CN103886541A - Image watermarking method based on Tchebichef moment affine invariant - Google Patents

Abstract

The invention provides an image watermarking algorithm based on the Tchebichef moment affine invariant, and provides a general algorithm for embedding, detecting and extracting digital image watermarking. The image watermarking algorithm can resist affine attacks more general than geometric attacks. According to the method, at first, the Tchebichef moment affine invariant is calculated and embedded into an invariant area of an original image, so that a watermarking image is obtained. The method can resist the traditional geometric attacks such as translation transformation, rotation and zooming (RST), and ensure correct extraction of watermarking information when being attacked by affine, and key indicators, namely, the invisibility, the watermarking embedding capacity and the robustness of the watermarking algorithm are well balanced.

Description

Based on the image watermark method of the affine invariant of Tchebichef square

Technical field

The invention belongs to image information safety technique field, relate to digital figure watermark safety technique, specifically relate to and a kind ofly can resist the watermarking algorithm that has more general affine attack than geometric attack, comprising the embedding grammar of watermark, detection method and extracting method.

Background technology

Along with the develop rapidly of network and multimedia technology, the media product of the digital forms such as image, text, Voice & Video has obtained propagating widely and using.The digital devices such as digital camera, video recorder, scanner and printer and the software that some are powerful, be widely used in the world creation and process digital multimedia data; And internet is also for distribution and the exchange of multimedia messages provide wide channel easily.People can carry out copy, download and the issue of Digital Media easily by internet, and this gives on the one hand people's the live and work condition of providing convenience, and has improved work efficiency, on the other hand also for the piracy of Digital Media provides convenience.Some lawless persons, in the case of the copyright owner of the Digital Media mandate that there is no goods, arbitrarily copy and propagate the Digital Media publication of copyright protection, therefrom speculate.Therefore, how to protect on the internet the copyright problem of Digital Media and information security to become an extremely urgent realistic problem.And digital watermark technology is as one of important means of the applications such as Digital Media copyright protection, content authentication, comment token, use control, has obtained in recent years increasing concern aspect copyright protection.

Digital watermarking belongs to the one of Information Hiding Techniques; its basic thought is can differentiate that by having capable information (watermark) secret is embedded in the digital multimedia products such as image, text, Voice & Video in the situation that not affecting product quality; make it as the part of raw data and be retained in wherein; to copying and transmitting of data implemented to follow the tracks of, realizes functions such as hiding transmission, storage, mark, identification, copyright protection.Visible, on the one hand, it can be used to prove the entitlement of authorship to its works, as the evidence of qualification, the illegal infringement of prosecution; On the other hand; author can also be by surveying and analyze to realize the dynamic tracking to works to the watermark in its digital product; thereby ensure the integrality of its works, therefore digital watermarking has become intellectual property protection and the false proof effective means of digital multimedia.

And robust digital watermark plays a decisive role to copyright protection, therefore need watermark to possess the function of the multiple Attack Digital Watermarking of opposing.Process as noise, filtering, compression etc. with respect to normal image, geometric attack is difficult to resist as translation, rotation, convergent-divergent etc. more.The topmost reason that digital watermark technology is difficult to resist geometric transformation is: although the watermark information in image is not removed in geometric transformation, make the detection of watermark and embed between lose and synchronize, thereby cause the inefficacy of watermark detection.Geometric attack has changed the corresponding relation between grey scale pixel value and coordinate in addition, has stoped the normal extraction of watermark signal.Therefore stationary problem is the gordian technique that the algorithm resilient geometric distortion will solve.In addition, invisibility, watermark embedding capacity and robustness are the topmost three norms of watermarking algorithm, but these indexs all condition each other between any two, the design that can reach preferably the watermarking algorithm of three indexs under different applied environments is simultaneously challenging problems.

Existing certain methods can solve part the problems referred to above, as the scholars such as tension force propose in " application of Tchebichef square in digital image watermarking " literary composition, utilize the value of one or more Tchebichef squares of original image to realize multiple different watermark information to realize (comprising DWT, DCT, FFT and spatial domain etc.) in different image processing domain embedding and the detection of watermark information, significantly strengthened the robustness of watermarking algorithm.The scholars such as Cheng Xinghong have proposed taking the feature of image normalization technology and Tchebichef moment coefficient as basis in " based on zero watermarking algorithm of image Tchebichef square resist geometric attacks " literary composition; first calculate original image unit circle inward turning and turn normalized Tchebichef square, the upper left corner part of Tchebichef square is scanned into numerical matrix; Then generate binary keys and be saved in zero watermark information storehouse according to numerical matrix and watermarking images, obtaining rotation, convergent-divergent and normal signal processing and combination attacks thereof are had to very strong robustness image watermark with this.

But above-mentioned existing method has only solved the resist geometric attacks of image watermark, do not consider than geometric transformation and have more general affined transformation, therefore existing algorithm cannot be resisted affine attack.In addition, existing algorithm is for topmost index in these three watermarking algorithms of invisibility, watermark embedding capacity and robustness unrealized good balance.

Summary of the invention

For addressing the above problem, the present invention is based on the affine invariant of Tchebichef square, propose opposing and had more the watermarking algorithm of general affine attack than geometric attack, and proposed digital figure watermark embedding, the general-purpose algorithm that detects and extract.

