CN103198448B - Threedimensional model digital watermark embedding based on vertex curvature and blind checking method - Google Patents

Abstract

The invention provides a kind of threedimensional model digital watermark embedding based on vertex curvature and blind checking method, watermark embedding method includes: be modulated watermark information, makes watermark information be in chaos state；Calculate the root-mean-square curvature undulating value on each summit of threedimensional model；Opposite vertexes presses the ascending sequence of undulating value, according to watermark figure place and watermark, the undulating value sequence after sequence is embedded number of times and is divided into some intervals；Undulating value sequence is carried out the unitization process in interval；Calculate undulating value meansigma methods Davg in each interval_i；By amendment Davg_iEmbed watermark；The model vertices coordinate in each interval is revised by alternative manner.The present invention can not only resist that the common attack of threedimensional model such as translates, rotates, scales, summit is out of order, noise, simplify, quantify, and there is higher robustness, can effectively reduce watermark simultaneously and embed the impact on threedimensional model shape, reduce model error, it is provided that the preferably transparency.

Description

Threedimensional model digital watermark embedding based on vertex curvature and blind checking method

Technical field

The present invention relates to computer graphics and technical field of multimedia information, particularly relate to a kind of threedimensional model digital watermark embedding based on vertex curvature and blind checking method.

Background technology

In recent years, digital watermark technology is as one of the effective technology means of copyright protection, it has also become the study hotspot of MultiMedia Field, and prevents infringement from playing an important role in communication for information.But the existing achievement overwhelming majority is both for rest image, audio stream and video flowing, and the achievement in research for threedimensional model digital watermark technology is less.1997, Ohbuchi etc. delivered the article about threedimensional model digital watermark technology first, had started the beginning of threedimensional model digital watermarking research.According to watermark detection process the need of primary object, it is divided into non-blind Detecting digital watermark and Blind detection technology.The research of digital watermark technology at present is concentrated mainly on non-blind Detecting digital watermark aspect, but owing to, in actually detected enforcement, great majority are not easy or can not obtain initial data credibly, thus Blind detection technology has more theory value and application prospect.Meanwhile, having higher transparent requirement to threedimensional model digital watermark technology, this includes two aspects, first, the consciousness transparency, i.e. embedding algorithm will not cause the obvious change of threedimensional model visual quality, and the perceptual organ of people cannot the change of perception threedimensional model；Second, use the transparency, i.e. embedding algorithm does not interferes with the normal use of threedimensional model, and this is even more important in computer-aided design.

Existing threedimensional model digital watermark embedding and blind checking method include following methods:

Utilize and watermark join by image watermark pixel value compared with this thought of low level, construct one group to the most constant parameter vector space of various map functions, embed watermark by revising the relative length of each vector.The method can preferably resist geometric transformation and affine transformation, but not enough for mesh reconstruction robustness.

Utilize vertex curvature to find maximum stable subregion, repeat watermark to be embedded in these subregions.Stablizing and repeating to embed the certain robustness that ensure that shearing and simplify due to subregion, but the foundation of subregion is relevant with model topology, therefore robustness is the highest.

In model conversion to spheric coordinate system, it is larger than or less than a fixed value by the parameter of amendment spherical coordinate, then model conversion is returned in former geometric space.The method is directly to parameter modification, and the amplitude of amendment is relatively big, transparency deficiency clearly.

Carry out archetype standardizing pretreatment and setting up subregion, then select partial-partition and embed the watermark of same position at same subregion.The method needs when setting up subregion to use model center of gravity, does not have a robustness to shearing, and it is bigger by causing same subregion to be partially submerged into the amendment amount of primitive all to embed the watermark of same position for same subregion so that it is the transparency is not enough.

Said method is mainly for the robustness of threedimensional model digital watermarking, but threedimensional model is very sensitive to the embedding of watermark, and outward appearance is easily changed, and even has obvious visual impact, and this makes watermark the most perceived, directly influences visual effect and the application of threedimensional model.

For the problems referred to above, in order to contradiction threedimensional model digital watermark method robustness and the transparency between is better balanced, it is necessary to provide one both to have higher robustness, there is again threedimensional model digital watermark embedding based on vertex curvature and the blind checking method of the preferably transparency.

Summary of the invention

For current threedimensional model digital watermark embedding and blind checking method antagonism common attack such as translation, rotate, scaling, summit is out of order, noise, simplify, quantify the robustness that exists more weak and to the threedimensional model alteration of form problem poor compared with the transparency caused greatly, the invention provides a kind of threedimensional model digital watermark embedding based on vertex curvature and blind checking method, the method can not only resist the common attack of threedimensional model such as translation, rotate, scaling, summit is out of order, noise, simplify, quantify, and there is higher robustness, can effectively reduce watermark simultaneously and embed the impact on threedimensional model shape, reduce model error, the preferably transparency is provided.

