CN103198448A - Three-dimensional model digital watermarking embedding method and blind detection method based on vertex curvature - Google Patents

Abstract

The invention provides a three-dimensional model digital watermarking embedding method and a blind detection method based on vertex curvature. The three-dimensional model digital watermarking embedding method based on the vertex curvature comprises the following steps: watermarking information is modulated, so that the watermarking information is in a chaos state; root mean square curvature fluctuating value of each vertex of a three-dimensional model is calculated; the vertexes are sequenced from small to large according to the fluctuating values, and a sequenced fluctuating value sequence is divided into a plurality of intervals according to watermarking digits and watermarking embedding times; unitization processing within the intervals is conducted on the fluctuating value sequence; an average value Davgi of the fluctuating values of each interval is calculated; watermarking is embedded by modifying the Davgi; and a model vertex coordinate of each interval is modified through an iterative method. The three-dimensional model digital watermarking embedding method and the blind detection method based on the vertex curvature have the advantages that not only common attacks such as translating, rotation, zooming, vertex derangement, noise, simplification and quantization of the three-dimensional model can be resisted, and high robustness is possessed, meanwhile, but also influence of watermarking embedding on shapes of the three-dimensional model can be effectively reduced, model errors are reduced, and good transparency is provided.

Description

Three-dimensional model digital watermarking embedding and blind checking method based on vertex curvature

Technical field

The present invention relates to computer graphics and multi-media information security technical field, relate in particular to a kind of three-dimensional model digital watermarking embedding and blind checking method based on vertex curvature.

Background technology

In recent years, digital watermark technology has become the research focus in multimedia field as one of effective technology means of copyright protection, and prevents that in information interchange infringement from playing an important role.But the existing achievement overwhelming majority all is at rest image, audio stream and video flowing, and is less for the achievement in research of three-dimensional model digital watermark technology.1997, Ohbuchi etc. delivered the article about the three-dimensional model digital watermark technology first, had started the beginning of three-dimensional model digital watermarking research.According to watermark detection process needs primary object whether, be divided into non-blind Detecting digital watermark and blind Detecting digital watermark.The research of digital watermark technology at present mainly concentrates on non-blind Detecting digital watermark aspect, but because on actual detected was implemented, great majority were not easy or can not obtain raw data credibly, thereby the blind Detecting digital watermark has more theoretical value and application prospect.Simultaneously, the three-dimensional model digital watermark technology is had higher transparent requirement, this comprises two aspects, first, the consciousness transparency, the i.e. embedding of digital watermarking can not cause the obvious change of three-dimensional model visual quality, the variation that people's perceptual organ can't the perception three-dimensional model; The second, use the transparency, i.e. the embedding of digital watermarking can not influence the normal use of three-dimensional model, and this is even more important in computer-aided design (CAD).

Existing three-dimensional model digital watermarking embedding and blind checking method comprise following method:

Utilize in the image watermark watermark is joined the pixel value than this thought of low level, construct one group to various map functions constant parameter vector space all, by revising each vectorial relative length embed watermark.This method can be resisted geometric transformation and affined transformation preferably, but for mesh reconstruction robustness deficiency.

Utilize vertex curvature to seek the maximum stable subregion, watermark is repeated to be embedded in these subregions.Since subregion stable and repeat to embed the certain robustness that has guaranteed shearing and simplifying, but the foundation of subregion is relevant with model topology, so robustness is not high.

In spheric coordinate system, make model conversion it be greater than or less than a fixed value by the parameter of revising spherical co-ordinate, again model conversion is got back in the former geometric space.This method is directly to parameter modification, and the amplitude of modification is bigger, transparency deficiency clearly.

To standardize pre-service and set up subregion of master pattern, select the part subregion then and embed same position watermark at same subregion.This method need be used the model center of gravity when setting up subregion, do not have robustness to shearing, and will cause the index word that is partially submerged into primitive of same subregion bigger and all embed same position watermark for same subregion, makes its transparency not enough.