In order to achieve the above object, the invention provides following technical scheme:

Based on an Image Watermarking for the affine invariant of Tchebichef square, comprise the steps:

Steps A, calculate Tchebichef square invariant:

Steps A-1, the affined transformation of definition image is:

$\begin{array}{c}{x}^{\′}=x_0+a_{11}x+x_{12}y\\ y^{\′}=y_0+a_{21}x+a_{22}y\end{array}---\left(1\right)$

As follows with matrix representation:

$\left(\begin{array}{c}{x}^{\′}\\ y^{\′}\end{array}\right)=A\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)---\left(2\right)$

Wherein, $A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{11}& a_{22}\end{array}\right),$ Be called affine transformation matrix;

Steps A-2, the 2D p+q rank Tchebichef square of definition image is:

$T_{\mathrm{pq}}=\underset{x=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{y=0}{\overset{M-1}{\mathrm{\Σ}}}{t}_p\left(x\right)t_q\left(y\right)f(x,y)---\left(3\right)$

Wherein, p, q=0,1,2 ..., p, q is integer, wherein t _p(x) be p rank Tchebichef polynomial expressions, be defined as:

$t_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\Σ}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\ρ}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}{(-x)}_r---\left(4\right)$

Above formula is expressed as follows by Matrix C:

$\begin{array}{c}{t}_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\Σ}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\ρ}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}\underset{k=0}{\overset{r}{\mathrm{\Σ}}}{(-1)}^r{S}_1(r,k)x^k\\ =\underset{k=0}{\overset{p}{\mathrm{\Σ}}}{c}_{p,k}^N{x}^k\end{array}---\left(5\right)$

S in above formula ₁(r, k) is Stiriling number, and Matrix C is defined as follows:

$c_{p,k}^N=\underset{r=k}{\overset{p}{\mathrm{\Σ}}}{(-1)}^r{S}_1(r,k)\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\ρ}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}---\left(6\right)$

The lower triangle battle array C of definition _minverse matrix D _m=(d _p,k), 0≤k≤p≤M, D _melement definition be:

$d_{p,k}^N=\underset{m=k}{\overset{p}{\mathrm{\Σ}}}{S}_2(k,m)\frac{\sqrt{\mathrm{\ρ}(k,N)}(2k+1){(m!)}^2(N-k-1)!}{(m+k+1)!(m-k)!(N-m-1)!},---\left(7\right)$

Can be obtained by above formula:

$x^p=\underset{k=0}{\overset{p}{\mathrm{\Σ}}}{d}_{p,k}{t}_k\left(x\right)---\left(8\right)$

Steps A-3, according to affine parameter, Tchebichef square is carried out being expressed as follows after affined transformation:

$T_{\mathrm{pq}}^{\′}=\det \left(A\right)\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}\underset{t=0}{\overset{n}{\mathrm{\Σ}}}\underset{i=0}{\overset{s+t}{\mathrm{\Σ}}}\underset{j=0}{\overset{m+n-s-t}{\mathrm{\Σ}}}\left(\begin{array}{c}m\\ s\end{array}\right)\left(\begin{array}{c}n\\ t\end{array}\right){\left(a_{11}\right)}^s{\left(a_{12}\right)}^{m-s}{\left(a_{21}\right)}^t{\left(a_{22}\right)}^{n-t}{c}_{p,m}^N{c}_{q,n}^M{d}_{s+t,i}^N{d}_{m+n-s-t,j}^M{T}_{\mathrm{ij}}---\left(9\right)$

Steps A-4, obtain the invariant of affine matrix: affine matrix A is carried out to XYS decomposition, and XYS decomposes the shearing that affine matrix A is resolved into an x direction, and the shearing of a y direction and a scaled matrix are as follows:

$\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}\mathrm{\α}& 0\\ 0& \mathrm{\δ}\end{array}\right]\left[\begin{array}{cc}1& 0\\ \mathrm{\γ}& 1\end{array}\right]\left[\begin{array}{cc}1& \mathrm{\β}\\ 0& 1\end{array}\right]---\left(10\right)$

Wherein, α, β, δ and γ are real number;

Through type (10), selects different a ₁₁, a ₁₂, a ₂₁, a ₂₂parameter substitution formula (9) obtains the invariant after affine matrix decomposes:

For given positive integer p and q, have

$I_{\mathrm{pq}}^{\mathrm{xsh}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}\underset{i=0}{\overset{s}{\mathrm{\Σ}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\Σ}}}\left(\begin{array}{c}m\\ s\end{array}\right){\mathrm{\β}}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{T}_{\mathrm{ij}}---\left(11\right)$

?

shearing to image x direction has unchangeability;

Order

$I_{\mathrm{pq}}^{\mathrm{ysh}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{t=0}{\overset{n}{\mathrm{\Σ}}}\underset{i=0}{\overset{m+t}{\mathrm{\Σ}}}\underset{j=0}{\overset{n-t}{\mathrm{\Σ}}}\left(\begin{array}{c}n\\ t\end{array}\right){\mathrm{\γ}}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{T}_{\mathrm{ij}}---\left(12\right)$

?

shearing to image y direction has unchangeability;

Order

$I_{\mathrm{pq}}^{\mathrm{as}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{i=0}{\overset{m}{\mathrm{\Σ}}}\underset{j=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}^{m+1}{\mathrm{\δ}}^{n+1}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{T}_{\mathrm{ij}}---\left(13\right)$

