Blind Watermarking Method Based on Polar Codes and Interleaving Algorithm

Abstract

The present invention claims protection for a strong robust blind watermarking algorithm in the NSCT-DCT domain that combines Polar codes with the SP (Successive Packing) two-dimensional interleaving algorithm, belonging to the field of image processing. This algorithm successively performs Logistic encryption on the watermark, Polar code encoding, SP two-dimensional interleaving, performs NSCT transformation on the carrier image, and embeds the watermark information according to the relationship between its coefficients and determinants, enabling blind extraction of the watermark. When extracting the watermark, geometric correction of the image is performed using the Radon transform. The results show that this algorithm not only makes the image after embedding the watermark have good invisibility, but also can effectively resist attacks such as adding noise, filtering, JPEG compression, shearing, translation, rotation, mosaic, and tampering. The NC value is above 0.9, and it also has strong robustness against combined attacks, having good practical value.

Description

Technical Field

[0001] The present invention belongs to the field related to image processing, and specifically relates to a strong robust blind watermarking algorithm in the NSCT-DCT domain based on the combination of Polar codes and the SP (Successive Packing) two-dimensional interleaving algorithm. Background Art

[0002] Digital watermarking technology is one of the important means for current copyright protection and information hiding. Common watermarking algorithms can be divided into spatial domain algorithms and transform domain algorithms, non-blind extraction algorithms and blind extraction algorithms. Among them, blind watermarking algorithms are the focus and hotspots of research. However, most blind watermarking algorithms are not very robust, and the watermark information is extremely vulnerable to geometric attacks such as rotation and shearing.

[0003] Spatial domain algorithms refer to directly modifying the pixel values of the carrier image. The algorithm complexity is low, but its ability to resist attacks is weak. For example, in the literature "Guoyin Z, Liang K, Liguo Z, et al. A New Digital Watermarking Method for Data Integrity Protection in the Perception Layer of IoT". In the literature "Block Error Diffusion Halftone Watermarking Algorithm Based on Parity Check", the parity of the image pixel blocks is modified to achieve the purpose of embedding the watermark. This algorithm has a good extraction effect for watermarks with high robustness. However, if the QR code watermark information is too compact, the extraction effect is not good.

[0004] The transform domain algorithm replaces the coefficients in the transform domain, making the watermark information more evenly embedded in the spatial domain, with visual masking characteristics and strong robustness. The literature "Feature Analysis of Watermarked Color Images Based on the Transform Relationship of Non-empty Subspaces in Inner Product Space" embeds watermarks in the wavelet domain and uses the feature points generated in the middle frequency region of the natural logarithm amplitude-frequency domain to solve the sensitivity of large-capacity watermarks to geometric deformation. This algorithm can resist conventional attacks and enable blind extraction. The literature "Robust Image Watermarking Algorithm Combining Blob-Harris Feature Regions with CT-SVD" proposes a robust image watermarking algorithm that combines Blob-Harris feature regions with CT-SVD, which has strong robustness against most attacks but fails to achieve blind extraction of watermarks and has poor effects on rotation attacks. The literature "Optimized Features of SIFT Transform Function for Digital Image Watermarking using Hybrid Swarm Intelligence and Neural Network" divides the image into blocks, and in the sub-block DCT domain, it is divided into an adaptive embedding region and an authentication information extraction region. Both have poor effects on noise attacks and geometric attacks. The algorithm in the literature "Wavelet Transform Modulus Maxima based Robust Logo Watermarking" increases invisibility and robustness in the wavelet domain and solves the problem of low-capacity embedding, but only provides limited robustness. The literature "A Blind Watermarking Algorithm Based on Adaptive Quantization in Contourlet Domain" uses singular value decomposition in the Contourlet domain to achieve blind extraction of watermarks in an adaptive quantization manner, with good invisibility and robustness. Cunha A.L. and Zhou J proposed a non-subsampled contourlet transform (NSCT) domain image transformation method in 2006, such as in the literature "The Nonsubsampled Contourlet Transform: Theory, Design, and Application". The NSCT transform can effectively represent images with more direction information compared to the traditional contourlet transform. The literature "Blind watermarking scheme based on Schur decomposition and non-subsampled contourlet transform" embeds watermarks using Schur decomposition in the NSCT domain and designs a synchronization mechanism based on scale-invariant feature transform to resist geometric attacks.The literature "Robust Watermarking Algorithm in NSCT Domain Based on BSVD Decomposition and Radon Transform" embeds watermarks in the NSCT domain using BSVD decomposition and corrects the attacked image by combining with Radon transform. This algorithm can effectively resist rotation attacks, but it fails to achieve blind extraction. The literature "Application of BSP Two-dimensional Block Interleaving Algorithm Combined with RS Error Correction Code in Watermarking" combines RS error correction code and two-dimensional block interleaving algorithm to embed watermark information in the middle frequency part of the block DCT coefficients. This algorithm can only well resist shear attacks and burst errors, and has poor effects on other attacks. The literature "Blind Watermarking Algorithm for Color Images Based on DWT-SVD and Turbo Codes" embeds watermarks in the wavelet domain by combining Turbo error correction code and SVD decomposition, and has good robustness against common attacks. Subsequently, the literature "Digital Watermarking Technology Based on LDPC Code Decoding Algorithm" combines LDPC code decoding algorithm with digital watermarking technology, reducing the bit error rate of watermark extraction, but the carrier image information is still required in the extraction process. The Polar code based on the channel polarization theory proposed by Arikan in 2009, such as the literature "A Method for Constructing Capacity-achieving Codes for Symmetric Binary-input Memoryless Channels", proves that the Polar code can theoretically reach the Shannon limit, making the Polar code a research hotspot. The literature "" verifies that the bit error rate of the Polar code is significantly reduced compared with the LDPC code in image transmission.