Said method is primarily aimed at the robustness of three-dimensional model digital watermarking, but three-dimensional model is very sensitive to the embedding of watermark, and outward appearance is subject to change, even has tangible visual impact, this makes watermark easily perceived, directly has influence on visual effect and the application of three-dimensional model.

At the problems referred to above, for the contradiction between balance three-dimensional model digital watermark method robustness and the transparency better, be necessary to provide a kind of higher robustness that both had, have three-dimensional model digital watermarking embedding and the blind checking method based on vertex curvature of the better transparency again.

Summary of the invention

At present three-dimensional model digital watermarking embedding and blind checking method antagonism common attack such as translation, rotation, convergent-divergent, the summit is out of order, noise, simplify, the robustness that quantize to exist transparent relatively poor problem more weak and that the three-dimensional model alteration of form is caused more greatly, the invention provides a kind of three-dimensional model digital watermarking embedding and blind checking method based on vertex curvature, this method can not only be resisted the common attack of three-dimensional model such as translation, rotation, convergent-divergent, the summit is out of order, noise, simplify, quantize, and has higher robustness, can effectively reduce simultaneously the watermark embedding to the influence of three-dimensional model shape, reduce model error, the transparency preferably is provided.

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

A kind of three-dimensional model data waterprint embedded method based on vertex curvature, described method comprises:

S11, with the logistic chaotic maps watermark information is modulated, made watermark information be in chaos state;

S12, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S13, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S14, the undulating quantity sequence is carried out unit processing in interval;

S15, calculate each interval B _iUndulating quantity mean value Davg _i

S16, by revising Davg _iEmbed watermark;

S17, revise each interval B by alternative manner _iIn the model vertices coordinate, make this interval undulating quantity average Davg _iSatisfy and be desired value Davg ' _i

As a further improvement on the present invention, described step S11 is specially:

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

As a further improvement on the present invention, described step S12 is specially:

S121, each vertex v of calculating three-dimensional 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) expression and v _iAdjacent interior angle, N1 are single order triangle neighborhood intermediate cam shape number, γ (e _{I, j}) (j=1,2 ..., N2) expression is with limit e _{I, j}Be the angle of two triangulation method vectors on limit, A _k(k=1,2 ..., N1) be v _iLeg-of-mutton area in the single order triangle neighborhood;

S122, calculate the root mean square curvature k on each summit of three-dimensional model according to Gaussian curvature K and mean curvature H _Rms(v):

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

The neighboring region on S123, definition summit according to watermark strength selected distance radius threshold value r, for the vertex v in the three-dimensional model, is 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|| is v and v _iBetween Euclidean distance;

The neighboring region N on S124, calculating summit _v(v r) with the root mean square curvature at the point of interface place of model, establishes v _eThe expression intersection point, v ₁And v ₂Be the model vertices at line segment two ends, intersection point place, then v _eRoot mean square curvature k _Rms(v _e) be:

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

Wherein, d ₁And d ₂Represent v respectively ₁And v ₂To v _eDistance;

The average root-mean-square curvature on S125, calculating summit, the neighboring region N on statistics and definite summit _v(described summit comprises the intersection point on summit and the border of each three-dimensional model that satisfies the neighborhood condition for v, the r) number of vertices in, utilizes the root mean square curvature on described summit to calculate the mean value of root mean square curvature 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) middle number of vertices;

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

To the undulating quantity sequence according to D ' _v=(D _v-D _Min)/((D _Max-D _Min)) carry out interval interior unit processing, wherein, D _Max, D _MinRepresent curvature undulating quantity minimum and maximum in this interval respectively, be distributed between [0,1] through the undulating quantity after the unitization.

As a further improvement on the present invention, " revise Davg among the described step S16 _i" specifically comprise:

S161, if embed watermark be 1:

S1611, initialization k=1;

S1612, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1613, judge whether to satisfy

If then k=k-Δ k returns execution in step S1612, if not, revise and finish, wherein

Intensity for embed watermark;

S162, if embed watermark be 0, then

S1621, initialization k=1;

S1622, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1623, judge whether to satisfy

If then k=k+ Δ k returns execution in step S1622, if not, revise and finish.

