CN111986067A

CN111986067A - Robust digital watermarking algorithm for non-subsampled contourlet transform

Info

Publication number: CN111986067A
Application number: CN202010761640.XA
Authority: CN
Inventors: 张天骐; 周琳; 张晓艳; 张刚; 胡延平
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2020-07-31
Filing date: 2020-07-31
Publication date: 2020-11-24

Abstract

The invention aims to solve the problem that the robustness of the pseudo-Zernike moment shear resistance and the scaling attack resistance in the digital watermarking technology is not strong, and belongs to the field of image and signal processing. The method comprises the steps of utilizing non-subsampled contourlet transformation to carry out three-layer decomposition on a carrier image to extract low-frequency components of the carrier image, carrying out sparsification on the low-frequency components through one-dimensional discrete wavelet transformation to obtain sparse bases, constructing a measurement matrix of the sparse bases, carrying out compressed sensing processing on the measurement matrix to obtain new low-frequency components, then calculating Zernike moments of the low-frequency components, and embedding watermark information in a mode of modulating and regularizing pseudo-Zernike moment amplitudes through dithering quantization. And finally, reconstructing image compressed sensing by utilizing a regularization orthogonal matching tracking algorithm. On the premise of ensuring the invisibility of the watermark, the method not only can effectively resist conventional attacks such as filtering, noise, compression and the like, but also has relatively strong robustness on geometric attacks such as scaling, shearing, rotation and the like, and has important reference significance for the subsequent research on solving the problem of robustness of the watermark against the geometric attacks.

Description

Robust digital watermarking algorithm for non-subsampled contourlet transform

Technical Field

The invention relates to a branch image watermark of an information hiding technology of image and signal processing, in particular to a robust digital watermark algorithm combining Compressed Sensing (CS) based on non-subsampled Contourlet Transform (NSCT) and a pseudo Zernike moment.

Background

Since the 21 st century, communication information technology and internet application have been widely spread, and the problem of counterfeiting of digital products by copying and embezzling needs to be solved, and digital information protection is particularly important, so that digital watermarking technology is developed. At present, the digital watermarking technology is well developed, general simple attacks can effectively resist because the synchronism of watermark detection is not damaged, but attacks such as rotation, scaling and shearing are accompanied by synchronous errors caused by geometric distortion, and most digital watermarks are difficult to resist, so that how to design a scheme capable of effectively resisting geometric attacks such as rotation, scaling and shearing is one of important topics needing to be researched by the current watermarking technology.

The scheme for resisting the geometric watermark proposed at present can be roughly divided into four types, namely a Jacobian-Fourier matrix, a Shifted Legendre matrix, a Chebichef matrix, Jordan transformation, a Zernike matrix and other geometric invariant domain schemes, which are common, but the method can only resist simple and conventional geometric attacks because the method is easily influenced by interpolation operation and embedding capacity, and the resistance to complex attacks such as shearing is relatively weak.

In recent years, watermarking schemes based on feature point extraction such as Harris (Harris), Scale Invariant Feature Transform (SIFT), and fast robust up robust features (SURF) have also made great progress, and the watermarking is not easily affected by synchronization errors during detection due to the extraction of important feature information of images. In the literature (Yi-Xin Z, Zheng-Ning T.the watermark affinity to geometry analysis based on SURF and RDWT [ J ]. electronic design engineering,2019,27(18):157 and 161), the SURF algorithm is used for extracting the characteristic points of the carrier image, the random sampling consistency algorithm RANSAC (random Sample consensus) is used for optimizing the characteristic point matching result, and then the SURF correction calculation is carried out on the attacked image to restore the original watermark, and the corrected rotation angle can be obtained through transformation, so that the method is effective in resisting rotation attack, but the robustness to scaling and shearing attack is not strong. The third type of watermark scheme based on template matching can avoid the problem of low robustness caused by geometric distortion, but the embedding capacity of watermark information is reduced due to the addition of the synchronous template in the watermark. The popular scheme of watermark technology research in recent years is to introduce machine learning in watermarking. The scheme generates a dynamic mode for embedding the watermark by combining an optimization algorithm of the population and a neural network model, thereby enhancing the geometric attack resistance of the watermark. Document (BasN D, Singh R P, Chaudhary V, et al. A Novel Blind Digital Watermarking Based SVD and Extreme Learning Machine [ J ]. Oriental Journal of Computer science and Technology,2017,10(1): 160-. The method meets various geometric attack resistance of the watermark, but sacrifices the invisibility index of the watermark.