?

image scaling is had to unchangeability;

Steps A-5, utilize the existing combination of Tchebichef square invariant to represent the Tchebichef square of the image after affined transformation:

Steps A-5-1, will calculate the shear invariant of x direction in the 2D p+q rank Tchebichef square substitution formula (11) of the image defining in steps A

Steps A-5-2, by the invariant obtaining in steps A-5-1

in substitution formula (12), calculate the combination invariant of the shearing of x direction and the shearing of y direction

Steps A-5-3, by the invariant obtaining in steps A-5-2

substitution formula obtains affine invariant in (13)

The invariant that steps A-5-1, steps A-5-2, steps A-5-1 are obtained carries out after inverse transformation, and Tchebichef square is expressed as follows by the linear combination of Tchebichef square invariant:

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}\underset{i=0}{\overset{s}{\mathrm{\Σ}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\Σ}}}\left(\begin{array}{c}m\\ s\end{array}\right){(-\mathrm{\β})}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{I}_{\mathrm{pq}}^{\mathrm{xsh}}---\left(14\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{t=0}{\overset{n}{\mathrm{\Σ}}}\underset{i=0}{\overset{m+t}{\mathrm{\Σ}}}\underset{j=0}{\overset{n-t}{\mathrm{\Σ}}}\left(\begin{array}{c}n\\ t\end{array}\right){(-\mathrm{\γ})}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{I}_{\mathrm{pq}}^{\mathrm{ysh}}---\left(15\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}\underset{n=0}{\overset{q}{\mathrm{\Σ}}}\underset{i=0}{\overset{m}{\mathrm{\Σ}}}\underset{j=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}^{-(m+1)}{\mathrm{\δ}}^{-(n+1)}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{I}_{\mathrm{pq}}^{\mathrm{as}}---\left(16\right)$

Step B, is embedded into Tchebichef square invariant in the invariant region of original image, obtains watermarking images, and embedding formula is:

$I_{\mathrm{pq}}^{\mathrm{as}\left(h\right)}=I_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}+s_{\mathrm{pq}}{I}_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}---\left(17\right)$

Watermark w is expressed as to the function of original image Tchebichef square invariant:

$T_{\mathrm{pq}}^{\left(h\right)}=(1+s_{\mathrm{pq}})T_{\mathrm{pq}}^{\left(f\right)}---\left(19\right)$

The orthogonality of utilizing Tchebichef square, obtains:

$h=f+w=f+\underset{p=0}{\overset{M}{\mathrm{\Σ}}}\underset{q=0}{\overset{M}{\mathrm{\Σ}}}{s}_{\mathrm{pq}}{P}_p\left(x\right)P_q\left(y\right)T_{\mathrm{pq}}^{\left(f\right)}---\left(20\right)$

Wherein M is the maximum order of square invariant, thereby completes the embedding of watermark.

The present invention also provides a kind of image watermark detection method based on the affine invariant of Tchebichef square, comprises the steps:

Steps A, obtains and receives image t and watermarking images h;

Step B, is calculated and is received image t and the watermarking images h distance at feature space by following formula:

$d(t,h)=\frac{|I\left(t\right)-\left(h\right)|}{\left|I\left(t\right)\right|}---\left(21\right)$

Here I (t) and I (h) represent respectively the function I of the Tchebichef square invariant that receives image and watermarking images,

Step C, relatively d (t, h) and predefined threshold value d _thif, d (t, h) <d _th, think that watermark is appraisable, if d (t, h)>=d _th, think that watermark is not appraisable.

As the preferred version of image watermark detection method, described I is mean value function:

$I=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{I}_i^{\mathrm{affne}}---\left(22\right)$

Wherein, L is the number of the square invariant that uses in watermark detection.

The present invention also provides a kind of image watermark extracting method based on the affine invariant of Tchebichef square, comprises the steps:

Steps A, obtains and receives image t and watermarking images h;

Step B obtains the parameter matrix m (h) of watermarking images from receive image t and watermarking images h by following formula

$m\left(h\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(h\right)& \mathrm{\&alpha;}\left(h\right)\mathrm{\&beta;}\left(h\right)\\ \mathrm{\&delta;}\left(h\right)\mathrm{\&gamma;}\left(h\right)& \mathrm{\&delta;}\left(h\right)(1+\mathrm{\&beta;}\left(h\right)\mathrm{\&gamma;}\left(h\right))\end{array}\right]---\left(23\right)$

Parameter matrix m (t) with reception image t:

$m\left(t\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(t\right)& \mathrm{\&alpha;}\left(t\right)\mathrm{\&beta;}\left(t\right)\\ \mathrm{\&delta;}\left(t\right)\mathrm{\&gamma;}\left(t\right)& \mathrm{\&delta;}\left(t\right)(1+\mathrm{\&beta;}\left(t\right)\mathrm{\&gamma;}\left(t\right))\end{array}\right]---\left(24\right)$

Step C, estimates affine transformation parameter from m (h) and m (t);

Step D, by matrix m (h) m ^{– 1}(t) obtain restored image f ';

Step e, deducts original image f ' and estimates the watermark of embedding with restored image f.