As a further improvement on the present invention, described step S17 is specially:

S171, to interval B _i, calculate the undulating quantity average Davg of this summit, interval root mean square curvature _iAnd with desired value Davg ' _iRelatively, 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+ Δ p; 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– Δ p.

S172, execution in step S171 repeatedly are up to interval B _iThe undulating quantity average Davg of the root mean square curvature on middle summit _iSatisfy | Davg _i-Davg ' _i|≤10 ^-5Till.

Correspondingly, a kind of blind checking method of the three-dimensional model data waterprint embedded method based on vertex curvature, described method comprises:

S21, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S22, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S23, the undulating quantity sequence is carried out unit processing in interval;

S24, calculate each interval B _iUndulating quantity mean value Davg _i

S25, extraction interval B _iIn watermark data;

S26, determine final watermark data;

S27, checking watermark correlativity.

As a further improvement on the present invention, extraction interval B among the 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 characterized in that described step S26 is specially:

The watermark data that extracts among the step S25 is carried out the statistics of corresponding positions, make j=i mod L, mod is that complementation is calculated, i=0, and 1 ..., if L * num-1 is w ' _jBe that 1 number is more than the number that is 0, then

Otherwise

And then extract the final watermark data that length is L

As a further improvement on the present invention, described step S27 is specially:

The watermark that calculating extracts and the correlation of original watermark and with given threshold ratio, have original watermark if correlation greater than given threshold value, is then judged in the model to be detected; Otherwise judge not have original watermark in the model to be detected, 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 ^dBe the watermark sequence that extracts, w is original watermark sequence, Be w ^dAverage,

It is the average of w.

The present invention has following beneficial effect:

Under the situation that does not need the original three-dimensional model data, utilize watermark embedding provided by the invention and method of detecting watermarks to solve a difficult problem that how watermark information is effectively extracted;

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

The watermark of this method embeds has the good transparency; can resist common three-dimensional model watermark such as summit rearrangement, rotation, translation, convergent-divergent attacks; and noise, quantification and simplification had good robustness, well balance be used for the three-dimensional model digital watermarking embedding of copyright protection and the contradiction between the blind checking method transparency and the robustness.

Description of drawings

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

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

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

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

Fig. 5 a, 5b are respectively in the present invention's one specific embodiment that watermark embeds forward and backward visual effect synoptic diagram on the bunny model;

Fig. 6 a, 6b are respectively in the present invention's one specific embodiment that watermark embeds forward and backward visual effect synoptic diagram on the horse model.

Embodiment

Describe the present invention below with reference to each embodiment shown in the drawings.But these embodiments do not limit the present invention, and the conversion on the structure that those of ordinary skill in the art makes according to these embodiments, method or the function all is included in protection scope of the present invention.

Join shown in Figure 1ly, a kind of three-dimensional model data waterprint embedded method based on vertex curvature of the present invention comprises:

S11, with the logistic chaotic maps watermark information is modulated, made watermark information be in chaos state;

S12, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S13, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S14, the undulating quantity sequence is carried out unit processing in interval;

S15, calculate each interval B _iUndulating quantity mean value Davg _i

S16, by revising Davg _iEmbed watermark;

S17, revise each interval B by alternative manner _iIn the model vertices coordinate, make this interval undulating quantity average Davg _iSatisfy and be desired value Davg ' _i

Join shown in Figure 2ly, the three-dimensional model data waterprint embedded method based on vertex curvature in an embodiment of the present invention is specially:

S11, modulation watermark information are used the logistic chaotic maps $\left\{\begin{array}{c}{x}_{k+1}=f\left(k\right)={\mathrm{\&mu;x}}_k(1-x_k)\\ x_{k+1}\&Element;\left(\mathrm{0,1}\right)\end{array},k=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;\right.$ Watermark information is modulated, and wherein 0≤μ≤4 are called branch parameter.For making value that watermark information is in chaos state μ in [3.569945,4], get key (μ, x ₀) as key, x wherein ₀Be the initial value of iteration, k is watermark length, thereby constructs the watermark sequence information that will embed.