The first watermarking technology of the geometric invariant domain is adopted, and a scheme of combining Compressive Sensing (CS) with pseudo-Zernike moments under non-subsampled Contourlet transform (NSCT) is provided for solving the problem that the pseudo-Zernike moments in the geometric invariant domain are not strong in shearing resistance and scaling attack resistance. Firstly, NSCT is carried out on an image, then low-frequency components of the image are extracted, sparse bases are obtained after the low-frequency components are subjected to sparse processing, a new low-frequency image is obtained through compressed sensing, and then watermark information is embedded in a mode of modulating and regularizing pseudo-Zernike moment amplitude values through dithering quantization. And finally, reconstructing the compressed sensing through regularized orthogonal matching pursuit. Simulation and experiment results show that the algorithm can effectively resist simple attacks of images and geometric attacks such as rotation, scaling, shearing and the like on the premise of meeting the invisibility of watermarks.

Disclosure of Invention

The technical problem to be solved is to solve the problem that the robustness of anti-shearing and scaling attack of a pseudo-Zernike matrix in a current geometric invariant domain of a geometric attack resistant watermark is not strong, and the solution is to provide a CS-Zernike matrix robust digital watermark under NSCT. By combining the non-downsampling contourlet transformation and the regularization Zernike moment thought, the problem that the robustness of the watermark against geometric attack is not strong is effectively solved.

The implementation method of the technical scheme provided by the invention for solving the technical problems comprises the following steps: firstly, a carrier image I is subjected to three-layer decomposition by utilizing non-subsampled contourlet transformation to extract the low frequency component I of the carrier image I_LLSparsifying the low-frequency component by one-dimensional discrete wavelet transform to obtain a sparse basis

Constructing a measurement matrix y of sparse bases_cAnd to y_cCarrying out compressed sensing processing to obtain new low-frequency component

Then calculate

And embedding watermark information in a mode of modulating and regularizing the amplitude of the pseudo-Zernike moment by dithering quantization. Low-frequency image containing watermark by using ROMP algorithm

Carrying out compressed sensing reconstruction to obtain a reconstructed low-frequency image containing watermark

To be modified

Binding antigenThe high-frequency components are reconstructed to obtain the watermark-containing image I' to be extracted.

The Zernike moments are defined as follows: it is a mapping of the original image onto a set of bases, defined as x within a unit circle²+y²Any square integrable function ≦ 1:

V_eq(x,y)＝V_eq(ρ,θ)＝R_eq(ρ)exp(jqθ) (1)

wherein R is_eq(p) is a radial polynomial of Zernike moments,

θ ═ arctan (y/x), e ═ 0,1,2, …, and denotes the order of the Zernike moments, q ═ 0, ± 1, ± 2, …, | q | < e, and e- | q | is an even number. V_eq(x, y) is a complex function set of Zernike moments with orthogonality.

V_eq(x, y) satisfies the formula:

wherein [ V ]_eq(x,y)]^*Represents V_eqThe complex conjugate of (x, y),

according to the orthogonal transformation theory, the continuous function f (x, y) satisfies x²+y²If the value is more than 1 and the function value is zero, V can be used_eq(x, y) unfolding:

wherein Z is_eqThe e-order q for f (x, y) is the Zernike moment. Namely:

the above equation is solved:

using x ═ ρ cos θ and y ═ ρ sin θ, Z is expressed by_eqThe rectangular coordinate representation of (a) is converted to a representation in polar coordinates:

the radial polynomial of the Zernike moments is defined as follows:

it is derived that the Zernike moments have rotational invariance, and the regularized Zernike moments can eliminate the effect of translational scaling on the image. The process of regularizing the Zernike moments is to actually average the gray values of the images, and the zeroth order moment of the images represents the overall gray value of the images, so the Zernike moments can be regularized by using the zeroth order moment of the images. The u + v order moment function of the image is defined as:

where f (x, y) represents an image pixel value. u, v ═ 0,1, 2.