Advantage of the present invention:

Adopt method provided by the invention to carry out after digital watermarking embedding image, not only can resist traditional translation transformation, rotation, the geometric attacks such as convergent-divergent (RST), in the time being subject to affine attack, still can ensure correct detection and the extraction of watermark information, and detect error and be less than existing method, have better robustness, the watermark information extracting is correctly complete, and identification degree is high.And obtain good balance between the leading indicator of invisibility, watermark embedding capacity and these three watermarking algorithms of robustness.

Brief description of the drawings

Fig. 1 is the Image Watermarking process flow diagram based on the affine invariant of Tchebichef square provided by the invention;

Fig. 2 is the original Lena image adopting in embodiment mono-, and it is of a size of 256 × 256;

Fig. 3 (a) is the image after original image embed watermark taking Fig. 2, and Fig. 3 (b) is revised watermarking images;

Fig. 4 is PSNR value and parameter s, between M, is related to schematic diagram, and wherein horizontal ordinate is s value, and ordinate is the PSNR value of Lena image;

Fig. 5 is the four width standard grayscale images that adopt in embodiment bis-;

Fig. 6 is the mean distance of the test pattern under various attack, wherein (a) to be rotation attack (b) attack (c) for convergent-divergent is JPEG attack for Gauss attacks (d);

Fig. 7 is image watermark extracting method process flow diagram provided by the invention;

Fig. 8 is the embed watermark figure of tri-kinds of employings of embodiment;

Fig. 9 is the watermarking images being subject to after affined transformation is attacked;

Figure 10 is the watermark Logo extracting from Fig. 9 watermarking images.

Embodiment

Below with reference to specific embodiment, technical scheme provided by the invention is elaborated, should understands following embodiment and only be not used in and limit the scope of the invention for the present invention is described.

Embodiment mono-:

Affined transformation is a kind of linear transformation of image space, and in some situation, the one that can be regarded as the projective transformation of image is similar to, the geometric transformation of image, as traditional translation transformation, rotation, the geometric attacks such as convergent-divergent (RST) can be considered to a kind of special case of affine attack.

Image Watermarking flow process based on the affine invariant of Tchebichef square provided by the invention as shown in Figure 1, specifically comprises the steps:

Steps A, calculate Tchebichef square invariant:

Steps A-1, the affined transformation of image is defined as:

$\begin{array}{c}{x}^{\&prime;}=x_0+a_{11}x+x_{12}y\\ y^{\&prime;}=y_0+a_{21}x+a_{22}y\end{array}---\left(1\right)$

As follows with matrix representation:

$\left(\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right)=A\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)---\left(2\right)$

Wherein, $A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{11}& a_{22}\end{array}\right),$ Be called affine transformation matrix,

Steps A-2, the 2D p+q rank Tchebichef square of definition image is:

$T_{\mathrm{pq}}=\underset{x=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{y=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{t}_p\left(x\right)t_q\left(y\right)f(x,y)---\left(3\right)$

Wherein, x, y is respectively horizontal ordinate and the ordinate of image, and N and M are picture size size, and f is gradation of image value.P, q=0,1,2 ..., p, q is integer, wherein t _p(x) be p rank Tchebichef polynomial expressions, be defined as:

$t_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\&Sigma;}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}{(-x)}_r---\left(4\right)$

Above formula is expressed as follows by Matrix C:

$\begin{array}{c}{t}_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\&Sigma;}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}\underset{k=0}{\overset{r}{\mathrm{\&Sigma;}}}{(-1)}^r{S}_1(r,k)x^k\\ =\underset{k=0}{\overset{p}{\mathrm{\&Sigma;}}}{c}_{p,k}^N{x}^k\end{array}---\left(5\right)$

S in above formula ₁(r, k) is Stiriling number, and Matrix C is defined as follows:

$c_{p,k}^N=\underset{r=k}{\overset{p}{\mathrm{\&Sigma;}}}{(-1)}^r{S}_1(r,k)\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}---\left(6\right)$

Note C _m=(c _p,k).By c _p,kdefinition, in the time that r is greater than p, (p-r) unequal to 0, therefore C _mfor lower triangle battle array.Because the diagonal element c of matrix _l,l≠ 0, therefore Matrix C _mthere is inverse matrix.Note D _m=(d _p,k), 0≤k≤p≤M, is C _minverse matrix, D _melement definition be

$d_{p,k}^N=\underset{m=k}{\overset{p}{\mathrm{\&Sigma;}}}{S}_2(k,m)\frac{\sqrt{\mathrm{\&rho;}(k,N)}(2k+1){(m!)}^2(N-k-1)!}{(m+k+1)!(m-k)!(N-m-1)!},---\left(7\right)$

By formula (5), we can obtain

$x^p=\underset{k=0}{\overset{p}{\mathrm{\&Sigma;}}}{d}_{p,k}{t}_k\left(x\right)---\left(8\right)$

Steps A-3, according to affine parameter, Tchebichef square is carried out being expressed as follows after affined transformation:

$T_{\mathrm{pq}}^{\&prime;}=\det \left(A\right)\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right)\left(\begin{array}{c}n\\ t\end{array}\right){\left(a_{11}\right)}^s{\left(a_{12}\right)}^{m-s}{\left(a_{21}\right)}^t{\left(a_{22}\right)}^{n-t}{c}_{p,m}^N{c}_{q,n}^M{d}_{s+t,i}^N{d}_{m+n-s-t,j}^M{T}_{\mathrm{ij}}---\left(9\right)$

Above formula shows that the Tchebichef square of the image after affined transformation can be expressed as the linear combination of the Tchebichef square before conversion.