To achieve these goals, the technical scheme that the embodiment of the present invention provides is as follows:

A kind of threedimensional model data waterprint embedded method based on vertex curvature, described method includes:

S11, by logistic chaotic maps, watermark information is modulated, makes watermark information be in chaos state；

S12, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value；

S13, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S14, unitization process undulating value sequence carried out in interval；

S15, calculate each interval B_iUndulating value meansigma methods Davg_i；

S16, by amendment Davg_iEmbed watermark；

S17, revise each interval B by alternative manner_iIn model vertices coordinate, make this interval undulating value average Davg_iMeet for desired value Davg '_i。

As a further improvement on the present invention, described step S11 particularly as follows:

Use logistic chaotic maps $\left\{\begin{array}{c}{x}_{k+1}=f\left(k\right)={\mathrm{\μx}}_k(1-x_k)\\ x_{k+1}\∈\left(\mathrm{0,1}\right)\end{array},k=\mathrm{0,1,2},\·\·\·\right.$ Being modulated watermark information, make watermark information be in chaos state, wherein the span of branch parameter μ is [3.569945,4], key (μ, x₀) as key, x₀For the initial value of iteration, k is watermark length.

As a further improvement on the present invention, described step S12 particularly as follows:

S121, the calculating each vertex v of threedimensional model_iGaussian curvature K and mean curvature H:

$K=\frac{2\mathrm{\π}-\underset{k=1}{\overset{N1}{\mathrm{\Σ}}}{\mathrm{\θ}}_k}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\Σ}}}{A}_k},$ $H=\frac{\underset{j=1}{\overset{N2}{\mathrm{\Σ}}}\mathrm{\γ}\left(e_{i,j}\right)}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\Σ}}}{A}_k},$

Wherein, θ_k(k=1,2 ..., N1) represent and v_iAdjacent interior angle, N1 is single order triangle neighborhood intermediate cam shape number, γ (e_i,j) (j=1,2 ..., N2) represent with limit e_i,jFor the angle of two triangulation method vectors on limit, A_k(k=1,2 ..., N1) it is v_iThe area of the triangle in single order triangle neighborhood；

S122, calculate root-mean-square curvature k on each summit of threedimensional model according to Gaussian curvature K and mean curvature H_rms(v):

$k_{\mathrm{rms}}\left(v\right)=\sqrt{4H^2-2K};$

S123, the neighboring region on definition summit, according to watermark strength selected distance radius threshold r, for the vertex v in threedimensional model, set up its neighboring region N_v(v r), is expressed as: N_v(v,r)={v_i|||v_i-v | |≤r}, | | v_i-v | | for v and v_iBetween Euclidean distance；

S124, the neighboring region N on calculating summit_v(v, root-mean-square curvature r) and at the point of interface of model, if v_eRepresent intersection point, v₁And v₂For the model vertices at line segment two ends, intersection point place, then v_eRoot-mean-square curvature k_rms(v_e) it is:

$k_{\mathrm{rms}}\left(v_e\right)=\frac{d_2}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_1\right)+\frac{d_1}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_2\right),$

Wherein, d₁And d₂Represent v respectively₁And v₂To v_eDistance；

S125, the average root-mean-square curvature on calculating summit, add up and determine the neighboring region N on summit_v(v, r) in number of vertices, described summit includes summit and the intersection point on border meeting each threedimensional model of Neighbor Condition, utilizes the meansigma methods of root-mean-square curvature estimation root-mean-square curvature on described summit as the average root-mean-square curvature on this summit:

$k_{\mathrm{rms}}(v,r)=\frac{\underset{i=1}{\overset{N3}{\mathrm{\Σ}}}{k}_{\mathrm{rms}}\left(v_i\right)}{N3},$

Wherein, N3 is N_v(v, r) in number of vertices；

S126, calculate the undulating value on summit, be defined as the standard deviation between the root-mean-square curvature on each summit in the neighboring region centered by vertex v and the average root-mean-square curvature on this summit:

$D_v=\sqrt{\frac{{\underset{i=1}{\overset{N3}{\mathrm{\Σ}}}(k_{\mathrm{rms}}(v,r)-k_{\mathrm{rms}}\left(v_i\right))}^2}{N3}}.$

As a further improvement on the present invention, described step S14 particularly as follows:

To undulating value sequence according to D '_v=(D_v-D_min)/((D_max-D_min)) carry out the unitization process in interval, wherein, D_max、D_minCurvature undulating value minimum and maximum in representing this interval respectively, the undulating value after unitization is distributed between [0,1].