Thus, the image zeroth order moments and the regularization Zernike moments are defined as:

the compression theory can be divided into 3 parts: sparsity of the signal, representation of the observation matrix, and reconstruction algorithms of the signal. The sparse basis of the signal can be obtained through a certain transformation or can be obtained through orthogonal sparse transformation:

wherein x is_sFor sampled signals of length N, s being x_sA matrix of non-zero coefficients on a basis of some kind, psi ═ psi₁,ψ₂,…,ψ_NIs x_sIs a sparse radical of x_sA set of N-dimensional orthogonal bases.

Signal x_sObtaining an observation vector y by compressed sensing_sNamely:

y_s＝φx_s＝φψs＝ξs (12)

where xi phi psi, y_sThe length is M, phi is the observation matrix, and the size is M multiplied by N.

The Regularized Orthogonal Matching Pursuit (ROMP) is one of the compressed perceptual reconstruction algorithms, and its flowchart is shown in fig. 1, and the specific steps are described as follows:

inputting sparsity n, observation matrix phi and observation value y_sAn error threshold λ;

and (3) outputting: signal x_sIs reconstructed signal x_outReconstructing the error r;

initial value: initial value of error r₀＝y_sReconstructing the signal

The iteration number t is 0, and the index set is lambada₀Phi, and the candidate set J phi;

step 1: calculating a correlation coefficient, namely: error r and the in-column product g of the observation matrix phi^t＝φ^λr^t-1；

Step 2: find the number g^tStoring the index values corresponding to the n maximum values into J;

and step 3: regularizing the correlation coefficient of the atom corresponding to the index value in J, and storing the result in J₀Performing the following steps;

and 4, step 4: update index set Λ^t＝Λ^t-1∪{J₀And atomic set

And 5: obtaining an approximation value according to a least square method

Step 6: update error r^t＝y_s-φx^tSatisfy | | | r^t-r^t-1When | | < lambda, the iteration is stopped, x_out＝x^t，r＝r^tOtherwise, turning to step 1.

Drawings

FIG. 1 shows a flow chart of a regularized orthogonal matching pursuit algorithm

Fig. 2 shows a process diagram of watermark embedding and extraction

FIG. 3 is a schematic representation of a hydrous image of Lena, Babon and Barbara

Figure 4 BER and NC values for rotation angle and scale factor at different watermark lengths L

Table 1 shows the resistance of the algorithm to simple attacks

Table 2 shows the resistance of the algorithm to shear attack

Detailed Description

The invention is further described with reference to the following drawings and specific examples.

Fig. 2 is a flow chart of the embedding and extracting of the algorithm, and the specific implementation process is as follows:

1) three-layer NSCT transformation is carried out on the original image I, and a low-frequency image I with the same size as the original image is extracted_LLTo 1, pair_LLPerforming sparsification processing, and extracting the detail coefficient vector by using discrete wavelet transform

I.e. obtaining sparse basis, after sparse representation

Carrying out compressed sensing to obtain a measurement vector y_cThe observation matrix is generated by a Gaussian random matrix with M rows and N columns, and M is less than N.

2) For y_cIncreasing dimension, expanding to N lines, and inverse wavelet transform to obtain new low-frequency components to be processed

3) Computing

And (5) simulating Zernike moments and carrying out regularization processing. When the pseudo-Zernike moments are calculated, the order e is selected to be crucial, the calculation result is deviated due to too high order, the objectivity of the experiment result is affected, theoretically, e is less than or equal to 30, the pseudo-Zernike moments with the order e of 25 and the repetition degree q ≠ 4i (i ═ 0,1,2, …) are more favorable for watermark embedding, and therefore, the set of the selected regularized pseudo-Zernike moments is as follows:

Z＝{Z_eq,e≤30,q≥0,q≠4i} (13)

4) and generating watermark information. Create l independent and identically distributed random number streams using a specific uniform pseudo random number generator algorithm, then assign the random number streams as the uniform random variables from which the rand function obtains 0-1 for X rows and Y columns, and take 1 if ω is greater than 0.5 and 0 otherwise.

