether vertex v (x, y, z) has embedded watermark, y-component is for being embedded in watermark information, and z-component is for being embedded in cipher-text information；Pass through
Double-goal optimal model selection can be embedded in vertex v (x, y, z), obtain a ring neighborhood vertex of vertex v (x, y, z), and to a ring
Neighborhood vertex is ranked up；The equal difference on vertex and minimum vertex after the sequence of a ring neighborhood vertex in a ring neighborhood is calculated, and is led to
The coordinate components of respective vertices are overregulated to change the geometrical relationship on vertex and a ring neighborhood, to embedded fragile watermark；
The embedded watermark of step (6) extraction, extraction process are as follows：
The central point O coordinates of step 6.1. computation models first, then calculate each vertex viTo the distance ρ of model center Oi, pass through
Maximum radius ρmaxWith least radius ρminIt determines the range each organized and model vertices is grouped；
Step 6.2. each two groups since second group form two tuples, compare the number of vertex of two groups in two tuples
Mesh；Previous group more than the latter group vertex number, then the watermark information extracted is " 1 ", conversely, the watermark information of extraction is
“0”；It traverses two all tuples and obtains complete robust watermarking；
The equal difference on step 6.3. computation models vertex and vertex in one ring neighborhood, passes through apex coordinate component x and equal difference
Quantitative relation judge whether the vertex has embedded watermark, if the vertex is the vertex of embedded watermark, using y-component extract it is crisp
Weak watermark extracts cipher-text information using z-component；
Obtained watermark information w and cipher-text information p is identified according to " 01111110 " and is carried out piecemeal by step 6.4., to every piece of watermark
Information carries out md5 encryption and obtains new cipher-text information p'；If p！=p' illustrates that the watermark block is tampered, if instead p=p',
Then illustrate that the watermark block is not tampered with, " 0 " added when removing embedded obtains fragile watermark.
2. the three-dimensional grid doubly time series model method according to claim 1 positioned based on grouping strategy and neighborhood relationships,
It is characterized in that step (1) is implemented as follows：
Enable (xi,yi,zi) represent with N number of vertex quantity threedimensional model i-th of vertex cartesian coordinate；It calculates three-dimensional
Center (the x of modelc,yc,zc), obtain main shaft v using principle component analysis；Set the origin of spherical coordinate systemLogical
Cross center (xc,yc,zc) on straight line along the directions main shaft v, as shown in formula (1)；
It is obtained by exhaustive search, the number of vertices distribution after grouping in each group can be made as uniform as possible, meet formula
(2) requirement；
[tmin,tmax] range of the t that will be considered is defined, which will meet origin (xc,yc,zc) in threedimensional model
In boundary, abs (x) represents the absolute value of x, | Bk| expression group BkThe number of inner vertex；
With spherical coordinate (ρi,φi,θi) indicate vertex (xi,yi,zi), and 1≤i≤N, ρi∈ [0 ,+∞), φi∈ [0, π] and
θi∈[0,2π)；Model is corresponded to radial coordinate P={ ρi:1≤i≤N } vertex be divided into K group B={ Bk:1≤k≤K },
BkIt is the subset of P, as shown in formula (3)；
Bk={ ρi:ρmin+(k-1)·Δρ≤ρi＜ ρmin+k·Δρ} (3)
ρminAnd ρmaxIt is the minimum value and maximum value of P, and
Δρ=(ρmax-ρmin)/K (4)
ΔρIt is each group of range size, sets ρmax∈BK。
3. the three-dimensional grid doubly time series model method according to claim 2 positioned based on grouping strategy and neighborhood relationships,
It is characterized in that step (2) is implemented as follows：
After the completion of opposite vertexes grouping, from second group B2Start, adjacent group is divided into binary group (B2,B3), (B4,B5) ...,
(Bk-2,Bk-1), it embeds watermark data into each embeddable two tuple；Meeting formula (5), then two tuples are embeddable；
|Bk|+|Bk+1|+|Bk+2|≥nthr(nthr≥1) (5)
nthrIt is an integer thresholds of setting, due to B1And BKIt is not involved in embedded watermark, therefore two projected on main shaft endpoint
ρminAnd ρmaxIt will not be moved in telescopiny；
By increasing or reducing triple (Bk,Bk+1,Bk+2) number on vertex in each group comes to two tuple (Bk,Bk+1) in
Embedded watermark bit wi；More specifically, in order to be embedded in wi=0, by vertex from BkAnd Bk+2Move Bk+1In, and meet formula
(6)：
|Bk+1|-|Bk|≥nthr (6)
Vertex is moved to Bk+1Mode there are two types of, one is from BkMiddle mobile nleftA element, according to formula (7)：
Another way is from Bk+2Middle mobile nrightA element, according to formula (8)：
Spherical coordinates is finally transformed into cartesian coordinate, obtains the threedimensional model of embedded robust watermarking.