[0005] To solve the problem of weak robustness of the blind extraction algorithm, this patent is based on the SP two-dimensional interleaving algorithm. First, the watermark information is encrypted by Logistics mapping, then the encrypted information after Polar code encoding is interleaved, the carrier image is NSCT-transformed, and the watermark is embedded using the relationship between the DCT coefficients of the low-pass sub-band and the coefficients and determinants of the band-pass sub-band. Before extraction, the image is first subjected to Radon geometric correction. Summary of the Invention

[0006] The technical problem to be solved by the present invention is that the image after embedding the watermark has good invisibility, as well as the robustness problem under image attack modes such as adding noise, JPEG compression, filtering, rotation, translation, shear, tampering, mosaic attack, and combined attack.

[0007] The technical solution of the present invention to solve the above technical problems is: based on the SP two-dimensional interleaving algorithm, first encrypt the watermark information by Logistics mapping, then interleave the encrypted information after Polar code encoding, NSCT-transform the carrier image, and embed the watermark using the relationship between the DCT coefficients of the low-pass sub-band and the coefficients and determinants of the band-pass sub-band. Before extraction, the image is first subjected to Radon geometric correction. Description of the Drawings

[0008] Figure 1 Three - level NSCT transformation and non - subsampled pyramid filter bank

[0009] Figure 2 Flow chart of watermark embedding

[0010] Figure 3 Flow chart of watermark extraction

[0011] Figure 4 Carrier image

[0012] Figure 5 Watermark - embedded image

[0013] Figure 6 Watermark image extracted without attack

[0014] Figure 7 Relationship between watermark embedding strength and PSNR

[0015] Figure 8 Original image, image after rotation attack, image after Rodan correction, and watermarks before and after correction

[0016] Figure 9 Images after combined attack and other attacks

[0017] Figure 10 Extracted watermark

[0018] Figure 11 Non - geometric attack experiment (NC)

[0019] Figure 12 Geometric attack result (NC)

[0020] Figure 13 Performance table of extraction correction and uncorrected at different rotation angles

[0021] Figure 14 Comparison of three watermark algorithms (BER) Detailed implementation manners

[0022] The following further describes the implementation of the present invention in combination with the drawings and specific examples.

[0023] Step 1: Logistics mapping analysis. The Logistics mapping is a widely used chaotic dynamical system, which is described in detail in the literature "Multi-dimensional Particle Swarm Optimization for Robust Blind Image Watermarking Using Intertwining Logistic Map and Hybrid Domain". The definition formula is as follows:

[0024] x n+1 = μx n (1 - x n ) (1)

[0025] where x n ∈(0,1). When μ ∈ [3.57, 4], the sequence is in a chaotic working state. This patent uses the Logistics mapping to generate a sequence for XOR encryption.