As a further improvement on the present invention, " amendment Davg in described step S16_i" specifically include:

If it is 1 that S161 embeds watermark:

S1611, initialization k=1；

S1612, calculate new undulating value average Davg '_i=(Davg_i)^k；

S1613, judge whether to meetThe most then k=k-Δ k, returns and performs step S1612, if it is not, amendment terminates, whereinFor embedding the intensity of watermark；

If it is 0 that S162 embeds watermark, then

S1621, initialization k=1；

S1622, calculate new undulating value average Davg '_i=(Davg_i)^k；

S1623, judge whether to meetThe most then k=k+ Δ k, returns and performs step S1622, if it is not, amendment terminates.

As a further improvement on the present invention, described step S17 particularly as follows:

S171, to interval B_i, calculate undulating value average Davg of this summit, interval root-mean-square curvature_iAnd with desired value Davg '_iCompare, if Davg_i≤Davg′_i, then to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j+ Δ p, y_j=y_j+ Δ p, z_j=z_j+Δp；If Davg_i＞ Davg '_iThen to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j-Δ p, y_j=y_j-Δ p, z_j=z_j–Δp。

S172, repeatedly execution step S171, until interval B_iUndulating value average Davg of the root-mean-square curvature on middle summit_iMeet | Davg_i-Davg′_i|≤10^-5Till.

Correspondingly, the blind checking method of a kind of threedimensional model data waterprint embedded method based on vertex curvature, described method includes:

S21, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value；

S22, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S23, unitization process undulating value sequence carried out in interval；

S24, calculate each interval B_iUndulating value meansigma methods Davg_i；

S25, extraction interval B_iIn watermark data；

S26, determine final watermark data；

S27, checking watermark dependency.

As a further improvement on the present invention, extraction interval B in described step S25_iIn the formula of watermark data be:

$w_i^{\&prime;}=\left\{\begin{array}{c}1,{\mathrm{Davg}}_i>0.5\\ 0,{\mathrm{Davg}}_i<0.5\end{array},0\&le;i\&le;L\&times;\mathrm{num}-1.\right.$

As a further improvement on the present invention, it is characterised in that described step S26 particularly as follows:

The watermark data extracted in step S25 carries out the statistics of corresponding positions, and making j=imodL, mod is that complementation calculates, i=0,1 ..., L × num-1, if w '_jBe 1 number more than be 0 number, thenOtherwiseAnd then extract the final watermark data of a length of L

As a further improvement on the present invention, described step S27 particularly as follows:

Calculate the correlation with given threshold ratio relatively of the watermark that extracts and original watermark, if correlation is more than given threshold value, then judge model to be detected exists original watermark；Otherwise judging not exist in model to be detected original watermark, described correlation value calculation formula is:

$\mathrm{Cor}(w^d,w)=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_j^d-\stackrel{\&OverBar;}{w^d})(w_i-\stackrel{\&OverBar;}{w})}{\sqrt{{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_j^d-\stackrel{\&OverBar;}{w^d})}^2{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_i-\stackrel{\&OverBar;}{w})}^2}},$

Wherein, w^dBeing the watermark sequence extracted, w is original watermark sequence,It is w^dAverage,It it is the average of w.

There is advantages that

In the case of need not original three-dimensional model data, watermark embedding that the present invention provides and method of detecting watermarks is utilized to solve the difficult problem how effectively to be extracted by watermark information；

Digital watermarking does not affect the serviceability of original three-dimensional model data, and it is the specific information being hidden in original three-dimensional model data, for copyright protection；

The watermark of the method embeds has the good transparency; can resist summit reset, rotate, translate, the common threedimensional model Attack Digital Watermarking such as scaling; and to noise, quantify and simplify that there is good robustness, balance well for the contradiction between the threedimensional model digital watermark embedding of copyright protection and the blind checking method transparency and robustness.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of present invention threedimensional model based on vertex curvature data waterprint embedded method；

Fig. 2 is the idiographic flow schematic diagram that in an embodiment of the present invention, watermark embeds；

Fig. 3 is the schematic flow sheet of present invention threedimensional model based on vertex curvature digital watermarking blind checking method；

Fig. 4 is the idiographic flow schematic diagram of watermark blind Detecting in an embodiment of the present invention；

Fig. 5 a, 5b are respectively the visual effect schematic diagram that in the present invention one specific embodiment, watermark embedding is forward and backward on bunny model；

Fig. 6 a, 6b are respectively the visual effect schematic diagram that in the present invention one specific embodiment, watermark embedding is forward and backward on horse model.

Detailed description of the invention

Describe the present invention below with reference to each embodiment shown in the drawings.But these embodiments are not limiting as the present invention, structure, method or conversion functionally that those of ordinary skill in the art is made according to these embodiments are all contained in protection scope of the present invention.