Steps A-4, obtain the invariant of affine matrix: owing to directly utilizing formula (9) to obtain comparatively difficulty of invariant, affine matrix A is carried out XYS decomposition by we, and XYS decomposes the shearing that affine matrix A is resolved into an x direction, and the shearing of a y direction and a scaled matrix are as follows:

$\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}\mathrm{\&alpha;}& 0\\ 0& \mathrm{\&delta;}\end{array}\right]\left[\begin{array}{cc}1& 0\\ \mathrm{\&gamma;}& 1\end{array}\right]\left[\begin{array}{cc}1& \mathrm{\&beta;}\\ 0& 1\end{array}\right]---\left(10\right)$

Wherein, α, β, δ and γ are real number.

By above relational expression, select different a ₁₁, a ₁₂, a ₂₁, a ₂₂parameter substitution formula (9), we can obtain the invariant after affine matrix decomposes:

For given positive integer p and q, have

$I_{\mathrm{pq}}^{\mathrm{xsh}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right){\mathrm{\&beta;}}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{T}_{\mathrm{ij}}---\left(11\right)$

?

shearing to image x direction has unchangeability.

Order

$I_{\mathrm{pq}}^{\mathrm{ysh}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}n\\ t\end{array}\right){\mathrm{\&gamma;}}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{T}_{\mathrm{ij}}---\left(12\right)$

?

shearing to image y direction has unchangeability.

Order

$I_{\mathrm{pq}}^{\mathrm{as}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}^{m+1}{\mathrm{\&delta;}}^{n+1}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{T}_{\mathrm{ij}}---\left(13\right)$

? image scaling is had to unchangeability.

Obtained by formula (11), (12), (13),

the shearing of the x direction to image respectively, shearing and the image scaling of y direction have unchangeability, and the affine invariant of Tchebichef square can be obtained by the linear combination of these three invariants.

Specifically be described below:

Steps A-5, utilize the existing combination of Tchebichef square invariant to represent the Tchebichef square of the image after affined transformation:

Steps A-5-1, utilizes formula (11) to calculate the shear invariant of x direction in this formula, the calculating of Tchebichef square is obtained by formula (3).

Steps A-5-2, utilizes formula (12) to obtain the combination invariant of the shearing of x direction and the shearing of y direction

in computation process by the invariant obtaining in steps A-5-1 replace the Tchebichef square on equal sign the right in formula (12).

Steps A-5-3, utilizes formula (13) to obtain affine invariant

in computation process by the invariant obtaining in steps A-5-2

replace the Tchebichef square on equal sign the right in formula (13).

Because equal sign the right of formula (10) is invertible matrix, the invariant that therefore we obtain based on steps A-5-1～steps A-5-3 carries out after inverse transformation, and Tchebichef square is expressed as follows by the linear combination of Tchebichef square invariant:

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right){(-\mathrm{\&beta;})}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{I}_{\mathrm{pq}}^{\mathrm{xsh}}---\left(14\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}n\\ t\end{array}\right){(-\mathrm{\&gamma;})}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{I}_{\mathrm{pq}}^{\mathrm{ysh}}---\left(15\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}^{-(m+1)}{\mathrm{\&delta;}}^{-(n+1)}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{I}_{\mathrm{pq}}^{\mathrm{as}}---\left(16\right)$

Step B, embed watermark in original image: by following formula, Tchebichef square invariant is embedded into the invariant region of original image, can obtains watermarking images:

$I_{\mathrm{pq}}^{\mathrm{as}\left(h\right)}=I_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}+s_{\mathrm{pq}}{I}_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}---\left(17\right)$

with

represent respectively the Tchebichef square invariant of original image f and watermarking images h, s _pqbe the parameter of controlling watermark strength, make watermarking images between robustness and invisibility, reach good balance.

We explain the embedment strength of image with the Y-PSNR (peak signal-to-noise ratio, PSNR) between original image f and watermarking images h.Conventionally, this value is greater than 40, makes the watermark of embedding invisible.PSNR between original image f and watermarking images h is defined as:

$\mathrm{PSNR}=101\mathrm{lo}{g}_{10}\frac{N^2{\left[\underset{x,y}{\max }f(x,y)\right]}^2}{\underset{x=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{y=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{[f(x,y)-h(x,y)]}^2}---\left(18\right)$

Here N × N is picture size.

We are expressed as watermark w the function of original image Tchebichef square invariant below.In fact, utilize formula (14-16), formula (17) can be write as:

$T_{\mathrm{pq}}^{\left(h\right)}=(1+s_{\mathrm{pq}})T_{\mathrm{pq}}^{\left(f\right)}---\left(19\right)$

The orthogonality of utilizing Tchebichef square, obtains:

$h=f+w=f+\underset{p=0}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=0}{\overset{M}{\mathrm{\&Sigma;}}}{s}_{\mathrm{pq}}{P}_p\left(x\right)P_q\left(y\right)T_{\mathrm{pq}}^{\left(f\right)}---\left(20\right)$

Here M is the maximum order of square invariant.