[0026] Step 2: Figure 1 is a three-level NSCT transform and a nonsubsampled pyramid filter bank. The NSCT transform is a super wavelet transform, such as the literature "The Nonsubsampled Contourlet Transform: Theory, Design, and Applications". It is a redundant transform with translational invariance. It obtains singularity information through nonsubsampled pyramid decomposition and provides the multiscale characteristics of NSCT; it uses a nonsubsampled directional filter to connect discontinuous points to approximate the original image and provides directionality.

[0027] Step 3: Polar code analysis. In a binary-input discrete memoryless channel (B-DMC), a B-DMC channel model can be expressed as W: X → Y, where X and Y represent the input and output symbols respectively. The transition probability is W(y|x), x ∈ X, y ∈ Y. For the row vector (y 1 , …, y N ), it is briefly denoted as W N represents that the channel W is used N times. Then the transition probability of the channel W N is expressed as:

[0028]

[0029] The Polar code encoding is determined by the information bits and the generating matrix. The encoding process is as follows:

[0030]

[0031] where, is a set of input variables, G N is the generator matrix, B N is an N×N bit transposition matrix. For any subset The above can be expressed as:

[0032]

[0033] where G N (A) is the generator matrix composed of the rows corresponding to set A in G N and A c is the complement of A. The encoding of the polar code can be determined by the following parameters: code length N, information bits A, the number of information bits K, K / N is the code rate, and the frozen bit u A , which is usually set to the "0" symbol, so it is expressed as

[0034] This patent adopts the SC decoding algorithm. The SC algorithm calculates the estimated value c and based on A, A Since the frozen position is the "0" symbol, the decoding is to generate the estimated value The SC decoding estimation method is:

[0035]

[0036] where h i is defined as:

[0037]

[0038] where respectively represent the probabilities of input 0 and 1 output under the condition that is known.

[0039] Theoretically, it can be obtained that in a binary-input discrete memoryless channel, the bit error rate of Polar is:

[0040]

[0041] where is 's Bhattacharyya parameter, and P e is the bit error rate.

[0042] Step 4: Analysis of the SP interleaving technique. Take a 2 n ×2 n matrix as the interleaving unit, and then divide this unit into four quadrants equally. Each quadrant is further divided into four quadrants, and so on until it is divided into the smallest 2×2 unit. The specific construction steps are as follows:

[0043] First, arrange the 4 elements in the 2×2 minimum unit into an interleaved square matrix, and then perform dimension elevation according to the algorithm to obtain a higher-order interleaved square matrix.

[0044]

[0045] Among them, 0, 1, 2, and 3 are all 2×2 matrices.

[0046] Step Five: Radon transform analysis. First, perform correction processing on the geometrically attacked image. Performing a Radon transform on the image f(x, y) is to calculate the projection of the image along a given angle, and the obtained projection is the sum of the pixel intensities in each direction, that is, a line integral. The definition of the Radon transform of the pixel matrix f(x, y) is:

[0047] P(γ,θ)=R(γ,θ)∫∫f(x,y)δ(γ - xcosθ - ysinθ)dxdy (10)

[0048] Among them, γ is the distance from the origin to the straight line, θ is the angle between the straight line and the coordinate axis, and δ is the line integral of f(x, y) with respect to γ - xcosθ - ysinθ. From this, the projection of f(x, y) along this straight line at (γ,θ) can be obtained.

[0049] The correction steps are as follows:

[0050] (1) Calculate the reference vector R(0): Perform a Radon transform on the original image to calculate the reference vector R(0).

[0051] (2) Obtain the detection vector R(θ), θ∈[1°, 2°, …, 180°]: Perform Radon transforms on the carrier image from 1 to 180°, obtain 180 detection vectors, and form "angle-detection vector pairs".

[0052] (3) Calculate the rotation angle: Compare the correlation coefficients of R(0) and R(θ), and the one with the largest correlation coefficient is the corresponding angle.

[0053] (4) Image correction. Perform inverse rotation on the obtained angle to obtain the corrected image.

[0054] Step Six: Figure 2 This is the watermark embedding process. Select a 256×256 carrier image, and the watermark is a 64×64 binary image w. First, perform watermark preprocessing. Select the initial values x(0) = 0.3 and μ = 4, and iterate 500 times to make the sequence fully reach the chaotic state. Then generate a Logistics sequence with the same length as the watermark, and binarize it. The obtained sequence is reshaped into a 64×64 binary image B. Perform exclusive OR encryption on the watermark w to obtain the encrypted watermark w'.