Shown in ginseng Fig. 1, a kind of based on vertex curvature the threedimensional model data waterprint embedded method of the present invention, including:

S11, by logistic chaotic maps, watermark information is modulated, makes watermark information be in chaos state；

S12, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value；

S13, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S14, unitization process undulating value sequence carried out in interval；

S15, calculate each interval B_iUndulating value meansigma methods Davg_i；

S16, by amendment Davg_iEmbed watermark；

S17, revise each interval B by alternative manner_iIn model vertices coordinate, make this interval undulating value average Davg_iMeet for desired value Davg '_i。

Ginseng Fig. 2 shown in, threedimensional model data waterprint embedded method based on vertex curvature in an embodiment of the present invention particularly as follows:

S11, modulation watermark information, use logistic chaotic maps $\left\{\begin{array}{c}{x}_{k+1}=f\left(k\right)={\mathrm{\&mu;x}}_k(1-x_k)\\ x_{k+1}\&Element;\left(\mathrm{0,1}\right)\end{array},k=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;\right.$ Being modulated watermark information, wherein 0≤μ≤4 are referred to as branch parameter.For making watermark information be in the value of chaos state μ in [3.569945,4], take key (μ, x₀) as key, wherein x₀For the initial value of iteration, k is watermark length, thus constructs watermark sequence information to be embedded.

S12, the calculating each vertex v of threedimensional model_i(i=1,2 ..., N) root-mean-square curvature undulating value, concretely comprise the following steps:

S121, the calculating each vertex v of threedimensional model_iGaussian curvature K and mean curvature H:

$K=\frac{2\mathrm{\&pi;}-\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_k}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{A}_k},$ $H=\frac{\underset{j=1}{\overset{N2}{\mathrm{\&Sigma;}}}\mathrm{\&gamma;}\left(e_{i,j}\right)}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{A}_k},$

Wherein, θ_k(k=1,2 ..., N1) represent and v_iAdjacent interior angle, N1 is single order triangle neighborhood intermediate cam shape number, γ (e_i,j) (j=1,2 ..., N2) represent with limit e_i,jFor the angle of two triangulation method vectors on limit, A_k(k=1,2 ..., N1) it is v_iThe area of the triangle in single order triangle neighborhood；

S122, calculate root-mean-square curvature k on each summit of threedimensional model according to Gaussian curvature K and mean curvature H_rms(v):

$k_{\mathrm{rms}}\left(v\right)=\sqrt{4H^2-2K};$

S123, the neighboring region on definition summit, according to watermark strength selected distance radius threshold r, for the vertex v in threedimensional model, set up its neighboring region N_v(v r), is expressed as: N_v(v,r)={v_i|||v_i-v | |≤r}, | | v_i-v | | for v and v_iBetween Euclidean distance；

S124, the neighboring region N on calculating summit_v(v, root-mean-square curvature r) and at the point of interface of model, if v_eRepresent intersection point, v₁And v₂For the model vertices at line segment two ends, intersection point place, then v_eRoot-mean-square curvature k_rms(v_e) it is:

$k_{\mathrm{rms}}\left(v_e\right)=\frac{d_2}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_1\right)+\frac{d_1}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_2\right),$

Wherein, d₁And d₂Represent v respectively₁And v₂To v_eDistance；

S125, the average root-mean-square curvature on calculating summit, add up and determine the neighboring region N on summit_v(v, r) in number of vertices, described summit includes summit and the intersection point on border meeting each threedimensional model of Neighbor Condition, utilizes the meansigma methods of root-mean-square curvature estimation root-mean-square curvature on described summit as the average root-mean-square curvature on this summit:

$k_{\mathrm{rms}}(v,r)=\frac{\underset{i=1}{\overset{N3}{\mathrm{\&Sigma;}}}{k}_{\mathrm{rms}}\left(v_i\right)}{N3},$

Wherein, N3 is N_v(v, r) in number of vertices；

S126, calculate the undulating value on summit, be defined as the standard deviation between the root-mean-square curvature on each summit in the neighboring region centered by vertex v and the average root-mean-square curvature on this summit:

$D_v=\sqrt{\frac{{\underset{i=1}{\overset{N3}{\mathrm{\&Sigma;}}}(k_{\mathrm{rms}}(v,r)-k_{\mathrm{rms}}\left(v_i\right))}^2}{N3}}.$

S13, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i(i=0,1,...,L×num-1)。

S14, unitization process undulating value sequence carried out in interval, i.e.

D′_v=(D_v-D_min)/((D_max-D_min))

Wherein, D_max、D_minCurvature undulating value minimum and maximum in representing this interval respectively, the undulating value Distribution value after unitization is between [0,1].