In experiment, we get s _pqfor steady state value,, for p and q arbitrarily, make s _pq=s, with the Lena image of 256 × 256 sizes that Figure 2 shows that standard as original image.Image after embed watermark as shown in Fig. 3 (a), s=0.0214 in this example, the difference of original image and watermarking images is exactly watermark, due to its invisibility, we by the gray scale of watermark be multiplied by 50 so as to show, as shown in Fig. 3 (b).

Fig. 4 has provided the parameter s of controlling intensity, the relation between the maximum order M of square invariant and the Y-PSNR PSNR of Lena image.As seen from the figure, the PSNR of image is subject to the impact of parameter s larger, and it reduces along with the increase of s, and maximum order M is little on its impact.

Embodiment bis-:

The present invention also provides and the corresponding image detection water mark method of above-mentioned Image Watermarking, and the distance of the square invariant of use watermarking images and reception image is as estimating, and therefore testing process does not need to use original image.Be that watermark detection process belongs to publicly-owned watermark detection.

Detection method comprises the steps:

Steps A, obtain and receive image t and watermarking images h, wherein receiving image t is image to be detected, has adopted the Image Watermarking embed watermark based on the affine invariant of Tchebichef square provided by the invention and may be subject to various attack, and watermarking images h is identical with h in embodiment mono-;

Step B, is calculated and is received image t and the watermarking images h distance at feature space by following formula:

$d(t,h)=\frac{|I\left(t\right)-\left(h\right)|}{\left|I\left(t\right)\right|}---\left(21\right)$

Here I (t) and I (h) represent respectively the function I of the Tchebichef square invariant that receives image and watermarking images, i.e. formula (11)～(13).In the present invention, we to get I be mean value function:

$I=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{I}_i^{\mathrm{affne}}---\left(22\right)$

Wherein, L is the number of the square invariant that uses in watermark detection.

Step C, relatively d (t, h) and predefined threshold value d _thif, d (t, h) <d _th, think that watermark is appraisable, if d (t, h)>=d _th, think that watermark is not appraisable.

In this example, we test with four width standard grayscale images.Figure 5 shows that the gray level image of four 256 × 256 sizes, in this experiment, use said method embed watermark, M is set to 20, to Lena, and photographer, this four width image of women and ship, parameter s is respectively 0.0214,0.0192, and 0.0189 and 0.0198.Their PSNR difference 40.00,40.01,40.02 and 40.06.

Attack to Four types in this experiment compares, and is respectively rotation, convergent-divergent, Gaussian noise and jpeg image compression.For image rotation, we by watermarking images from 0 ° to 120 ° every 20 ° of rotations once.Then watermarking images is carried out convergent-divergent by we, and zoom factor from 0.1 to 0.6 does change of scale one time every 0.1.Attack for Gaussian noise, we add white Gaussian noise to watermarking images, and noise variance from 5 to 30 is every 5 variation one sub-values.Under jpeg image compression attack, compressibility factor from 10 to 60 every 10 conversion once.Four width test patterns, being subject to four kinds of mean distances under attack condition as experimental result, show in Fig. 6.As can be seen from Figure 6, under these are attacked, our method detects error and is less than existing method, and therefore our method has better robustness.

Embodiment tri-:

The present invention also provides and the corresponding image watermark extracting method of a kind of Image Watermarking of embodiment, needs to use original image in leaching process, and therefore it belongs to privately owned watermark extraction process, and its process flow diagram as shown in Figure 7, comprises the steps:

Steps A, obtain and receive image t and watermarking images h, wherein receiving image t is image to be detected, has adopted the Image Watermarking embed watermark based on the affine invariant of Tchebichef square provided by the invention and may be subject to various attack, and watermarking images h is identical with h in embodiment mono-;

Step B obtains the parameter matrix m (h) of watermarking images from receive image t and watermarking images h by following formula

$m\left(h\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(h\right)& \mathrm{\&alpha;}\left(h\right)\mathrm{\&beta;}\left(h\right)\\ \mathrm{\&delta;}\left(h\right)\mathrm{\&gamma;}\left(h\right)& \mathrm{\&delta;}\left(h\right)(1+\mathrm{\&beta;}\left(h\right)\mathrm{\&gamma;}\left(h\right))\end{array}\right]---\left(23\right)$

Parameter matrix m (t) with reception image t:

$m\left(t\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(t\right)& \mathrm{\&alpha;}\left(t\right)\mathrm{\&beta;}\left(t\right)\\ \mathrm{\&delta;}\left(t\right)\mathrm{\&gamma;}\left(t\right)& \mathrm{\&delta;}\left(t\right)(1+\mathrm{\&beta;}\left(t\right)\mathrm{\&gamma;}\left(t\right))\end{array}\right]---\left(24\right)$

Step C, according to m (h) and m (t), by the α in computing formula (10), β, δ and γ, estimate affine transformation parameter;

Step D, by matrix m (h) m ^{– 1}(t) obtain restored image f ';

Step e, deducts original image f and can estimate the watermark of embedding with restored image f '.

We using the Logo of information engineering university as embed watermark, as shown in Figure 8.Telescopiny still adopts formula (17), just Logo image is replaced to the square invariant in formula

logo is embedded in four width test patterns, is subject to the watermarking images of affine attack as shown in Figure 9.Table 1 has provided the result of parameter estimation, and in form, the first row is the parameter of the affine attack of simulation, and the second row is the parameter value that utilizes our method to estimate, by finding out in table, the result of parameter estimation is very accurate.