[0055]

[0056] Perform a 4×1 block on w', and encode each block with N = 64, K = 4, and code rate r = 1 / 16. Select Relatively small K = r×N = 4, and all i form set A. Matrix G 64 Generate matrix G 64 (A) from the rows corresponding to set A in it, and a polar code with a code length of 64 can be obtained from (2). After completing the block encoding, matrix w b . For w b Reduce the dimension to a one-dimensional sequence, perform SP two-dimensional interleaving to form an interleaved square matrix S, and perform secondary encryption on the watermark. S is the interleaved square matrix with watermark information to be embedded in the carrier image.

[0057] Before watermark embedding and image restoration, perform a Radon transform on the host image to obtain a reference vector R(0) for detecting and correcting rotation attacks. Perform a J-level (J = 3 in this patent) NSCT transform on the host image I to obtain the low-pass subband L J and each directional subband where j represents the j-th level of non-subsampled pyramid decomposition, and k represents the k-th directional subband of the l j -th level of non-subsampled directional filter bank decomposition. The main energy of the image is concentrated in the low-pass subband L J Perform a DCT transform on it to obtain the coefficient L D , embed the watermark in it, and the image has a better visual effect. Establish the relationship between the NSCT coefficients and the determinant, and embed the interleaved square matrix S with watermark information in it. Calculate the value of its determinant according to Equation (12).

[0058]

[0059] where, A 1 = d J,0 , A 2 = d J,1 , A 3 = d J,2 , A 4 = d J,3 . d J,0 , d J,1 , d J,2 , d J,3 are the J-level directional subbands. From the relationship between A 1 (i,j) and det(i,j), embed the watermark in the following way according to Equation (13):

[0060]

[0061] Among them, L w is the modified coefficient L D , Lg is the logo matrix after embedding the watermark, and α is the embedding strength. w By performing inverse DCT transform, the restored NSCT low-frequency subband coefficients can be obtained, and then NSCT reconstruction with the directional subband can be performed to obtain the image embedded with the watermark.

[0062] Step 7: Figure 3 The watermark extraction process is shown in Figure 2. Before watermark extraction, the rotation angle of the carrier image is detected. The vector to be tested is calculated and compared with the reference vector R(0). The detected angle is the angle of rotation attack, and the image is corrected. The image embedded with the watermark is transformed by J-level NSCT. According to the DCT coefficient L of the J-level low-frequency subband, the image is corrected. D '(i,j) and directional subband coefficient A 2 '(i,j),A 3 '(i,j),A 4 '(i,j) calculate det'(i,j):

[0063]

[0064] By det'(i,j), A 1 '(i,j), Lg(i,j) is used to extract the watermark information S'(i,j).

[0065]

[0066] Perform SP two-dimensional deinterleaving on s′, upgrade the dimension, and decode the block polar code to obtain w". Finally, perform Logistics decryption on w" according to (16) to obtain the original watermark information wa.

[0067]

[0068] Step 8: Figure 4 , Figure 5 They are the carrier image and the image after embedding the watermark, and the peak signal-to-noise ratio (PSNR) is used to evaluate the invisibility of the image after embedding the watermark. The definition of PSNR is as follows:

[0069]

[0070] Among them, m×n is the size of the image, I w (i,j) and I(i,j) are the pixel values ​​of the (i,j)th point in the watermarked image and the original image. When the embedding strength α=0.03, PSNR=42.2414.

[0071] Step 9: Figure 6For the watermark image extracted without attack, the watermark information can be completely extracted by this algorithm, and it has good invisibility. This patent conducts simulation experiments in Matlab2017a. The 256×256 Lena, house, and plane grayscale images are used as carrier images, and the 64×64 binary image is used as the watermark image.

[0072] Step ten: Figure 7 is the relationship between the watermark embedding strength and PSNR. It can be seen from it that as the embedding strength α increases, the PSNR value decreases. When α = 0.005, the PSNR reaches about 70, and when α = 0.03, the PSNR is greater than 40.

[0073] Step eleven: Robustness test and analysis. The normalized correlation coefficient (NC) and bit error rate (BER) between the extracted watermark and the original watermark are used

[0074]

[0075] Among them, is the 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.