S15, calculate each interval B_iUndulating value meansigma methods Davg_i(i=0,1,...,L×num-1)。

S16, by amendment Davg_iEmbed watermark, to Davg_iAmending method specifically includes:

If it is 1 that S161 embeds watermark:

S1611, initialization k=1；

S1612, calculate new undulating value average Davg '_i=(Davg_i)^k；

S1613, judge whether to meetThe most then k=k-Δ k, returns and performs step S1612, if it is not, amendment terminates, whereinFor embedding the intensity of watermark；

If it is 0 that S162 embeds watermark, then

S1621, initialization k=1；

S1622, calculate new undulating value average Davg '_i=(Davg_i)^k；

S1623, judge whether to meetThe most then k=k+ Δ k, returns and performs step S1622, if it is not, amendment terminates.

Wherein, Δ k value is 0.001 in the present embodiment.

S17, revise each interval B by alternative manner_iIn model vertices coordinate, make this interval undulating value average Davg_iMeet for desired value Davg '_i.Specifically comprise the following steps that

S171, to interval B_i, calculate undulating value average Davg of this summit, interval root-mean-square curvature_iAnd with desired value Davg '_iCompare, if Davg_i≤Davg′_i, then to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j+ Δ p, y_j=y_j+ Δ p, z_j=z_j+Δp；If Davg_i＞ Davg '_i, then to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j-Δ p, y_j=y_j-Δ p, z_j=z_j–Δp.Preferably, Δ p value is 0.0001 in the present embodiment.

S172, repeatedly execution step S171, until interval B_iUndulating value average Davg of the root-mean-square curvature on middle summit_iMeet | Davg_i-Davg′_i|≤10^-5Till.

Shown in ginseng Fig. 3, the blind checking method of a kind of based on vertex curvature the threedimensional model data waterprint embedded method of the present invention, including:

S21, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value；

S22, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S23, unitization process undulating value sequence carried out in interval；

S24, calculate each interval B_iUndulating value meansigma methods Davg_i；

S25, extraction interval B_iIn watermark data；

S26, determine final watermark data；

S27, checking watermark dependency.

Ginseng Fig. 4 shown in, in an embodiment of the present invention threedimensional model data waterprint embedded method based on vertex curvature blind checking method particularly as follows:

S21, the calculating each vertex v of threedimensional model_i(i=1,2 ..., N) root-mean-square curvature undulating value, concretely comprise the following steps:

S211, the calculating each vertex v of threedimensional model_iGaussian curvature K and mean curvature H:

$K=\frac{2\mathrm{\&pi;}-\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_k}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{A}_k},$ $H=\frac{\underset{j=1}{\overset{N2}{\mathrm{\&Sigma;}}}\mathrm{\&gamma;}\left(e_{i,j}\right)}{\frac{1}{3}\underset{k=1}{\overset{N1}{\mathrm{\&Sigma;}}}{A}_k},$

Wherein, θ_k(k=1,2 ..., N1) represent and v_iAdjacent interior angle, N1 is single order triangle neighborhood intermediate cam shape number, γ (e_i,j) (j=1,2 ..., N2) represent with limit e_i,jFor the angle of two triangulation method vectors on limit, A_k(k=1,2 ..., N1) it is v_iThe area of the triangle in single order triangle neighborhood；

S212, calculate root-mean-square curvature k on each summit of threedimensional model according to Gaussian curvature K and mean curvature H_rms(v):

$k_{\mathrm{rms}}\left(v\right)=\sqrt{4H^2-2K};$

S213, the neighboring region on definition summit, according to watermark strength selected distance radius threshold r, for the vertex v in threedimensional model, set up its neighboring region N_v(v r), is expressed as: N_v(v,r)={v_i|||v_i-v | |≤r}, | | v_i-v | | for v and v_iBetween Euclidean distance；

S214, the neighboring region N on calculating summit_v(v, root-mean-square curvature r) and at the point of interface of model, if v_eRepresent intersection point, v₁And v₂For the model vertices at line segment two ends, intersection point place, then v_eRoot-mean-square curvature k_rms(v_e) it is:

$k_{\mathrm{rms}}\left(v_e\right)=\frac{d_2}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_1\right)+\frac{d_1}{d_1+d_2}{k}_{\mathrm{rms}}\left(v_2\right),$

Wherein, d₁And d₂Represent v respectively₁And v₂To v_eDistance；

S215, the average root-mean-square curvature on calculating summit, add up and determine the neighboring region N on summit_v(v, r) in number of vertices, described summit includes summit and the intersection point on border meeting each threedimensional model of Neighbor Condition, utilizes the meansigma methods of root-mean-square curvature estimation root-mean-square curvature on described summit as the average root-mean-square curvature on this summit:

$k_{\mathrm{rms}}(v,r)=\frac{\underset{i=1}{\overset{N3}{\mathrm{\&Sigma;}}}{k}_{\mathrm{rms}}\left(v_i\right)}{N3},$

Wherein, N3 is N_v(v, r) in number of vertices；

S216, calculate the undulating value on summit, be defined as the standard deviation between the root-mean-square curvature on each summit in the neighboring region centered by vertex v and the average root-mean-square curvature on this summit:

$D_v=\sqrt{\frac{{\underset{i=1}{\overset{N3}{\mathrm{\&Sigma;}}}(k_{\mathrm{rms}}(v,r)-k_{\mathrm{rms}}\left(v_i\right))}^2}{N3}}.$

S22, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S23, unitization process undulating value sequence carried out in interval, i.e.

