CN113870086A - Blind watermark algorithm based on Polar code and interleaving algorithm - Google Patents

Abstract

The invention discloses an NSCT-DCT domain strong robustness blind watermarking algorithm aiming at the combination of Polar codes and SP (successful packing) two-dimensional interleaving algorithms, belonging to the field of image processing. The algorithm sequentially carries out Logistic encryption, Polar code coding and SP two-dimensional interweaving on the watermark, carries out NSCT transformation on a carrier image, embeds watermark information according to the relation of the coefficient and the determinant, and can realize blind extraction of the watermark. And when the watermark is extracted, carrying out geometric correction on the image by utilizing Radon transformation. The result shows that the algorithm not only enables the image after the watermark is embedded to have good invisibility, but also can effectively resist attacks such as noise adding, filtering, JPEG compression, shearing, translation, rotation, mosaic, tampering and the like, the NC value is more than 0.9, the robustness to combined attack is strong, and the algorithm has good practical value.

Description

Blind watermark algorithm based on Polar code and interleaving algorithm

Technical Field

The invention belongs to the field related to image processing, and particularly relates to an NSCT-DCT domain strong robustness blind watermarking algorithm based on the combination of Polar codes and SP (successful packing) two-dimensional interleaving algorithm.

Background

Digital watermarking technology is one of the important means for copyright protection and information hiding at present. Common watermarking algorithms can be classified into a spatial domain algorithm and a transform domain algorithm, and a non-blind extraction algorithm and a blind extraction algorithm. The blind watermarking algorithm is a key point and a hotspot of research, but most of the blind watermarking algorithms are not strong in robustness, and watermarking information and the watermarking information are easily damaged by geometric attacks such as rotation and shearing.

Spatial domain algorithms refer to direct modification of the pixel values of the carrier image, with low algorithm complexity, but weak resistance to attacks, such as the document "Guoyin Z, Liang K, Liguo Z, et al. The document 'block error dispersion half-toning watermarking algorithm based on parity check' modifies the parity of an image pixel block to achieve the purpose of embedding a watermark.

The transform domain algorithm replaces coefficients of a transform domain, so that watermark information is more uniformly embedded in a spatial domain, and the method has a visual masking characteristic and strong robustness. The document 'watermark-containing color image characteristic analysis based on the inner product space non-empty subspace transformation relation' embeds watermarks in a wavelet domain, and solves the problem that a large-capacity watermark is sensitive to geometric deformation by using characteristic points generated in an intermediate frequency region of a natural logarithmic magnitude frequency domain. The algorithm is resistant to conventional attacks and is capable of blind extraction. The document 'a robust image watermarking algorithm combining a Blob-Harris characteristic region with a CT-SVD' proposes a robust image watermarking algorithm combining a Blob-Harris characteristic region with a CT-SVD, which has stronger robustness to most attacks, but fails to realize blind extraction of watermarks and has poor effect on rotary attacks. The document "Optimized Features of SIFT Transform Function for Digital Image Watermarking using Hybrid search and Neural Network" divides an Image into blocks, and divides the Image blocks into an adaptive embedding area and an authentication information extraction area in a sub-block DCT domain. Both of which are ineffective against noise attacks and geometric attacks. The literature "Wavelet Transform module largest based Robust Logo Watermarking" algorithm increases invisibility and robustness in the Wavelet domain and addresses low-volume embedding, but provides only limited robustness. The document "A Blind watermark Based on Adaptive Quantization in Contourlet Domain" realizes Blind extraction of watermarks by singular value decomposition and adopting an Adaptive Quantization mode, and has better invisibility and robustness. CunhaA.L. and Zhou J proposed in 2006 a non-subsampled Contourlet Transform (NSCT) domain image Transform approach as described in The document "The Nonsubsampled Contourlet Transform: Theory, Design, and Application". The NSCT transform can effectively represent an image having more directional information than the conventional contourlet transform. The document "bland watermark based on scheme decoded and non-subsampled contourlet transform" utilizes the scheme to decompose and embed the watermark in the NSCT domain, and designs a synchronization mechanism based on the scale-invariant feature transform to resist the geometric attack. In the document, "NSCT domain robust watermarking algorithm based on BSVD decomposition and Radon transformation" embeds watermarks in the NSCT domain by means of BSVD decomposition, and combines with Radon transformation to correct attacked images, the algorithm can effectively resist rotation attack, but blind extraction cannot be achieved. In the document, "application of a BSP two-dimensional block interleaving algorithm in combination with an RS error correcting code in watermarking", watermark information is embedded in an intermediate frequency part of a block DCT coefficient in combination with the RS error correcting code and the two-dimensional block interleaving algorithm, and the algorithm only has good resistance to shearing attack and burst error and has a poor effect on other attacks. The document 'DWT-SVD and Turbo code-based color image blind watermarking algorithm' combines Turbo error correcting code and SVD decomposition embedding watermarking in a wavelet domain, and has better robustness to common attacks. Subsequently, in the literature, "digital watermarking technology based on LDPC code decoding algorithm" combines the LDPC code decoding algorithm with the digital watermarking technology, and extracts watermark information with a reduced error rate, but the extraction process still requires carrier image information. Polar Codes based on the channel polarization theory proposed by Arikan in 2009, such as the document "a Method for Constructing Capacity-interference Codes for symmetry Binary-input Channels", prove that Polar Codes can reach shannon limit theoretically, so that Polar Codes become the hot point of research. Document "" verifies that the error rate of Polar codes is remarkably reduced compared with that of LDPC codes in image transmission.