S12, each vertex v of calculating three-dimensional model _i(i=1,2 ..., root mean square curvature undulating quantity N), concrete steps are:

S121, each vertex v of calculating three-dimensional 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) expression and v _iAdjacent interior angle, N1 are single order triangle neighborhood intermediate cam shape number, γ (e _{I, j}) (j=1,2 ..., N2) expression is with limit e _{I, j}Be the angle of two triangulation method vectors on limit, A _k(k=1,2 ..., N1) be v _iLeg-of-mutton area in the single order triangle neighborhood;

S122, calculate the root mean square curvature k on each summit of three-dimensional model according to Gaussian curvature K and mean curvature H _Rms(v):

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

The neighboring region on S123, definition summit according to watermark strength selected distance radius threshold value r, for the vertex v in the three-dimensional model, is 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|| is v and v _iBetween Euclidean distance;

The neighboring region N on S124, calculating summit _v(v r) with the root mean square curvature at the point of interface place of model, establishes v _eThe expression intersection point, v ₁And v ₂Be the model vertices at line segment two ends, intersection point place, then v _eRoot mean square curvature k _Rms(v _e) be:

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

Wherein, d ₁And d ₂Represent v respectively ₁And v ₂To v _eDistance;

The average root-mean-square curvature on S125, calculating summit, the neighboring region N on statistics and definite summit _v(described summit comprises the intersection point on summit and the border of each three-dimensional model that satisfies the neighborhood condition for v, the r) number of vertices in, utilizes the root mean square curvature on described summit to calculate the mean value of root mean square curvature 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) middle number of vertices;

S126, calculate the undulating quantity on summit, be defined as the standard deviation between the average root-mean-square curvature on the root mean square curvature on each summit in the neighboring region centered by vertex v and 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, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i(i=0,1 ..., L * num-1).

S14, the undulating quantity sequence is carried out unit processing in interval, namely

D′ _v＝(D _v-D _min)/((D _max-D _min))

Wherein, D _Max, D _MinRepresent curvature undulating quantity minimum and maximum in this interval respectively, be distributed between [0,1] through the undulating quantity value after the unitization.

S15, calculate each interval B _iUndulating quantity mean value Davg _i(i=0,1 ..., L * num-1).

S16, by revising Davg _iEmbed watermark is to Davg _iAmending method specifically comprises:

S161, if embed watermark be 1:

S1611, initialization k=1;

S1612, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1613, judge whether to satisfy

If then k=k-Δ k returns execution in step S1612, if not, revise and finish, wherein

Intensity for embed watermark;

S162, if embed watermark be 0, then

S1621, initialization k=1;

S1622, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1623, judge whether to satisfy

If then k=k+ Δ k returns execution in step S1622, if not, revise and finish.

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

S17, revise each interval B by alternative manner _iIn the model vertices coordinate, make this interval undulating quantity average Davg _iSatisfy and be desired value Davg ' _iConcrete steps are as follows:

S171, to interval B _i, calculate the undulating quantity average Davg of this summit, interval root mean square curvature _iAnd with desired value Davg ' _iRelatively, 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+ Δ p; 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– Δ p.Preferably, Δ p value is 0.0001 in the present embodiment.

S172, execution in step S171 repeatedly are up to interval B _iThe undulating quantity average Davg of the root mean square curvature on middle summit _iSatisfy | Davg _i-Davg ' _i|≤10 ^-5Till.

Join shown in Figure 3ly, the blind checking method of a kind of three-dimensional model data waterprint embedded method based on vertex curvature of the present invention comprises:

S21, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S22, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S23, the undulating quantity sequence is carried out unit processing in interval;

S24, calculate each interval B _iUndulating quantity mean value Davg _i

S25, extraction interval B _iIn watermark data;

S26, determine final watermark data;

S27, checking watermark correlativity.