D′_v=(D_v-D_min)/((D_max-D_min)),

Wherein, D_max、D_minCurvature undulating value minimum and maximum in representing this interval respectively.

S24, calculate each interval B_iUndulating value meansigma methods Davg_i(i=0,1,...,L×num-1)。

S25, extraction interval B_iIn watermark data: $w_i^{\&prime;}=\left\{\begin{array}{c}1,{\mathrm{Davg}}_i>0.5\\ 0,{\mathrm{Davg}}_i<0.5\end{array},0\&le;i\&le;L\&times;\mathrm{num}-1.\right.$

S26, determine final watermark data:

The watermark data extracted in step S25 carries out the statistics of corresponding positions, and making j=imodL, mod is that complementation calculates, i=0,1 ..., L × num-1, if w '_jBe 1 number more than be 0 number, thenOtherwiseAnd then extract the final watermark data of a length of L

S27, checking watermark dependency:

Calculate the correlation with given threshold ratio relatively of the watermark that extracts and original watermark, if correlation is more than given threshold value, then judge model to be detected exists original watermark；Otherwise judge model to be detected does not exist original watermark.

Wherein correlation value calculation formula is:

$\mathrm{Cor}(w^d,w)=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_j^d-\stackrel{\&OverBar;}{w^d})(w_i-\stackrel{\&OverBar;}{w})}{\sqrt{{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_j^d-\stackrel{\&OverBar;}{w^d})}^2{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_i-\stackrel{\&OverBar;}{w})}^2}},$

Wherein, w^dBeing the watermark sequence extracted, w is original watermark sequence,It is w^dAverage,It it is the average of w.

By above-mentioned seven steps, watermark data can be extracted from model to be detected and judge whether model to be detected includes original watermark, if including original watermark just can verify that the copyright holder that holder is threedimensional model of this watermark.

Below in conjunction with specific embodiment, the present invention is further described:

Bunny and the Horse model that test model selects Stanford university to provide is tested, and wherein Bunny has 34835 summits and 69666 dough sheets, and Horse has 112642 summits and 225280 dough sheets.

Specific embodiment 1: the application on bunny model

1, watermark embeds

Taking watermarking modulation key μ=3.6, x0=0.9, length k=100, the watermark information of generation is:

1100010101010001000100010101000100010101010101000100010101000100010001010100010101010001000100010001；

Value 0.02.

2, watermark detection

In order to verify the robustness of the method, we to embed bunny model after watermark carry out respectively resetting through translation, summit, uniformly scaling, rotations, noise, quantify, simplify the common attacks such as attack after, the 3-DMeshWatermarkingBenchmark software of attack employing LIRIS development in laboratory is carried out.The difference between the watermark sequence of model extraction and original watermark sequence is weighed by design factor dependency, and carry out the model of quantitative measurement archetype and the embedding watermark collimation error after attack by maximum square maxrootmeansquare (MRMS), the collimation error is joined shown in Fig. 5 a, 5b.Experimental result is as shown in table 1.

From experimental result it can be seen that the application present invention, archetype has good watermark after embedding watermark and embeds visual masking effect.After all kinds of attacks, the watermark extracted from model to be detected and original watermark have higher correlation, show that the present invention can preferably resist various common attack, i.e. have higher robustness, can preferably protect the copyright of threedimensional model.

Bunny model M RMS experimental result is 0.55 × 10^-3。

Table 1bunny model dependency experimental result

Specific embodiment 2: the application on horse model

1, watermark embeds

Take watermarking modulation key μ=3.7, x₀=0.7, length k=256, the watermark information of generation is:

1000101000000001010000001000100010100000101010000000010000010001000101010101010101000000101010001000001010001010101000100010101000101000000010101000000100010101010100000000000100010000001000001010101000100000000000010001000000101000101000001000001010000001；

Value 0.01.