In order to solve the problem of weak robustness of a blind extraction algorithm, the method is based on an SP two-dimensional interleaving algorithm, firstly Logitics mapping encryption is carried out on watermark information, then interleaving is carried out on encrypted information after polar code encoding, NSCT transformation is carried out on a carrier image, and watermarks are embedded by utilizing the relation between low-pass sub-band DCT coefficients and the coefficients and determinant of band-pass sub-bands. Radon geometric correction is performed on the image before extraction.

Disclosure of Invention

The technical problems to be solved by the invention are that the image after the watermark is embedded has good invisibility and robustness under the condition of image attack modes such as noise adding, JPEG (joint photographic experts group) compression, filtering, rotation, translation, shearing, tampering, mosaic attack, combined attack and the like.

The technical scheme for solving the technical problems is as follows: based on SP two-dimensional interleaving algorithm, firstly performing Logitics mapping encryption on watermark information, then interleaving the encrypted information after polar code encoding, performing NSCT (non-subsampled Contourlet transform) transformation on a carrier image, and embedding the watermark by utilizing the relation between low-pass sub-band DCT (discrete cosine transform) coefficients and band-pass sub-band coefficients and determinant. Radon geometric correction is performed on the image before extraction.

Drawings

FIG. 1 is a three-level NSCT transform and non-downsampling pyramid filter bank;

fig. 2 is a flow chart of watermark embedding;

fig. 3 is a flow chart of extraction of a watermark;

FIG. 4 a carrier image;

FIG. 5 embedding a watermark image;

FIG. 6 shows watermark images extracted without attack;

FIG. 7 watermark embedding strength versus PSNR;

FIG. 8 is a diagram of an original image, an image after a rotational attack, an image after Rodan correction, and watermarks before and after correction;

FIG. 9 images after a combination attack and other attacks;

fig. 10 extracted watermark;

FIG. 11 non-geometric attack experiment (NC)

FIG. 12 geometric attack results (NC)

FIG. 13 is a table of performance of different rotation angles for extracting calibration and uncorrected

FIG. 14 three watermark algorithm comparisons (BER)

Detailed Description

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

The method comprises the following steps: and (5) performing Logitics mapping analysis. The logics mapping is a chaotic power system with wide application, and the document 'Multi-dimensional partial sweep Optimization for Robust Image Water marking Using interleaving logic Map and Hybrid Domain' is described in detail and defined as follows:

x_n+1＝μx_n(1-x_n) (1)

in the formula x_nE (0,1), when mu e is 3.57,4]When the sequence is in a chaotic working state. This patent adopts the Logitics mapping to generate and is used for the encrypted sequence of exclusive OR.

Step two: FIG. 1 is a three-level NSCT Transform and a non-downsampled pyramid filter bank, The NSCT Transform is an ultra-small wave Transform, such as The Nonsubsampled Contourlet Transform, Theory, Design, and Applications, a redundant Transform with translation invariance, and singular point information is obtained by non-downsampled pyramid decomposition to provide The multi-scale characteristics of NSCT; and a non-downsampling direction filter is used for connecting discontinuous points to approximate the original image, so that the directionality is provided.