5) Selecting L suitable regularized pseudo-Zernike moments from Z in step 3

The embedding of the watermark is completed, wherein the embedding needs to be combined with the participation of a Key Key1, and the corresponding L amplitudes are

6) Regularization with dithered quantization modulationEmbedding watermark in a mode of pseudo Zernike moment amplitude, and setting the quantized amplitude as

The quantization formula is as follows:

wherein [. cndot. ] represents rounding off; Δ represents a quantization step; d (-) represents a quantizer, dependent on Δ, that satisfies the formula:

7) to ensure that the reconstructed image pixel values are real, the amplitude values need to be quantized simultaneously

And its conjugate matrix amplitude

Using ROMP algorithm to print low frequency image with water

8) And generating a watermark-containing image. To be modified

And reconstructing by combining the original high-frequency components to obtain the watermark-containing image I' to be extracted.

9) Carrying out three-layer NSCT transformation on the image I ' to be extracted to obtain a low-frequency watermark-containing image I ' with the same size as the original image '_LLTo l'_LLPerforming sparse representation, and acquiring sparsity by using one-dimensional wavelet transformAnd performing compressed sensing on the sparse vector to obtain a measurement vector y'_c. Wherein the measurement matrix is generated by a Gaussian random matrix with M rows and N columns.

10) Will y'_cThe line number of the measurement matrix is expanded to the column number of the measurement matrix, and a new low-frequency watermark-containing image I' is obtained by using wavelet inverse transformation_LL。

11) Calculate I ″)_LLNormalized pseudo-Zernike moments. And utilizes Key1 to select L pseudo-Zernike moments

Corresponding to a magnitude of moment of

The watermark information is generated as embedded.

12) The process of quantitative extraction is as follows:

the amplitudes of the pseudo-Zernike matrices are quantized separately using quantization functions d (0), d (1)

Extracted by quantization of the formula (16)

Comparing two groups of watermark dithering quantization distances d₀And d₁And extracting the watermark.

Wherein abs (. cndot.) represents an absolute value, and [ cndot ] in formula (16)]Represents rounding off, Δ is the quantization step, j is 0, 1; res ═ d₀-d₁If res is less than 0, ω' is 0; otherwise ω' is 1.

FIG. 3 shows the watermark-containing images of Lena, Baboon and Barbara, the original image being set to 256 × 256 standard by the present inventionTaking a random digital stream with L being 5489 and independent and same distribution, selecting 1 row and 64 columns of uniform random variables from the random digital stream, so that the length L of the watermark information is 64bit, and setting N as 64bit in the text

Satisfies that M < N, and M is 0.7N. The Zernike moment order is set to 25 and the quantization step size delta is set to 0.07. The NSCT pyramid filter type is 'maxflat' and the directional filter type is 'dmaxflat 7'. As can be seen from fig. 3, the peak snr of the three images is 41.56,40.29,42.43, and the PSNR reaches above 40dB, which is almost the same as that of the original image in visual effect, so the watermark has good invisibility.

Table 1 resistance of the algorithm herein to simple attacks

As can be seen from table 1, the algorithm has strong resistance to general attacks such as image filtering, noise, JPEG compression, and gray level change, the number of error bits of the extracted watermark is less than 6, and the NC value can be more than 0.9, and especially for white gaussian noise, gaussian filtering, and JPEG compression attacks, the NC value is almost 1, so the algorithm has relatively strong robustness to simple attacks.