Table 1

As shown in figure 10, as can be seen from Figure, after affine attack, the watermark information that our method extracts is still correctly complete to adopt in the watermarking images of method provided by the invention from attacking the watermark of extracting, and identification degree is high.

The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned embodiment, also comprises the technical scheme being made up of above technical characterictic combination in any.It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.

Claims (4)

1. the Image Watermarking based on the affine invariant of Tchebichef square, is characterized in that, comprises the steps:

Steps A, calculate Tchebichef square invariant:

Steps A-1, the affined transformation of definition image is:

$\begin{array}{c}{x}^{\&prime;}=x_0+a_{11}x+x_{12}y\\ y^{\&prime;}=y_0+a_{21}x+a_{22}y\end{array}---\left(1\right)$

As follows with matrix representation:

$\left(\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right)=A\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)---\left(2\right)$

Wherein, $A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{11}& a_{22}\end{array}\right),$ Be called affine transformation matrix;

Steps A-2, the 2D p+q rank Tchebichef square of definition image is:

$T_{\mathrm{pq}}=\underset{x=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{y=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{t}_p\left(x\right)t_q\left(y\right)f(x,y)---\left(3\right)$

Wherein, p, q=0,1,2 ..., p, q is integer, wherein t _p(x) be p rank Tchebichef polynomial expressions, be defined as:

$t_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\&Sigma;}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}{(-x)}_r---\left(4\right)$

Above formula is expressed as follows by Matrix C:

$\begin{array}{c}{t}_p\left(x\right)=\underset{r=0}{\overset{p}{\mathrm{\&Sigma;}}}\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}\underset{k=0}{\overset{r}{\mathrm{\&Sigma;}}}{(-1)}^r{S}_1(r,k)x^k\\ =\underset{k=0}{\overset{p}{\mathrm{\&Sigma;}}}{c}_{p,k}^N{x}^k\end{array}---\left(5\right)$

S in above formula ₁(r, k) is Stiriling number, and Matrix C is defined as follows:

$c_{p,k}^N=\underset{r=k}{\overset{p}{\mathrm{\&Sigma;}}}{(-1)}^r{S}_1(r,k)\frac{{(-1)}^p(p+r)!(N-r-1)!}{\sqrt{\mathrm{\&rho;}(p,N)}(p-r)!{(r!)}^2(N-p-1)!}---\left(6\right)$

The lower triangle battle array C of definition _minverse matrix D _m=(d _p,k), 0≤k≤p≤M, D _melement definition be:

$d_{p,k}^N=\underset{m=k}{\overset{p}{\mathrm{\&Sigma;}}}{S}_2(k,m)\frac{\sqrt{\mathrm{\&rho;}(k,N)}(2k+1){(m!)}^2(N-k-1)!}{(m+k+1)!(m-k)!(N-m-1)!},---\left(7\right)$

Can be obtained by above formula:

$x^p=\underset{k=0}{\overset{p}{\mathrm{\&Sigma;}}}{d}_{p,k}{t}_k\left(x\right)---\left(8\right)$

Steps A-3, according to affine parameter, Tchebichef square is carried out being expressed as follows after affined transformation:

$T_{\mathrm{pq}}^{\&prime;}=\det \left(A\right)\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right)\left(\begin{array}{c}n\\ t\end{array}\right){\left(a_{11}\right)}^s{\left(a_{12}\right)}^{m-s}{\left(a_{21}\right)}^t{\left(a_{22}\right)}^{n-t}{c}_{p,m}^N{c}_{q,n}^M{d}_{s+t,i}^N{d}_{m+n-s-t,j}^M{T}_{\mathrm{ij}}---\left(9\right)$

Steps A-4, obtain the invariant of affine matrix: affine matrix A is carried out to XYS decomposition, and XYS decomposes the shearing that affine matrix A is resolved into an x direction, and the shearing of a y direction and a scaled matrix are as follows:

$\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}\mathrm{\&alpha;}& 0\\ 0& \mathrm{\&delta;}\end{array}\right]\left[\begin{array}{cc}1& 0\\ \mathrm{\&gamma;}& 1\end{array}\right]\left[\begin{array}{cc}1& \mathrm{\&beta;}\\ 0& 1\end{array}\right]---\left(10\right)$

Wherein, α, β, δ and γ are real number;

Through type (10), selects different a ₁₁, a ₁₂, a ₂₁, a ₂₂parameter substitution formula (9) obtains the invariant after affine matrix decomposes:

For given positive integer p and q, have

$I_{\mathrm{pq}}^{\mathrm{xsh}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right){\mathrm{\&beta;}}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{T}_{\mathrm{ij}}---\left(11\right)$

?

shearing to image x direction has unchangeability;

Order

$I_{\mathrm{pq}}^{\mathrm{ysh}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}n\\ t\end{array}\right){\mathrm{\&gamma;}}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{T}_{\mathrm{ij}}---\left(12\right)$

?

shearing to image y direction has unchangeability;

Order

$I_{\mathrm{pq}}^{\mathrm{as}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}^{m+1}{\mathrm{\&delta;}}^{n+1}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{T}_{\mathrm{ij}}---\left(13\right)$