Step three: polar code analysis. In a binary input discrete memoryless channel (B-DMC), a B-DMC channel model may be represented as W: X → Y, X, Y representing input and output symbols, respectively. The transition probability is W (Y | X), X ∈ X, Y ∈ Y for the row vector (Y ∈ Y)₁,…,y_N) Abbreviated as

W^NIndicating that channel W is used N times, then channel W^NThe transition probability is expressed as:

the polar code coding is determined by information bits and a generating matrix, and the coding process is as follows:

wherein the content of the first and second substances,

as a set of input variables, G_NIs to generate a matrix of the data to be transmitted,

B_Nis an N x N bit transpose matrix that, for any subset a,

the above formula can be represented as:

wherein G is_N(A) Is G_NA generator matrix formed by the corresponding rows of the A set, A^cIs the complement of A. The encoding of the polarization code can be determined by the following parameters, the code length N, the information bit A, the number K of the information bits, K/N is the code rate, and the frozen bit (frozen bit) u_AUsually, it is set to "0" symbol, so it is expressed as

The patent adopts SC decoding algorithm according to A and A^cAnd

calculating an estimated value

Since the symbol of the position '0' is frozen, the decoding is to generate an estimated value

The SC decoding estimation method comprises the following steps:

wherein h is_iIs defined as:

wherein the content of the first and second substances,

are respectively shown in

Under the condition of inputting 0,1 output

The probability of (c).

Theoretically, it can be concluded that, in a binary input discrete memoryless channel, the bit error rate of Polar is:

wherein the content of the first and second substances,

is composed of

Babbitt parameter of (P)_eIs the bit error rate.

Step four: and (5) analyzing an SP interleaving technology. Handle 2ⁿ×2ⁿThe matrix of (a) is used as an interleaved unit, and the unit is equally divided into four quadrants, each quadrant is divided into four quadrants, and so on until the unit is divided into 2 × 2 minimum units. Concrete structureThe manufacturing steps are as follows:

firstly, 4 elements in the 2 multiplied by 2 minimum unit are arranged into an interleaving square matrix, and the dimension is increased according to an algorithm to obtain a high-order interleaving square matrix.

Wherein 0,1,2,3 are all 2 × 2 matrices.

Step five: radon transform analysis. The image subjected to geometric attack is corrected and processed. Radon transform an image f (x, y) is a calculation of the projection of the image along a given angle, the resulting projection being the sum of the pixel intensities in each direction, i.e. the line integral. The pixel matrix f (x, y) Radon transform is defined as:

P(γ,θ)＝R(γ,θ)∫∫f(x,y)δ(γ-xcosθ-ysinθ)dxdy (10)

wherein gamma is the distance from the origin to the straight line, theta is the angle between the straight line and the coordinate axis, and delta is the line integral of f (x, y) to gamma-xcos theta-ysin theta. From this, the projection of f (x, y) along the line at (γ, θ) can be obtained.

The correction steps are as follows:

(1) calculate reference vector R (0): the original image is subjected to Radon transformation, and a reference vector R (0) is calculated.

(2) Obtaining a detection vector R (theta), theta epsilon [1 degrees, 2 degrees, 180 degrees ]: and respectively carrying out 1-180-degree Radon transformation on the carrier image to obtain 180 detection vectors to form an angle-detection vector pair.

(3) Calculating a rotation angle: and comparing the correlation coefficients of R (0) and R (theta), wherein the maximum correlation coefficient is the corresponding angle.

(4) And (6) correcting the image. And carrying out reverse rotation on the obtained angle to obtain a corrected image.

Step six: fig. 2 shows a watermark embedding process. And selecting a 256 × 256 carrier image, and watermarking the carrier image into a 64 × 64 binary image w. Firstly, carrying out watermark preprocessing, selecting an initial value x (0) to be 0.3 and a mu to be 4, iterating for 500 times to enable the sequence to fully reach a chaotic state, then generating a Logitics sequence with the same length as the watermark, carrying out binarization on the Logitics sequence, and readjusting the obtained sequence to be a 64 x 64 binary image B in a reshape mode to carry out XOR encryption on the watermark w to obtain an encrypted watermark w'.

W' is divided into 4 × 1 blocks, and each block is encoded with N64, K4, and code rate r 1/16. Selecting

Relatively small K × N × 4, all i make up set a. Matrix G₆₄Generating matrix G with rows corresponding to set A₆₄(A) And (2) obtaining polar code with the code length of 64. Matrix w after block coding_b. To w_bReducing dimension into a one-dimensional sequence, performing SP two-dimensional interweaving to form an interweaving square matrix S, and performing secondary encryption on the watermark. And S is an interweaving square matrix with watermark information to be embedded into a carrier image.

