CN102999881A - Producing method and extraction method of fragile watermarks of three-dimensional model with robustness - Google Patents

Abstract

The invention discloses a producing method and an extraction method of fragile watermarks of a three-dimensional model with robustness. The producing method includes: 1) partitioning and scrambling original binary watermark images; 2) manufacturing sorted vertex sequences for embedding in the watermark images; 3) generating novel binary watermarks and novel hashed value blocks; and 4) embedding the novel binary watermarks and the novel hashed value blocks in the vertex sequences respectively, and obtain the three-dimensional model with embedded watermark images. The extraction method comprises: 1) judging whether the watermarks are imbedded in vertexes; 2) obtaining binary watermarks with inserted 0 and corresponding hashed values when the watermarks are embedded; 3) judging suspicious vertexes; 4) obtaining the scrambled binary watermark images during embedding; and 5) performing anti-scrambling on the obtained scrambled binary watermark images, and finishing extraction of the binary watermark images. The producing method and the extraction method of fragile watermarks of the three-dimensional model with the robustness are free of blocking effect and good in robustness, can detect any change of the model during extraction, and can locate tampered areas.

Description

Three-dimensional model fragile watermark production method and extracting method thereof with robustness

Technical field

The present invention relates to video image information safety technique field, relate in particular to a kind of three-dimensional model fragile watermark production method and extracting method thereof with robustness.

Background technology

In recent years, the achievement of relevant digital watermarking both at home and abroad increases day by day.Since Japanese Ohbuchi in 1997 proposed the three-dimensional model digital watermark for the first time, the research of three-dimensional model digital watermark technology had obtained very great development.Yet, the most paper is all about robust digital watermark, only having the minority achievement is Fragile Watermark Algorithm about 3D model integrity checking aspect, and in fact, the Fragile Watermark Algorithm of first piece of 3D model integrity checking aspect is that Yeo and Yeung propose.The method of Fornaro and Sanna reference 2D fragile watermark has proposed the 3D PKI Fragile Watermark Algorithm of CSG model.

All only have one owing to carrying out the Hash watermark information of processing and the information bit of storing the Hash functional value, this Hash function that has caused using in some achievements can only be h (w _i)=w _i, h (w _i)=0.5w _iDeng some simple Hash functions, these simple Hash functions are easy to just can guess out their hash value, be easy to they are implemented to attack.Process if the watermark information that can process carries out Hash by piece, the hash value that obtains is also stored by piece, utilize simultaneously some safe hash algorithms such as MD5 just can more effective opposing attack.

Summary of the invention

In order to overcome the deficiencies in the prior art, the purpose of this invention is to provide a kind of hidden performance is good, reliability is high, have simultaneously robustness three-dimensional model fragile watermark production method and extracting method thereof.

For achieving the above object, technical scheme of the present invention is: a kind of three-dimensional model fragile watermark production method with robustness, comprise the embedding of binary bitmap, and it may further comprise the steps:

1) original binary bitmap is carried out piecemeal and process, adopt identical scramble template to carry out scramble to each block image simultaneously, and repeat n arrangement, obtain the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n), described scramble is: the information order of image is upset, the a pixel is moved on the position of b pixel, the b pixel moves on the position of c pixel ... make it be transformed into the image of disorderly and unsystematic almost illegible, select simultaneously the grid image M (V of the three-dimensional model of watermarking images to be embedded, C), wherein V is the set on summit among the grid image M of three-dimensional model, and C is the annexation on summit among the grid image M of three-dimensional model;

2) the random summit V (x among the selected V ₁, x ₂, x ₃) in order to the embed watermark image, and will select the summit of embed watermark image and the summit adjacent with it according to the size ordering of apex coordinate, the vertex sequence V after obtaining sorting _i(x ₁, x ₂, x ₃), described ordering rule is as follows:

First according to x ₁Coordinate size ordering, if x ₁Coordinate is identical, then according to x ₂Coordinate size ordering, if x ₁And x ₂Coordinate all identical, then according to x ₃Coordinate size ordering;

3) to the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n) insert 0 step, described 0 step of inserting is: as binary bitmap W=(w ₁, w ₂..., w _n) occur continuous 51 o'clock, then inserting one 0 thereafter, obtain inserting binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n);