Fig. 4 shows the variation of NC values and BER for different watermark sequences L with rotation angle and scale factor. As can be seen from fig. 4(a) and (b), when rotated by the same angle, the smaller L, the larger NC value, and the smaller BER. This is because the selected quantization step is fixed, more watermark information is embedded, and the robustness of the watermark is relatively weakened. When L is 64bit, the lowest NC value can reach more than 0.7, and the highest BER is about 0.34. The law of change of the NC values at different L is consistent with each 10 ° rotation angle increase, i.e.: when the rotation angle is a multiple of 90 degrees with 90 degrees as a period, the NC value can reach 1, the number of accepted error bits is almost 0, and as can be seen from the figure, the NC value and BER are not ideal when the rotation angle is 40 degrees and-40 degrees, because of the influence caused by interpolation calculation of pixel values and image sparse representation in compressed sensing. In the overall effect, the requirement that the watermark can be effectively extracted is met, and the algorithm has stronger resistance to the rotation attack. As can be seen from fig. 4(c) and (d), the NC value of the scaling factor between 0.7 and 2 can be 0.8 or more and the error rate is 0.2 or less, except that the NC value and BER are not optimistic when the scale factor is 0.6. The reason is that the watermark information is lost correspondingly due to the over-reduction of the image, and in addition, the compressed sensing processing is carried out after the watermark image is zoomed, the compressed sensing processing is essentially carried out by utilizing the low-dimensional information to restore the original high-dimensional data with the maximum efficiency, and actually, the image compression is also carried out, so the watermark information is seriously lost under the condition of the over-zooming. But the influence of the expansion of the image scale on the extraction of the watermark is small, when the scale factor reaches more than 0.9, the NC value of the extracted watermark approaches to 1, the number of the detected error bits of the watermark is less than 3, and the error rate is lower than 0.05, so that the algorithm can effectively resist the scaling attack under most scales. The extraction of the watermark has a certain relation with the quantization step length, due to the influence of delta, the effect of the NC value and the BER is the best along with the change situation of the scaling factor when L is 64 bits, the watermark can be basically and completely recovered when the scaling factor is higher than 1, and the error rate is almost 0.

Table 2 resistance of the algorithm herein to shear attack

Table 2 shows the resistance of the algorithm to edge shear as well as center shear attack at different shear strengths. As can be seen from table 2, the algorithm can resist the attack of which the cropping area reaches 1/2, and can still well resist such a large-area attack when 50% of the image is cropped in the center, the NC value can reach 0.8, the number of detected false watermark bits is less than 15 bits, the BER is less than 0.24, whether the cropping area is middle or edge cropping, when the cropping area is between 5% and 50%, the NC value can reach 1 at maximum, and the error rate is 0 at minimum, so the algorithm has relatively strong robustness to the cropping attack.

The invention provides a CS-Zernike digital watermarking algorithm based on non-subsampled contourlet transformation, aiming at solving the problem that the robustness of pseudo-Zernike moments to scaling and shearing attacks is not strong. Therefore, the algorithm has good application prospect in the robustness research of the digital watermarking technology.

Claims

1. A non-downsampling contourlet transform robust digital watermarking algorithm comprises the following steps: firstly, carrying out three-layer decomposition on a carrier image by utilizing non-subsampled contourlet transformation to extract a low-frequency component of the carrier image, carrying out sparsification on the low-frequency component by utilizing one-dimensional discrete wavelet transformation to obtain a sparse base, constructing a measurement matrix of the sparse base, carrying out compressed sensing treatment on the measurement matrix to obtain a new low-frequency component, then calculating a Zernike moment of the low-frequency component, and embedding watermark information in a mode of modulating and regularizing a pseudo-Zernike moment amplitude by dithering quantization. And finally, reconstructing image compressed sensing by utilizing a regularization orthogonal matching tracking algorithm. The watermark extraction does not need to use the information of the original image, so the algorithm belongs to a blind extraction algorithm of the watermark.

2. The algorithm according to claim 1, wherein the low-frequency image I is required to be processed before the compressed sensing processing of the image_LLPerforming sparsification processing, and extracting detail coefficient vector I by using discrete wavelet transform_LLcDNamely, obtaining sparse base, and carrying out sparse representation on I_LLcDCompressed sensing is carried out to obtain a measurement vector y_cWhen performing inverse wavelet transform, y needs to be matched_cAscending the vitamin, namely: will y_cThe number of rows is expanded to the number of columns of the measurement matrix.

3. The algorithm according to claim 1 or 2, characterized by the steps of: the size of the low-frequency component of the original image can be kept unchanged by utilizing non-downsampling contourlet transformation, then high-dimensional information of the low-frequency component is restored to the maximum extent by carrying out compressed sensing through the low-dimensional information, and ROMP is utilized to carry out compressed sensing reconstruction, which is equivalent to coding and decoding processing on the original image, so that the security and reliability of watermark embedding are increased, and the regularized Zernike moment theory is combined, so that the attack of any rotation angle and any scaling scale can be resisted, and the robustness of the watermark against geometric attack is greatly improved.