And then carrying out Radon transformation on the host image before watermark embedding for watermark embedding and image restoration to obtain a reference vector R (0) for detecting and correcting the rotation attack. Carrying out J-level (J is 3 in the patent) NSCT transformation on the host image I to obtain a low-pass sub-band L_JAnd each direction sub-band

Wherein j represents the j-th non-downsampled pyramid decomposition, and k represents l_jThe kth directional subband of the non-downsampled directional filter decomposition is ranked. The image main energy is concentrated in the low-pass sub-band L_JThen DCT transform is performed to obtain the coefficient L_DThe watermark is embedded in the image, and the image has a good visual effect. And establishing the relation between the NSCT coefficient and the determinant, and embedding the interleaving square matrix S with the watermark information into the relation. The determinant value is obtained from equation (11).

Wherein A is₁＝d_J,0，A₂＝d_J,1，A₃＝d_J,2，A₄＝d_J,3。d_J,0，d_J,1，d_J,2，d_J,3Are J-order directional subbands. From A₁(i, j) and det (i, j), embedding the watermark as (12):

wherein L is_wIs L after modifying the coefficient_DLg is the mark matrix after embedding the watermark, and alpha is the embedding strength. To L_wAnd performing DCT inverse transformation to obtain the restored NSCT low-frequency sub-band coefficient, and performing NSCT reconstruction with the directional sub-band to obtain the image embedded with the watermark.

Step seven: fig. 3 shows the watermark extraction process. The rotation angle of the carrier image is detected before watermark extraction. And calculating a vector to be detected and a reference vector R (0) for comparison, wherein the detected angle is the angle of the rotary attack, and correcting the image. Performing J-level NSCT transformation on the image embedded with the watermark according to DCT coefficient L of J-level low-frequency sub-band_D' (i, j) and the directional subband coefficient A₂'(i,j)，A₃'(i,j)，A₄'(i, j) calculate det' (i, j):

from det' (i, j), A₁'(i, j), Lg (i, j) extracts watermark information S' (i, j).

And performing SP-removing two-dimensional de-interleaving and dimension-increasing on the s ', and decoding the partitioned polar code to obtain w'. Finally, Lotistics decryption is carried out on w' according to (16). Original watermark information wa is obtained.

Step eight: fig. 4 and 5 show a carrier image and an image after embedding a watermark, respectively, and the invisibility of the image after embedding the watermark is evaluated by peak signal-to-noise ratio (PSNR). PSNR is defined as follows:

where m × n is the size of the image, I_wAnd (I, j) and I (I, j) are pixel values of (I, j) th points of the image embedded with the watermark and the original image. When the embedding strength α is 0.03, PSNR is 42.2414.

Step nine: fig. 6 shows a watermark image extracted without attack, the algorithm can completely extract watermark information and has good invisibility, and a simulation experiment is performed in Matlab2017 a. 256 × 256 Lena, house, plane grayscale images are used as carrier images, and 64 × 64 binary images are used as watermark images.

Step ten: fig. 7 is a relation of watermark embedding strength and PSNR, from which it can be seen that the PSNR value decreases as the embedding strength α increases. PSNR is about 70 when α is 0.005, and is greater than 40 when α is 0.03.

Step eleven: and (5) robustness test analysis. The normalized correlation coefficient (NC) and the error bit rate (BER) of the extracted watermark and the original watermark are adopted

Wherein the content of the first and second substances,

for exclusive-or operation, W (i, j) is the original watermark image, W' (i, j) is the extracted watermark image, and m × n is the size of the image.

Step twelve: FIG. 11 shows the results of non-geometric attacks on three images, with mean 0, variance 0.01 and 0.03 Gaussian noise, salt and pepper noise, and multiplicative noise; low-pass filtering, wiener filtering, and the size of the template is 3 × 3 and 9 × 9; the JPEG compression factors are 10 and 50. The three carrier images reach NC of more than 0.95, the minimum is 0.9553 and the maximum is 1.0000 for different types of noise attacks. The effect of noise attack on Lena images with rich textures is good. For filtering attack, the NC values are all above 0.99, which shows that the algorithm can effectively resist the filtering attack. For JPEG compression, the lowest NC is still above 0.9913 at a compression factor of 20. The NSCT-DCT has good denoising performance and strong stability, and the error correction coding technology is added, so that the algorithm has strong robustness in resisting non-geometric attacks.

Step thirteen: fig. 12 shows the results of geometric attack experiments, which select to make clockwise rotation, shearing and translation attacks on three images. For the rotation attack, the NC values are all above 0.9, and the rotation attack can be effectively resisted. For shearing and translation attacks, under the condition of 1/4 shearing, NC is larger than 0.9, burst errors are prevented due to the addition of the SP two-dimensional interleaving algorithm, only a part of characteristics are affected, and therefore good robustness is achieved for the shearing attacks. Under the attack of the cut 1/2, the NC value drops to 0.65, and the extraction effect becomes poor because the image information is excessively lost. In the aspect of the translation attack, because the whole pixel value is moved, when the pixel value is only translated to the right 10 or the down 20, the NC is more than 0.92, and simultaneously, the pixel value is translated to the right down 30, and the NC is also about 0.84, the robustness to the translation attack is good.