4) to insert binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n) carry out piecemeal according to 128 as a watermark block, and each watermark piecemeal is carried out the Hash function encrypting of MD5 according to following rule, and the indications of adding 01111110 before each watermark piecemeal is in order to represent the beginning of piece:

If the r piece is W ' _r=(w ' _R1, w ' _R2..., w ' _R128), then

P wherein _s ^rBe hashed value, S is hash length, and S=128; At the r piece W ' with 128 _r=(w ' _R1, w ' _R2..., w ' _R128) indications of front adding 01111110, then produce the new binary watermarking W with 136 " _r

W″ _r＝(0,1,1,1,1,1,1,0,w′ _r1,w′ _r2,...,w′ _rn)

Simultaneously at 128

The front add 01111110 in order to represent the indications of hashed value BOB(beginning of block), then produce the new hashed value piece P ' also have 136 _r

$P_r^{\′}=(\mathrm{0,1,1,1,1,1,1,0},p_1^r,p_2^r,...,p_{128}^r)$

Equally all be 136 new binary watermarking W " _rWith new hashed value piece P ' _rBi-level digital on the correspondence position form 136 to (w ' _i, p _i);

5) incite somebody to action (w ' _i, p _i) deposit vertex sequence V after the ordering in according to following embedding method respectively successively _i(x ₁, x ₂, x ₃) the x of correspondence ₂And x ₃In, namely obtaining the three-dimensional model of embed watermark image, described embedding method is:

For vertex sequence V _i(x ₁, x ₂, x ₃) in come top minimum vertex and be designated as V ' ₁(x ' ₁, x ' ₂, x ' ₃), then its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates

Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v),

For given key parameter N, when j=1, so

And vertex v _iBe designated as d _I1=| x ₁|, following relation is then arranged:

If in vertex v _i(x ₁, x ₂, x ₃) embed watermark, the merchant Q of division arranged _IjBe necessary for odd number, if namely

Be odd number, then

And R _I1=d _I1%S _I1If

Be not odd number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

If in vertex v _i(x ₁, x ₂, x ₃) there are not an embed watermark, the merchant Q of division _IjBe necessary for even number, if namely

Be even number, then And R _I1=d _I1%S _I1If

Be not even number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

Also namely insert vertex v after the watermark ' _iD ' _I1Satisfy following relational expression:

Make M=Q _Ij%2 is by adjusting v _i(x ₁, x ₂, x ₃) x ₁Coordinate changes d _I1, also namely:

For given key parameter N,

And vertex v _iBe designated as d _Ij=| x _j|, if j=2,3, then it all satisfies following relation:

(w _i, p _i) be to embed x ₂, x ₃Watermark, if w _i, p _i1, so must Q _Ij%2=1 also is the merchant Q of division _IjMust be odd number, that is to say if

Be odd number, then And R _I1=d _I1%S _I1

If

Be not odd number and R _Ij＞S _Ij/ 2, then

And R _I1=d _I1%S _I1

If

Be not odd number and R _Ij≤ S _Ij/ 2, then

And R _I1=d _I1%S _I1

Q wherein _IjThe merchant of division, R _I1It is remainder;

If w _i, p _i0, so must Q _Ij%2=0 also is the merchant Q of division _IjMust be even number, that is to say if

Be even number, then And R _I1=d _I1%S _I1If

Be not even number and R _Ij＞S _Ij/ 2, then And R _I1=d _I1%S _I1If

Be not even number and R _Ij≤ S _Ij/ 2, then And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

By adjusting v _i(x ₁, x ₂, x ₃) x _jCoordinate changes d _Ij, namely satisfy:

Relation.

The present invention also provides a kind of extracting method with three-dimensional model fragile watermark of robustness, and it may further comprise the steps:

1) for vertex v ' _i(x ₁, x ₂, x ₃), its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v);

2) judge each vertex v _i(x ₁, x ₂, x ₃) whether having embedded watermark, its judgment rule is: given key parameter N during for embed watermark, note For vertex v ' _iNote d ' _I1=| x ' ₁|, so

R ' _I1=d ' _I1%S ' _I1Q ' wherein _I1The merchant of division, R ' _I1Remainder, if Q _I1Be odd number, there is embed watermark on this summit so, otherwise this summit does not have embed watermark;