?

image scaling is had to unchangeability;

Steps A-5, utilize the existing combination of Tchebichef square invariant to represent the Tchebichef square of the image after affined transformation:

Steps A-5-1, will calculate the shear invariant of x direction in the 2D p+q rank Tchebichef square substitution formula (11) of the image defining in steps A

Steps A-5-2, by the invariant obtaining in steps A-5-1

in substitution formula (12), calculate the combination invariant of the shearing of x direction and the shearing of y direction

Steps A-5-3, by the invariant obtaining in steps A-5-2

substitution formula obtains affine invariant in (13)

The invariant that steps A-5-1, steps A-5-2, steps A-5-1 are obtained carries out after inverse transformation, and Tchebichef square is expressed as follows by the linear combination of Tchebichef square invariant:

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{s=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{s}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m+n-s}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}m\\ s\end{array}\right){(-\mathrm{\&beta;})}^{m-s}{c}_{p,m}^N{c}_{q,n}^M{d}_{s,i}^N{d}_{m+n-s,j}^M{I}_{\mathrm{pq}}^{\mathrm{xsh}}---\left(14\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{t=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m+t}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n-t}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}n\\ t\end{array}\right){(-\mathrm{\&gamma;})}^t{c}_{p,m}^N{c}_{q,n}^M{d}_{m+t,i}^N{d}_{n-t,j}^M{I}_{\mathrm{pq}}^{\mathrm{ysh}}---\left(15\right)$

$T_{\mathrm{ij}}=\underset{m=0}{\overset{p}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{q}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}^{-(m+1)}{\mathrm{\&delta;}}^{-(n+1)}{c}_{p,m}^N{c}_{q,n}^M{d}_{m,i}^N{d}_{n,j}^M{I}_{\mathrm{pq}}^{\mathrm{as}}---\left(16\right)$

Step B, is embedded into Tchebichef square invariant in the invariant region of original image, obtains watermarking images, and embedding formula is:

$I_{\mathrm{pq}}^{\mathrm{as}\left(h\right)}=I_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}+s_{\mathrm{pq}}{I}_{\mathrm{pq}}^{\mathrm{as}\left(f\right)}---\left(17\right)$

Watermark w is expressed as to the function of original image Tchebichef square invariant:

$T_{\mathrm{pq}}^{\left(h\right)}=(1+s_{\mathrm{pq}})T_{\mathrm{pq}}^{\left(f\right)}---\left(19\right)$

The orthogonality of utilizing Tchebichef square, obtains:

$h=f+w=f+\underset{p=0}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=0}{\overset{M}{\mathrm{\&Sigma;}}}{s}_{\mathrm{pq}}{P}_p\left(x\right)P_q\left(y\right)T_{\mathrm{pq}}^{\left(f\right)}---\left(20\right)$

Wherein M is the maximum order of square invariant, thereby completes the embedding of watermark.

2. the image watermark detection method based on the affine invariant of Tchebichef square, is characterized in that, comprises the steps:

Steps A, obtains and receives image t and watermarking images h;

Step B, is calculated and is received image t and the watermarking images h distance at feature space by following formula:

$d(t,h)=\frac{|I\left(t\right)-\left(h\right)|}{\left|I\left(t\right)\right|}---\left(21\right)$

Here I (t) and I (h) represent respectively the function I of the Tchebichef square invariant that receives image and watermarking images

Step C, relatively d (t, h) and predefined threshold value d _thif, d (t, h) <d _th, think that watermark is appraisable, if d (t, h)>=d _th, think that watermark is not appraisable.

3. the image watermark detection method based on the affine invariant of Tchebichef square according to claim 2, is characterized in that, described I is mean value function:

$I=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{I}_i^{\mathrm{affne}}---\left(22\right)$

Wherein, L is the number of the square invariant that uses in watermark detection.

4. the image watermark extracting method based on the affine invariant of Tchebichef square, is characterized in that, comprises the steps:

Steps A, obtains and receives image t and watermarking images h;

Step B obtains the parameter matrix m (h) of watermarking images from receive image t and watermarking images h by following formula

$m\left(h\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(h\right)& \mathrm{\&alpha;}\left(h\right)\mathrm{\&beta;}\left(h\right)\\ \mathrm{\&delta;}\left(h\right)\mathrm{\&gamma;}\left(h\right)& \mathrm{\&delta;}\left(h\right)(1+\mathrm{\&beta;}\left(h\right)\mathrm{\&gamma;}\left(h\right))\end{array}\right]---\left(23\right)$

Parameter matrix m (t) with reception image t:

$m\left(t\right)=\left[\begin{array}{cc}\mathrm{\&alpha;}\left(t\right)& \mathrm{\&alpha;}\left(t\right)\mathrm{\&beta;}\left(t\right)\\ \mathrm{\&delta;}\left(t\right)\mathrm{\&gamma;}\left(t\right)& \mathrm{\&delta;}\left(t\right)(1+\mathrm{\&beta;}\left(t\right)\mathrm{\&gamma;}\left(t\right))\end{array}\right]---\left(24\right)$

Step C, estimates affine transformation parameter from m (h) and m (t);

Step D, by matrix m (h) m ^{– 1}(t) obtain restored image f ';

Step e, deducts original image f ' and estimates the watermark of embedding with restored image f.

Images