4. the three-dimensional grid doubly time series model method according to claim 3 positioned based on grouping strategy and neighborhood relationships,
It is characterized in that step (3) is implemented as follows：
When handling biobjective scheduling problem selection insertion fragile watermark vertex, propose to be based on frontier distance (Boundary
Distance, BD) method choice fragile watermark insertion vertex.
5. the three-dimensional grid doubly time series model method according to claim 3 positioned based on grouping strategy and neighborhood relationships,
It is characterized in that step (5) is implemented as follows：
Step 5.1. is first ranked up the vertex of threedimensional model：First sort according to the size of x, if x's is equal in magnitude,
It sorts by the size of y, and so on；By piecemeal to watermark information and encryption, 136 W can be obtainedr' and identical length
The P of degreer'；Then, (wi,pi) be not embedded into the y and z of model vertices coordinate components as a binary composition；
Step 5.2. is by i-th of vertex viVertex in (x, y, z) ring neighborhood is ranked up：It first sorts according to the size of x, such as
Fruit x's is equal in magnitude, then the size for pressing y sorts, and so on；Then v is obtainediThe one ring neighborhood vertex sequence v of (x, y, z)j(j
=1,2 ...), vjIndicate viVertex in one ring neighborhood；The vertex for coming sequence foremost is v1, while v1It is also a ring neighborhood
In minimum vertex, be labeled as vm(xm,ym,zm)；DefinitionIt is the vertex in mono- ring neighborhoods of vertex v i and a ring neighborhood
Minimum vertex v after the sequence of vertexm(xm,ym,zm) equal difference, as shown in formula (9)：
Wherein, N (v) indicates vertex viThe set on vertex in (x, y, z) ring neighborhood, | N (v) | indicate vertex in a ring neighborhood
Quantity；
Step 5.3. sets a parameter lambda, for vertex viRemember SixAnd dixValue such as formula (10) shown in：
Then the relationship of formula (11) is obtained：
Wherein QixIt is quotient's then value after rounding still further below of two floating numbers, RixBoth it is after complementation as a result, illustrating here
Once, because of Ri1It is the remainder of two floating numbers, can be calculated by formula (12)：
Rix=dix-Qix·Six (12)
By the BD distances on each vertex of the seismic responses calculated of doubly time series model coupling processing, each insertion for ensureing selection is needed
The one ring neighborhood on vertex is independent from each other, that is to say, that the point on a ring neighborhood on each embedded vertex does not overlap each other；It is right
A marker bit is arranged in all vertex of threedimensional model after sequence；It finally selects while meeting Optimized model and a ring neighborhood phase
Mutual independent vertex is that fragile watermark is embedded in vertex；
Assuming that selection is in vertex viWatermark information is embedded in (x, y, z), then QixValue need the requirement for meeting odd number, if QixIt is
Even number then changes d'ix=dix+Six；If vertex vi(x, y, z) is not selected embedded vertex, then QixValue must be even
Number, if Qi1It is odd number, similarly changes d'ix=dix+Six, as shown in formula (13)：
Wherein η=Qix%2, dix=| x |, therefore can be by adjusting vertex viThe x coordinate component of (x, y, z) marks embedded top
Point, shown in adjustment mode such as formula (14)：
Set Siy,Siz,diy,dizValue such as formula (15)：
Then formula (16) is obtained：
Wherein QiyAnd QizIt is quotient's then value after rounding still further below of two floating numbers, RiyAnd RizIt is the result after the two complementation；
Two tuple (wi,pi) it is to be respectively embedded in vertex v as watermark informationiY and z coordinate component in, so by adjusting y
It is embedded in watermark with the coordinate value of z；QiyAnd QizIf being adjusted to even number indicates embedded 0, it is adjusted to odd number and indicates embedded 1；In order to
Make Qiy%2=wiAnd Qiz%2=pi, by the value of embedded watermark come jitter modulation distance diyAnd diz；Concrete operations such as formula
(17) and shown in formula (18)：
Because of diy=| y |, diz=| z | it can be by changing vertex viThe y and z coordinate component of (x, y, z) adjusts diyAnd diz。
6. the three-dimensional grid doubly time series model method according to claim 5 positioned based on grouping strategy and neighborhood relationships,
It is characterized in that step 6.3 is implemented as follows：
For vertex v 'i(x', y', z'), definitionBe vertex v 'iVertex in one ring neighborhood and a ring neighborhood vertex
Minimum vertex v after sequencem(xm,ym,zm) equal difference, as shown in formula (19)：
For the parameter lambda used in telescopiny, note
It can obtain relationship：
For Q 'ixValue be odd number vertex, extracted from the y-component on the vertex and w' and extract p' from z-component；For watermark
The parameter lambda used in telescopiny, note：
It can obtain following relationship：
Finally extract watermark information and encryption information：
W'=Q 'iy%2, p'=Q 'iz%2 (24).
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