3) summit of embed watermark is arranged for each, from its coordinate x ₂Middle extraction w ' is from coordinate x ₃Middle extraction p ', given key parameter N during for embed watermark, note

For vertex v ' _iBe designated as d ' _Ij=| x ' _j|,

If j=2,3; Then

R ' _Ij=d ' _Ij%S ' _Ij, w '=Q ' _I2%2, p '=Q ' _I3%2, wherein Q ' _IjThe merchant of division, R ' _IjRemainder,

All w' and p' form the W ' that contains identifier 01111110, P ', and with W ', then P ' piecemeal removes respectively block identifier 01111110 by block identifier 01111110, the binary watermarking W ' after slotting 0 when the obtaining embed watermark _rAnd corresponding hashed value P ' _r

4) judge suspicious summit, its judgment rule is: calculate P _r=H (W ' _r), if P _rUnequal to P ' _rThen with these summits and adjacent summit thereof as suspicious summit;

5) the binary watermarking W ' after 0 of inserting to obtaining _r0 method of inserting when embedding is carried out inverse operation, in order to remove insert inserted in 0 o'clock 0, the binary bitmap when obtaining embedding behind the scramble;

6) to obtaining the unrest that is inverted of binary bitmap behind the scramble, namely obtain the original binary bitmap that embeds, finish the extraction of binary bitmap.

The present invention adopts above technical scheme, when at first embedding, we have carried out piecemeal and scramble to original binary bitmap, after realizing embedding algorithm, original binary bitmap blocking effect can not occur, then come watermark information is carried out piecemeal with the method for the indications of inserting special character 01111110, then adopt safe Hash function MD5 that watermark block is encrypted, increase the robustness that watermarking images embeds.Use the three-dimensional model of the method embedding of this embed watermark image, and utilize the method for extraction watermarking images of the present invention, can detect any change to model, and can orient the zone of distorting.

Description of drawings

The present invention is further detailed explanation below in conjunction with the drawings and specific embodiments:

Fig. 1 is the schematic flow sheet that the present invention has the three-dimensional model fragile watermark production method of robustness;

Fig. 2 is the schematic flow sheet that the present invention has the three-dimensional model fragile watermark extracting method of robustness.

Embodiment

Shown in Fig. 1 or 2, technical scheme of the present invention is: a kind of three-dimensional model fragile watermark production method with robustness, comprise the embedding of binary bitmap, and it may further comprise the steps:

1) original binary bitmap is carried out piecemeal and process, adopt identical scramble template to carry out scramble to each block image simultaneously, and repeat n arrangement, obtain the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n), described scramble is: the information order of image is upset, the a pixel is moved on the position of b pixel, the b pixel moves on the position of c pixel ... make it be transformed into the image of disorderly and unsystematic almost illegible, select simultaneously the grid image M (V of the three-dimensional model of watermarking images to be embedded, C), wherein V is the set on summit among the grid image M of three-dimensional model, and C is the annexation on summit among the grid image M of three-dimensional model;

2) the random summit V (x among the selected V ₁, x ₂, x ₃) in order to the embed watermark image, and will select the summit of embed watermark image and the summit adjacent with it according to the size ordering of apex coordinate, the vertex sequence V after obtaining sorting _i(x ₁, x ₂, x ₃), described ordering rule is as follows:

First according to x ₁Coordinate size ordering, if x ₁Coordinate is identical, then according to x ₂Coordinate size ordering, if x ₁And x ₂Coordinate all identical, then according to x ₃Coordinate size ordering;

3) to the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n) insert 0 step, described 0 step of inserting is: as binary bitmap W=(w ₁, w ₂..., w _n) occur continuous 51 o'clock, then inserting one 0 thereafter, obtain inserting binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n);

4) to insert binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n) carry out piecemeal according to 128 as a watermark block, and each watermark piecemeal is carried out the Hash function encrypting of MD5 according to following rule, and the indications of adding 01111110 before each watermark piecemeal is in order to represent the beginning of piece:

If the r piece is W ' _r=(w ' _R1, w ' _R2..., w ' _R128), then

P wherein _s ^rBe hashed value, S is hash length, and S=128; At the r piece W ' with 128 _r=(w ' _R1, w ' _R2..., w ' _R128) indications of front adding 01111110, then produce the new binary watermarking W with 136 " _r