Join shown in Figure 4ly, the blind checking method based on the three-dimensional model data waterprint embedded method of vertex curvature in an embodiment of the present invention is specially:

S21, each vertex v of calculating three-dimensional model _i(i=1,2 ..., root mean square curvature undulating quantity N), concrete steps are:

S211, each vertex v of calculating three-dimensional 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) expression and v _iAdjacent interior angle, N1 are single order triangle neighborhood intermediate cam shape number, γ (e _{I, j}) (j=1,2 ..., N2) expression is with limit e _{I, j}Be the angle of two triangulation method vectors on limit, A _k(k=1,2 ..., N1) be v _iLeg-of-mutton area in the single order triangle neighborhood;

S212, calculate the root mean square curvature k on each summit of three-dimensional model according to Gaussian curvature K and mean curvature H _Rms(v):

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

The neighboring region on S213, definition summit according to watermark strength selected distance radius threshold value r, for the vertex v in the three-dimensional model, is 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|| is v and v _iBetween Euclidean distance;

The neighboring region N on S214, calculating summit _v(v r) with the root mean square curvature at the point of interface place of model, establishes v _eThe expression intersection point, v ₁And v ₂Be the model vertices at line segment two ends, intersection point place, then v _eRoot mean square curvature k _Rms(v _e) be:

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

Wherein, d ₁And d ₂Represent v respectively ₁And v ₂To v _eDistance;

The average root-mean-square curvature on S215, calculating summit, the neighboring region N on statistics and definite summit _v(described summit comprises the intersection point on summit and the border of each three-dimensional model that satisfies the neighborhood condition for v, the r) number of vertices in, utilizes the root mean square curvature on described summit to calculate the mean value of root mean square curvature 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) middle number of vertices;

S216, calculate the undulating quantity on summit, be defined as the standard deviation between the average root-mean-square curvature on the root mean square curvature on each summit in the neighboring region centered by vertex v and 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, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S23, the undulating quantity sequence is carried out unit processing in interval, namely

D′ _v＝(D _v-D _min)/((D _max-D _min))，

Wherein, D _Max, D _MinRepresent curvature undulating quantity minimum and maximum in this interval respectively.

S24, calculate each interval B _iUndulating quantity mean value 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 that extracts among the step S25 is carried out the statistics of corresponding positions, make j=i mod L, mod is that complementation is calculated, i=0, and 1 ..., if L * num-1 is w ' _jBe that 1 number is more than the number that is 0, then

Otherwise And then extract the final watermark data that length is L

S27, checking watermark correlativity:

The watermark that calculating extracts and the correlation of original watermark and with given threshold ratio, have original watermark if correlation greater than given threshold value, is then judged in the model to be detected; Otherwise judge and do not have original watermark in the model to be detected.

Wherein the 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 ^dBe the watermark sequence that extracts, w is original watermark sequence, Be w ^dAverage,

It is the average of w.

By above-mentioned seven steps, can from model to be detected, extract watermark data and judge whether include original watermark in the model to be detected, just can verify that the holder of this watermark is the copyright holder of three-dimensional model if include original watermark.

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

Bunny and Horse model that test model selects for use Stanford university to provide experimentize, 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 the bunny model

1, watermark embeds

Water intaking seal 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 this method, we to embed watermark after the bunny model carry out respectively resetting through translation, summit, evenly after the common attacks such as convergent-divergent, rotation, noise, quantification, simplification attack, attacking and adopt the 3-D Mesh Watermarking Benchmark software of LIRIS development in laboratory to carry out.Weigh the watermark sequence of model extraction and the difference between the original watermark sequence by the design factor correlativity, and quantitatively weigh the collimation error of model after attack of master pattern and embed watermark with maximum square max root mean square (MRMS), shown in collimation error ginseng Fig. 5 a, the 5b.Experimental result is as shown in table 1.

From experimental result as can be seen, use the present invention, master pattern has good watermark and embeds the visual masking effect behind embed watermark.After all kinds of attacks of process, the watermark that extracts from model to be detected and original watermark have higher correlation, show that the present invention can resist various common attacks preferably, namely have higher robustness, can protect the copyright of three-dimensional model preferably.