Fourteen steps: fig. 13 is a table of performance of different rotation angle extraction correction and uncorrect, fig. 8 is a table of rotation attack and watermark extraction, and it can be seen from fig. 13 and 8 that the NC value of the extracted watermark information is significantly increased and the BER is significantly decreased after the update of Rodan. Due to the fact that 'black edges' are generated in the rotation attack, partial information of the image is lost, even if Radon correction is carried out, the effect after correction is obviously superior to the effect of extraction without correction. When the rotation angle is an integral multiple of 90 °, the image information is not lost, and the watermark information can be completely recovered by correction.

Step fifteen: fig. 9 shows the image after the combined attack and other attacks, and the performance of the image is tested by adopting the combined attack, the mosaic attack and the tampering attack. The attack parameters are as follows: (a) gaussian noise (mean 0, variance 0.03) + rotation attack 20 °, (b) salt and pepper noise (mean 0, variance 0.03) + shear attack (left top shear 1/4), (c) rotation attack 20 ° + translation attack (right shift 10, down shift 10), (d) shear (center shear 1/4) + JPEG compression (compression factor 50), (e) mosaic attack (4 × 4), (f) tamper attack (tamper size 64).

Sixthly, the steps are as follows: the extracted watermarks in fig. 10 correspond to the images in fig. 9, respectively. In fig. 8 the combined attack severely distorts the image quality, but the watermark extraction is clearer. The watermarks extracted by the 4 x 4 mosaic attack and the 64 x 64 tampering attack are clearly visible and have good effect. The combined attack can change the pixel value of the image and also change the position of the image, and the algorithm combines the double transform domain and the Radon correction, so the combined attack can be well resisted.

Seventeen steps: fig. 14 shows three watermark algorithm comparisons (BER). Selecting a Lena carrier image, and carrying out a comparison experiment on the algorithm with documents of 'Blind water marking scheme based on Schur decoding and non-subsampled contourlet transform' and 'a color image Blind watermarking algorithm based on DWT-SVD and Turbo code'. As can be seen from the document "DWT-SVD and Turbo code-based color image Blind watermarking algorithm", the document "Black watermark scheme based on Schur decoding and non-subsampled contourlet transform" is significantly inferior to the document "DWT-SVD and Turbo code-based color image Blind watermarking algorithm" and the algorithm of the present document in terms of noise immunity and geometric attack resistance. Compared with the color image Blind watermarking algorithm based on DWT-SVD and Turbo code in the literature, the BER of the algorithm is higher than that of the color image Blind watermarking algorithm based on DWT-SVD and Turbo code in the literature only under the scaling attack and Gaussian noise attack, but the difference is not large, and the performance of the algorithm is better than that of the literature 'Blind watermarking scheme based on Schur decoding and non-subsampled consistent watermark transform' under other attacks. In conclusion, the robustness of the algorithm is better than that of the documents 'Blind watermarking scheme based on Schur decoding and non-subsampled decoding transform' and 'color image Blind watermarking algorithm based on DWT-SVD and Turbo code'.

Claims (4)

1. A blind watermarking algorithm for Polar codes and an interleaving algorithm, wherein the blind watermarking algorithm comprises:

performing Logistic encryption on the watermark, encoding Polar codes, performing SP two-dimensional interleaving, and performing NSCT conversion on the carrier image;

watermark information is embedded according to the relation between the coefficient and the determinant, so that blind extraction of the watermark can be realized;

and when the watermark is extracted, carrying out geometric correction on the image by utilizing Radon transformation.

2. The blind watermarking algorithm of claim 1, wherein the blind extraction process of the watermark utilizes the performance advantage of Polar codes in image transmission, so that error bits can be effectively corrected when the watermark is extracted, and the blind watermarking algorithm has stronger robustness to shearing attack.

3. The blind watermarking algorithm according to claim 1, wherein the blind watermarking algorithm has good robustness against non-geometric attacks, geometric attacks and rotation attacks, and the maximum NC value can reach 0.9979 when the rotation attacks are carried out.

4. The blind watermarking algorithm according to claim 1, wherein the embedding rule is constructed by using the relation between the NSCT coefficient and the determinant, the watermark extraction process does not need the information of the original image, and the blind watermarking algorithm has good use value.

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