W″ _r＝(0,1,1,1,1,1,1,0,w′ _r1,w′ _r2,...,w′ _rn)

Simultaneously at 128

The front add 01111110 in order to represent the indications of hashed value BOB(beginning of block), then produce the new hashed value piece P ' also have 136 _r

$P_r^{\′}=(\mathrm{0,1,1,1,1,1,1,0},p_1^r,p_2^r,...,p_{128}^r)$

Equally all be 136 new binary watermarking W " _rWith new hashed value piece P ' _rBi-level digital on the correspondence position form 136 to (w ' _i, p _i);

5) incite somebody to action (w ' _i, p _i) deposit vertex sequence V after the ordering in according to following embedding method respectively successively _i(x ₁, x ₂, x ₃) the x of correspondence ₂And x ₃In, namely obtaining the three-dimensional model of embed watermark image, described embedding method is:

For vertex sequence V _i(x ₁, x ₂, x ₃) in come top minimum vertex and be designated as V ' ₁(x ' ₁, x ' ₂, x ' ₃), then its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates

Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v),

For given key parameter N, when j=1, so

And vertex v _iBe designated as d _I1=| x ₁|, following relation is then arranged:

If in vertex v _i(x ₁, x ₂, x ₃) embed watermark, the merchant Q of division arranged _IjBe necessary for odd number, if namely

Be odd number, then And R _I1=d _I1%S _I1If

Be not odd number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

If in vertex v _i(x ₁, x ₂, x ₃) there are not an embed watermark, the merchant Q of division _IjBe necessary for even number, if namely

Be even number, then

And R _I1=d _I1%S _I1If

Be not even number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

Also namely insert vertex v after the watermark ' _iD ' _I1Satisfy following relational expression:

Make M=Q _Ij%2 is by adjusting v _i(x ₁, x ₂, x ₃) x ₁Coordinate changes d _I1, also namely:

For given key parameter N,

And vertex v _iBe designated as d _Ij=| x _j|, if j=2,3, then it all satisfies following relation:

(w _i, p _i) be to embed x ₂, x ₃Watermark, if w _i, p _i1, so must Q _Ij%2=1 also is the merchant Q of division _IjMust be odd number, that is to say if

Be odd number, then

And R _I1=d _I1%S _I1

If

Be not odd number and R _Ij＞S _Ij/ 2, then And R _I1=d _I1%S _I1

If

Be not odd number and R _Ij≤ S _Ij/ 2, then

And R _I1=d _I1%S _I1

Q wherein _IjThe merchant of division, R _I1It is remainder;

If w _i, p _i0, so must Q _Ij%2=0 also is the merchant Q of division _IjMust be even number, that is to say if

Be even number, then

And R _I1=d _I1%S _I1If Be not even number and R _Ij＞S _Ij/ 2, then

And R _I1=d _I1%S _I1If

Be not even number and R _Ij≤ S _Ij/ 2, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

By adjusting v _i(x ₁, x ₂, x ₃) x _jCoordinate changes d _Ij, namely satisfy:

Relation.

The present invention also provides a kind of extracting method with three-dimensional model fragile watermark of robustness, and it may further comprise the steps:

1) for vertex v ' _i(x ₁, x ₂, x ₃), its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates

Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v);

2) judge each vertex v _i(x ₁, x ₂, x ₃) whether having embedded watermark, its judgment rule is: given key parameter N during for embed watermark, note

For vertex v ' _iNote d ' _I1=| x ' ₁|, so

R ' _I1=d ' _I1%S ' _I1Q ' wherein _I1The merchant of division, R ' _I1Remainder, if Q _I1Be odd number, there is embed watermark on this summit so, otherwise this summit does not have embed watermark;

3) summit of embed watermark is arranged for each, from its coordinate x ₂Middle extraction w ' is from coordinate x ₃Middle extraction p ', given key parameter N during for embed watermark, note

For vertex v ' _iBe designated as d ' _Ij=| x ' _j|,

If j=2,3; Then

R ' _Ij=d ' _Ij%S ' _Ij, w '=Q ' _I2%2, p '=Q ' _I3%2, wherein Q ' _IjThe merchant of division, R ' _IjRemainder,

All w' and p' form the W ' that contains identifier 01111110, P ', and with W ', then P ' piecemeal removes respectively block identifier 01111110 by block identifier 01111110, the binary watermarking W ' after slotting 0 when the obtaining embed watermark _rAnd corresponding hashed value P ' _r