2, watermark detection

In order to verify the robustness of the method, we to embed horse model after watermark carry out respectively resetting through translation, summit, uniformly scaling, rotations, noise, quantify, simplify the common attacks such as attack after, the 3-DMeshWatermarkingBenchmark software of attack employing LIRIS development in laboratory is carried out.Weighing the difference between the watermark sequence of model extraction and original watermark sequence by design factor dependency, and carry out the model of quantitative measurement archetype and the embedding watermark collimation error after attack with MRMS, the collimation error is joined shown in Fig. 6 a, 6b.Experimental result is as shown in table 2.

From experimental result it can be seen that the application present invention, archetype has good watermark after embedding watermark and embeds visual masking effect.After all kinds of attacks, the watermark extracted from model to be detected and original watermark have higher correlation, show that the present invention can preferably resist various common attack, i.e. have higher robustness, can preferably protect the copyright of threedimensional model.

Horse model M RMS experimental result is 0.58 × 10^-3。

Table 2horse model dependency experimental result

By embodiment of above it can be seen that compared with prior art, present invention threedimensional model based on vertex curvature digital watermark embedding has the advantages that with blind checking method

In the case of need not original three-dimensional model data, watermark embedding that the present invention provides and method of detecting watermarks is utilized to solve the difficult problem how effectively to be extracted by watermark information；

Digital watermarking does not affect the serviceability of original three-dimensional model data, and it is the specific information being hidden in original three-dimensional model data, for copyright protection；

The watermark of the method embeds has the good transparency; can resist summit reset, rotate, translate, the common threedimensional model Attack Digital Watermarking such as scaling; and to noise, quantify and simplify that there is good robustness, balance well for the contradiction between the threedimensional model digital watermark embedding of copyright protection and the blind checking method transparency and robustness.

It is to be understood that, although this specification is been described by according to embodiment, but the most each embodiment only comprises an independent technical scheme, this narrating mode of description is only for clarity sake, those skilled in the art should be using description as an entirety, technical scheme in each embodiment can also form, through appropriately combined, other embodiments that it will be appreciated by those skilled in the art that.

The a series of detailed description of those listed above is only for illustrating of the feasibility embodiment of the present invention; they also are not used to limit the scope of the invention, and all equivalent implementations or changes made without departing from skill of the present invention spirit should be included within the scope of the present invention.

Claims (7)

1. a threedimensional model data waterprint embedded method based on vertex curvature, it is characterised in that described method includes:

S11, by logistic chaotic maps, watermark information is modulated, makes watermark information be in chaos state；

S12, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value, particularly as follows:

S121, the calculating each vertex v of threedimensional model_iGaussian curvature K and mean curvature H:

$K=\frac{2\mathrm{\&pi;}-\underset{k=1}{\overset{N1}{\&Sigma;}}{\mathrm{\&theta;}}_k}{\frac{1}{3}\underset{k=1}{\overset{N1}{\&Sigma;}}{A}_k},H=\frac{\underset{j=1}{\overset{N2}{\&Sigma;}}{\mathrm{\&gamma;e}}_{i,j}}{\frac{1}{3}\underset{k=1}{\overset{N1}{\&Sigma;}}{A}_k},$

Wherein, θ_k, k=1,2 ..., N1, represent and v_iAdjacent interior angle, N1 is vertex v_iSingle order triangle neighborhood intermediate cam shape number, N2 represents vertex v_iSingle order summit neighborhood in the number of adjacent vertex, e_i,jRepresent vertex v_iThe limit constituted with the adjacent vertex in its single order summit neighborhood, γ e_i,j, j=1,2 ..., N2, represent with limit e_i,jFor the angle of two triangulation method vectors on limit, A_k, k=1,2 ..., N1, for v_iThe area of the triangle in single order triangle neighborhood；

S122, calculate root-mean-square curvature k on each summit of threedimensional model according to Gaussian curvature K and mean curvature H_rms(v):

$k_{rms}\left(v\right)=\sqrt{4H^2-2K};$

S123, the neighboring region on definition summit, according to watermark strength selected distance radius threshold r, for the vertex v in threedimensional model, set up its neighboring region N_v(v r), is expressed as: N_v(v, r)=v_i|||v_i-v | |≤r, | | v_i-v | | for v and v_iBetween Euclidean distance；

S124, the neighboring region N on calculating summit_v(v, root-mean-square curvature r) and at the point of interface of model, if v_eRepresent intersection point, v₁And v₂For the model vertices at line segment two ends, intersection point place, then v_eRoot-mean-square curvature k_rms(v_e) it is:

$k_{rms}\left(v_e\right)=\frac{d_2}{d_1+d_2}{k}_{rms}\left(v_1\right)+\frac{d_1}{d_1+d_2}{k}_{rms}\left(v_2\right),$

Wherein, d₁And d₂Represent v respectively₁And v₂To v_eDistance；

S125, the average root-mean-square curvature on calculating summit, add up and determine the neighboring region N on summit_v(v, r) in number of vertices, described summit includes summit and the intersection point on border meeting each threedimensional model of Neighbor Condition, utilizes the meansigma methods of root-mean-square curvature estimation root-mean-square curvature on described summit as the average root-mean-square curvature on this summit:

$k_{rms}(v,r)=\frac{\underset{i=1}{\overset{N3}{\&Sigma;}}{k}_{rms}\left(v_i\right)}{N3},$

Wherein, N3 is N_v(v, r) in number of vertices；

S126, calculate the undulating value on summit, be defined as the standard deviation between the root-mean-square curvature on each summit in the neighboring region centered by vertex v and the average root-mean-square curvature on this summit:

$D_v=\sqrt{\frac{\underset{i=1}{\overset{N3}{\&Sigma;}}{k}_{rms}(v,r)-k_{rms}{\left(v_i\right)}^2}{N3}};$

S13, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S14, unitization process undulating value sequence carried out in interval；

S15, calculate each interval B_iUndulating value meansigma methods Davg_i；

S16, by amendment Davg_iEmbed watermark, specifically include:

If it is 1 that S161 embeds watermark:

S1611, initialization k=1；

S1612, calculate new undulating value average Davg'_i(Davg_i)^k；

S1613, judge whether to meetThe most then k=k-Δ k, Δ k represent the knots modification of watermark length k, return and perform step S1612, if it is not, amendment terminates, whereinFor embedding the intensity of watermark；

If it is 0 that S162 embeds watermark, then

S1621, initialization k=1；

S1622, calculate new undulating value average Davg'_i(Davg_i)^k；

S1623, judge whether to meetThe most then k=k+ Δ k, Δ k represent the knots modification of watermark length k, return and perform step S1622, if it is not, amendment terminates；

S17, revise each interval B by alternative manner_iIn model vertices coordinate, make this interval undulating value average Davg_iMeet for desired value Davg'_i。

Watermark embedding method the most according to claim 1, it is characterised in that described step S11 particularly as follows:

Use logistic chaotic mapsBeing modulated watermark information, make watermark information be in chaos state, wherein the span of branch parameter μ is [3.569945,4], key (μ, x₀) as key, x₀For the initial value of iteration, k is watermark length.

Watermark embedding method the most according to claim 1, it is characterised in that described step S14 particularly as follows:

To undulating value sequence according to D'_v=(D_v-D_min)/(D_max-D_min)) carry out the unitization process in interval, wherein, D_max、D_minCurvature undulating value minimum and maximum in representing this interval respectively, the undulating value after unitization is distributed between [0,1].

Watermark embedding method the most according to claim 1, it is characterised in that described step S17 particularly as follows:

S171, to interval B_i, calculate undulating value average Davg of this summit, interval root-mean-square curvature_iAnd with desired value Davg'_iCompare, if Davg_i≤Davg'_i, then to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j+ Δ p, y_j=y_j+ Δ p, z_j=z_j+Δp；If Davg_i>Davg'_i, then to the summit V in interval_j=(x_j,y_j,z_j), revise its coordinate: x_j=x_j-Δ p, y_j=y_j-Δ p, z_j=z_j–Δp；Δ p represents the knots modification of apex coordinate；

S172, repeatedly execution step S171, until interval B_iUndulating value average Davg of the root-mean-square curvature on middle summit_iMeet | Davg_i-Davg'_i|≤10^-5Till.

5. the blind checking method of a threedimensional model data waterprint embedded method based on vertex curvature as claimed in claim 1, it is characterised in that described method includes:

S21, the calculating each vertex v of threedimensional model_iRoot-mean-square curvature undulating value；

S22, opposite vertexes press the ascending sequence of undulating value, according to watermark figure place L and watermark, the undulating value sequence after sequence is embedded frequency n um and is divided into L × num interval B_i；

S23, unitization process undulating value sequence carried out in interval；

S24, calculate each interval B_iUndulating value meansigma methods Davg_i；

S25, extraction interval B_iIn watermark data；

S26, determine final watermark data；

S27, checking watermark dependency.

Watermark blind detection the most according to claim 5, it is characterised in that extraction interval B in described step S25_iIn the formula of watermark data be:

$w_i^{\&prime;}=\left\{\begin{array}{c}1,{\mathrm{Davg}}_i>0.5\\ 0,{\mathrm{Davg}}_i<0.5\end{array}\right.,0\&le;i\&le;L\&times;num-1.$

Watermark blind detection the most according to claim 5, it is characterised in that described step S26 particularly as follows:

The watermark data extracted in step S25 carries out the statistics of corresponding positions, and making j=imodL, mod is that complementation calculates, i=0,1 ..., L × num-1, if w'_jBe 1 number more than be 0 number, thenOtherwiseAnd then extract the final watermark data of a length of L