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

Table 1bunny model dependency experimental result

Specific embodiment 2: the application on the horse model

1, watermark embeds

Water intaking seal modulation key μ=3.7, x ₀=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 this method, we to embed watermark after the horse model carry out respectively resetting through translation, summit, evenly after the common attacks such as convergent-divergent, rotation, noise, quantification, simplification attack, attacking and adopt the 3-D Mesh Watermarking Benchmark software of LIRIS development in laboratory to carry out.Weigh watermark sequence that model extracts and the difference between the original watermark sequence by the design factor correlativity, and quantitatively weigh the collimation error of model after attack of master pattern and embed watermark with MRMS, the collimation error is joined shown in Fig. 6 a, the 6b.Experimental result is as shown in table 2.

From experimental result as can be seen, use the present invention, master pattern has good watermark and embeds the visual masking effect behind embed watermark.After all kinds of attacks of process, the watermark that extracts from model to be detected and original watermark have higher correlation, show that the present invention can resist various common attacks preferably, namely have higher robustness, can protect the copyright of three-dimensional model preferably.

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

Table 2horse model dependency experimental result

By above embodiment as can be seen, compared with prior art, the three-dimensional model digital watermarking embedding and the blind checking method that the present invention is based on vertex curvature have following beneficial effect:

Under the situation that does not need the original three-dimensional model data, utilize watermark embedding provided by the invention and method of detecting watermarks to solve a difficult problem that how watermark information is effectively extracted;

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

The watermark of this method embeds has the good transparency; can resist common three-dimensional model watermark such as summit rearrangement, rotation, translation, convergent-divergent attacks; and noise, quantification and simplification had good robustness, well balance be used for the three-dimensional model digital watermarking embedding of copyright protection and the contradiction between the blind checking method transparency and the robustness.

Be to be understood that, though this instructions is described according to embodiment, but be not that each embodiment only comprises an independently technical scheme, this narrating mode of instructions only is for clarity sake, those skilled in the art should make instructions as a whole, technical scheme in each embodiment also can form other embodiments that it will be appreciated by those skilled in the art that through appropriate combination.

Above listed a series of detailed description only is specifying at feasibility embodiment of the present invention; they are not in order to limiting protection scope of the present invention, allly do not break away from equivalent embodiment or the change that skill spirit of the present invention does and all should be included within protection scope of the present invention.

Claims (10)

1. three-dimensional model data waterprint embedded method based on vertex curvature is characterized in that described method comprises:

S11, with the logistic chaotic maps watermark information is modulated, made watermark information be in chaos state;

S12, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S13, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S14, the undulating quantity sequence is carried out unit processing in interval;

S15, calculate each interval B _iUndulating quantity mean value Davg _i

S16, by revising Davg _iEmbed watermark;

S17, revise each interval B by alternative manner _iIn the model vertices coordinate, make this interval undulating quantity average Davg _iSatisfy and be desired value Davg ' _i

2. watermark embedding method according to claim 1 is characterized in that, described step S11 is specially:

Use the logistic chaotic maps $\left\{\begin{array}{c}{x}_{k+1}=f\left(k\right)={\mathrm{\&mu;x}}_k(1-x_k)\\ x_{k+1}\&Element;\left(\mathrm{0,1}\right)\end{array},k=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;\right.$ Watermark information is modulated, made watermark information be in chaos state, wherein the span of branch parameter μ is [3.569945,4], key (μ, x ₀) as key, x ₀Be the initial value of iteration, k is watermark length.

3. watermark embedding method according to claim 1 is characterized in that, described step S12 is specially:

S121, each vertex v of calculating three-dimensional 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) expression and v _iAdjacent interior angle, N1 are single order triangle neighborhood intermediate cam shape number, γ (e _{I, j}) (j=1,2 ..., N2) expression is with limit e _{I, j}Be the angle of two triangulation method vectors on limit, A _k(k=1,2 ..., N1) be v _iLeg-of-mutton area in the single order triangle neighborhood;

S122, calculate the root mean square curvature k on each summit of three-dimensional model according to Gaussian curvature K and mean curvature H _Rms(v):

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

The neighboring region on S123, definition summit according to watermark strength selected distance radius threshold value r, for the vertex v in the three-dimensional model, is 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|| is v and v _iBetween Euclidean distance;