4) judge suspicious summit, its judgment rule is: calculate P _r=H (W ' _r), if P _rUnequal to P ' _rThen with these summits and adjacent summit thereof as suspicious summit;

5) the binary watermarking W ' after 0 of inserting to obtaining _r0 method of inserting when embedding is carried out inverse operation, in order to remove insert inserted in 0 o'clock 0, the binary bitmap when obtaining embedding behind the scramble;

6) to obtaining the unrest that is inverted of binary bitmap behind the scramble, namely obtain the original binary bitmap that embeds, finish the extraction of binary bitmap.

Claims (2)

1. have the three-dimensional model fragile watermark production method of robustness, comprise the embedding of binary bitmap, it is characterized in that: it may further comprise the steps:

1) original binary bitmap is carried out piecemeal and process, adopt identical scramble template to carry out scramble to each block image simultaneously, and repeat n arrangement, obtain the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n), described scramble is: the information order of image is upset, the a pixel is moved on the position of b pixel, the b pixel moves on the position of c pixel ... make it be transformed into the image of disorderly and unsystematic almost illegible, select simultaneously the grid image M (V of the three-dimensional model of watermarking images to be embedded, C), wherein V is the set on summit among the grid image M of three-dimensional model, and C is the annexation on summit among the grid image M of three-dimensional model;

2) the random summit V (x among the selected V ₁, x ₂, x ₃) in order to the embed watermark image, and will select the summit of embed watermark image and the summit adjacent with it according to the size ordering of apex coordinate, the vertex sequence V after obtaining sorting _i(x ₁, x ₂, x ₃), described ordering rule is as follows:

First according to x ₁Coordinate size ordering, if x ₁Coordinate identical, then according to x ₂Coordinate size ordering, if x ₁And x ₂Coordinate all identical, then according to x ₃Coordinate size ordering;

3) to the binary bitmap W=(w behind the scramble ₁, w ₂..., w _n) insert 0 step, described 0 step of inserting is: as binary bitmap W=(w ₁, w ₂..., w _n) occur continuous 51 o'clock, then inserting one 0 thereafter, obtain inserting binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n);

4) to insert binary bitmap W ' after 0=(w ' ₁, w ' ₂..., w ' _n) carry out piecemeal according to 128 as a watermark block, and each watermark piecemeal is carried out the Hash function encrypting of MD5 according to following rule, and the indications of adding 01111110 before each watermark piecemeal is in order to represent the beginning of piece:

If the r piece is W ' _r=(w ' _R1, w ' _R2..., w ' _R128), then

P wherein _s ^rBe hashed value, S is hash length, and S=128; At the r piece W ' with 128 _r=(w ' _R1, w ' _R2..., w ' _R128) indications of front adding 01111110, then produce the new binary watermarking W with 136 " _r

W″ _r＝(0,1,1,1,1,1,1,0,w′ _r1,w′ _r2,...,w′ _rn)

Simultaneously at 128 The front add 01111110 in order to represent the indications of hashed value BOB(beginning of block), then produce the new hashed value piece P ' also have 136 _r

$P_r^{\′}=(\mathrm{0,1,1,1,1,1,1,0},p_1^r,p_2^r,...,p_{128}^r)$

Equally all be 136 new binary watermarking W " _rWith new hashed value piece P ' _rBi-level digital on the correspondence position form 136 to (w ' _i, p _i);

5) incite somebody to action (w ' _i, p _i) deposit vertex sequence V after the ordering in according to following embedding method respectively successively _i(x ₁, x ₂, x ₃) the x of correspondence ₂And x ₃In, namely obtaining the three-dimensional model of embed watermark image, described embedding method is:

For vertex sequence V _i(x ₁, x ₂, x ₃) in come top minimum vertex and be designated as V ' ₁(x ' ₁, x ' ₂, x ' ₃), then its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates

Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v),

For given key parameter N, when j=1, so

And vertex v _iBe designated as d _I1=| x ₁|, following relation is then arranged:

If in vertex v _i(x ₁, x ₂, x ₃) embed watermark, the merchant Q of division arranged _IjBe necessary for odd number, if namely