The neighboring region N on S124, calculating summit _v(v r) with the root mean square curvature at the point of interface place of model, establishes v _eThe expression intersection point, v ₁And v ₂Be the model vertices at line segment two ends, intersection point place, then v _eRoot mean square curvature k _Rms(v _e) be:

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

Wherein, d ₁And d ₂Represent v respectively ₁And v ₂To v _eDistance;

The average root-mean-square curvature on S125, calculating summit, the neighboring region N on statistics and definite summit _v(described summit comprises the intersection point on summit and the border of each three-dimensional model that satisfies the neighborhood condition for v, the r) number of vertices in, utilizes the root mean square curvature on described summit to calculate the mean value of root mean square curvature 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) middle number of vertices;

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

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

4. watermark embedding method according to claim 1 is characterized in that, described step S14 is specially:

To the undulating quantity sequence according to D ' _v=(D _v-D _Min)/((D _Max-D _Min)) carry out interval interior unit processing, wherein, D _Max, D _MinRepresent curvature undulating quantity minimum and maximum in this interval respectively, be distributed between [0,1] through the undulating quantity after the unitization.

5. watermark embedding method according to claim 1 is characterized in that, " revises Davg among the described step S16 _i" specifically comprise:

S161, if embed watermark be 1:

S1611, initialization k=1;

S1612, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1613, judge whether to satisfy

If then k=k-Δ k returns execution in step S1612, if not, revise and finish, wherein

Intensity for embed watermark;

S162, if embed watermark be 0, then

S1621, initialization k=1;

S1622, the new undulating quantity average Davg ' of calculating _i=(Davg _i) ^k

S1623, judge whether to satisfy

If then k=k+ Δ k returns execution in step S1622, if not, revise and finish.

6. watermark embedding method according to claim 1 is characterized in that, described step S17 is specially:

S171, to interval B _i, calculate the undulating quantity average Davg of this summit, interval root mean square curvature _iAnd with desired value Davg ' _iRelatively, 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+ Δ p; 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– Δ p.

S172, execution in step S171 repeatedly are up to interval B _iThe undulating quantity average Davg of the root mean square curvature on middle summit _iSatisfy | Davg _i-Davg ' _i|≤10 ^-5Till.

7. the blind checking method of the three-dimensional model data waterprint embedded method based on vertex curvature as claimed in claim 1 is characterized in that described method comprises:

S21, each vertex v of calculating three-dimensional model _iRoot mean square curvature undulating quantity;

S22, the ascending ordering of undulating quantity is pressed on the summit, the undulating quantity sequence after the ordering is embedded frequency n um according to watermark figure place L and watermark be divided into L * num interval B _i

S23, the undulating quantity sequence is carried out unit processing in interval;

S24, calculate each interval B _iUndulating quantity mean value Davg _i

S25, extraction interval B _iIn watermark data;

S26, determine final watermark data;

S27, checking watermark correlativity.

8. watermark blind checking method according to claim 7 is characterized in that, extraction interval B among the described step S25 _iIn the formula of watermark data be:

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

9. watermark blind checking method according to claim 7 is characterized in that, described step S26 is specially:

The watermark data that extracts among the step S25 is carried out the statistics of corresponding positions, make j=i mod L, mod is that complementation is calculated, i=0, and 1 ..., if L * num-1 is w ' _jBe that 1 number is more than the number that is 0, then

Otherwise

And then extract the final watermark data that length is L $w^d=(w_0^d,w_1^d,\&CenterDot;\&CenterDot;\&CenterDot;w_{L-1}^d).$

10. watermark blind checking method according to claim 7 is characterized in that, described step S27 is specially:

The watermark that calculating extracts and the correlation of original watermark and with given threshold ratio, have original watermark if correlation greater than given threshold value, is then judged in the model to be detected; Otherwise judge not have original watermark in the model to be detected, described correlation value calculation formula is:

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

Wherein, w ^dBe the watermark sequence that extracts, w is original watermark sequence,

Be w ^dAverage,

It is the average of w.

Images