Be odd number, then

And R _I1=d _I1%S _I1If

Be not odd number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

If in vertex v _i(x ₁, x ₂, x ₃) there are not an embed watermark, the merchant Q of division _IjBe necessary for even number, if namely

Be even number, then

And R _I1=d _I1%S _I1If

Be not even number, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

Also namely insert vertex v after the watermark ' _iD ' _I1Satisfy following relational expression:

Make M=Q _Ij%2 is by adjusting v _i(x ₁, x ₂, x ₃) x ₁Coordinate changes d _I1, also namely:

For given key parameter N,

And vertex v _iBe designated as d _Ij=| x _j|, if j=2,3, then it all satisfies following relation:

(w _i, p _i) be to embed x ₂, x ₃Watermark, if w _i, p _i1, so must Q _Ij%2=1 also is the merchant Q of division _IjMust be odd number, that is to say if

Be odd number, then

And R _I1=d _I1%S _I1

If

Be not odd number and R _Ij＞S _Ij/ 2, then And R _I1=d _I1%S _I1

If Be not odd number and R _Ij≤ S _Ij/ 2, then

And R _I1=d _I1%S _I1

Q wherein _IjThe merchant of division, R _I1It is remainder;

If w _i, p _i0, so must Q _Ij%2=0 also is the merchant Q of division _IjMust be even number, that is to say if

Be even number, then

And R _I1=d _I1%S _I1

If

Be not even number and R _Ij＞S _Ij/ 2, then

And R _I1=d _I1%S _I1If

Be not even number and R _Ij≤ S _Ij/ 2, then

And R _I1=d _I1%S _I1, Q wherein _IjThe merchant of division, R _I1It is remainder;

By adjusting v _i(x ₁, x ₂, x ₃) x _jCoordinate changes d _Ij, namely satisfy:

Relation.

2. have the extracting method of the three-dimensional model fragile watermark of robustness, it is characterized in that: it may further comprise the steps:

1) for vertex v ' _i(x ₁, x ₂, x ₃), its adjacent vertex and minimum vertex V ' ₁(x ' ₁, x ' ₂, x ' ₃) the average of coordinate difference of respective coordinates

Satisfy following relation:

$x_{\mathrm{ij}}^c=\frac{1}{\left|N\left(v\right)\right|}\underset{i=N\left(v\right)}{\mathrm{\Σ}}(x_{\mathrm{ij}}-x_j^{\′}),j=\mathrm{1,2,3},$

Wherein N (v) is vertex v _i(x ₁, x ₂, x ₃) set of adjacent vertex, | N (v) | be the number on the summit of set N (v);

2) judge each vertex v _i(x ₁, x ₂, x ₃) whether having embedded watermark, its judgment rule is: given key parameter N during for embed watermark, note

For vertex v ' _iNote d ' _I1=| x ' ₁|, so

R ' _I1=d ' _I1%S ' _I1Q ' wherein _I1The merchant of division, R ' _I1Remainder, if Q _I1Be odd number, there is embed watermark on this summit so, otherwise this summit does not have embed watermark;

3) summit of embed watermark is arranged for each, from its coordinate x ₂Middle extraction w ' is from coordinate x ₃Middle extraction p ', given key parameter N during for embed watermark, note For vertex v ' _iBe designated as d ' _Ij=| x ' _j|,

If j=2,3; Then

R ' _Ij=d ' _Ij%S ' _Ij, w '=Q ' _I2%2, p '=Q ' _I3%2, wherein Q ' _IjThe merchant of division, R ' _IjRemainder,

All w' and p' form the W' that contains identifier 01111110, P', and with W ', then P ' piecemeal removes respectively block identifier 01111110 by block identifier 01111110, the binary watermarking W ' after slotting 0 when the obtaining embed watermark _rAnd corresponding hashed value P ' _r

4) judge suspicious summit, its judgment rule is: calculate P _r=H (W ' _r), if P _rUnequal to P ' _rThen with these summits and adjacent summit thereof as suspicious summit;

5) the binary watermarking W ' after 0 of inserting to obtaining _r0 method of inserting when embedding is carried out inverse operation, in order to remove insert inserted in 0 o'clock 0, the binary bitmap when obtaining embedding behind the scramble;

6) to obtaining the unrest that is inverted of binary bitmap behind the scramble, namely obtain the original binary bitmap that embeds, finish the extraction of binary bitmap.

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