[0076] Step twelve: Figure 11 is the experimental result of non-geometric attacks. Gaussian noise with a mean of 0 and variances of 0.01 and 0.03, salt and pepper noise, and multiplicative noise are respectively applied to the three images; low-pass filtering, Wiener filtering, with template sizes of 3*3 and 9*9; JPEG compression factors of 10 and 50. For different types of noise attacks on the three carrier images, the NC all reaches above 0.95, the lowest is 0.9553, and the highest reaches 1.0000. For the Lena image with relatively rich texture, the effect of noise attack is also good. For filtering attacks, the NC values are all above 0.99, indicating that the algorithm of this patent can effectively resist filtering attacks. For JPEG compression, when the compression factor is 20, the lowest NC is still above 0.9913. Due to the good denoising performance and strong stability of the NSCT-DCT transform, combined with the error correction coding technology, the algorithm in this paper has strong robustness in resisting non-geometric attacks.

[0077] Step thirteen: Figure 12For the geometric attack experiment results, three images were respectively subjected to clockwise rotation, shearing, and translation attacks. For the rotation attack, the NC values are all above 0.9, which can effectively resist the rotation attack. For the shearing and translation attacks, in the case of 1 / 4 shearing, the NC is also greater than 0.9. Due to the addition of the SP two-dimensional interleaving algorithm to prevent burst errors, only a part of the features are affected, so it has good robustness against the shearing attack. Under the 1 / 2 shearing attack, the NC value drops to 0.65 and the extraction effect deteriorates because too much image information is lost. In terms of the translation attack, since the overall pixel values move, when translating only 10 to the right or 20 downwards, the NC values are all above 0.92. When translating 30 to the right and 20 downwards at the same time, the NC is also around 0.84. Therefore, it also has good robustness against the translation attack.

[0078] Step Fourteen: Figure 13 Table of extraction correction and uncorrected performance for different rotation angles Figure 8 For rotation attack and watermark extraction, from Figure 13 and Figure 8 It can be seen that for the watermark information extracted after Rodan correction, its NC value increases significantly and the BER decreases significantly. Due to the generation of "black edges" during the rotation attack, some image information will be lost, and this still exists even after Radon correction. However, the corrected effect is significantly better than the uncorrected extraction effect. When the rotation angle is an integer multiple of 90°, no image information is lost, and the watermark information can be completely restored after correction.

[0079] Step Fifteen: Figure 9 Images after combined attacks and other attacks are shown. The combined attack, mosaic attack, and tampering attack are used to test their performance. 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) + shearing attack (upper-left shearing 1 / 4), (c) rotation attack 20° + translation attack (shift 10 to the right, shift 10 downwards), (d) shearing (center shearing 1 / 4) + JPEG compression (compression factor 50), (e) mosaic attack (4*4), (f) tampering attack (tampering size 64*64).

[0080] Step Sixteen: Figure 10 respectively correspond to the Figure 9 watermarks extracted from the images in. In Figure 8 the combined attack severely distorts the image quality, but the watermark extraction is relatively clear. For the 4*4 mosaic attack and the 64*64 tampering attack, the extracted watermarks are clearly visible and the effect is good. The combined attack can not only change the pixel values of the image but also change their positions. This algorithm combines the double transform domain and Radon correction, so it can well resist the combined attack.

[0081] Step 17: Figure 14 For the comparison of three watermarking algorithms (BER). The Lena carrier image is selected, and the algorithm in this paper is compared with the literature "Blind watermarking scheme based on Schur decomposition and non-subsampled contourlet transform" and "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes". It can be seen from the literature "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes" that the anti-noise performance and anti-geometric attack ability of the literature "Blind watermarking scheme based on Schur decomposition and non-subsampled contourlet transform" are significantly inferior to those of the literature "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes" and the algorithm in this paper. Compared with the literature "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes", the BER of the algorithm in this paper is higher than that of the literature "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes" only under scaling attack and Gaussian noise attack, but the difference is not significant. Under other attacks, the performance is better than that of the literature "Blind watermarking scheme based on Schur decomposition and non-subsampled contourlet transform". In summary, the robustness of the algorithm in this paper is overall better than that of the literature "Blind watermarking scheme based on Schur decomposition and non-subsampled contourlet transform" and "Blind color image watermarking algorithm based on DWT-SVD and Turbo codes".

Claims

1. A blind watermarking method for Polar codes and interleaving algorithms, characterized in that, the blind watermarking method includes: performing Logistic encryption on the watermark, Polar code encoding, and SP two-dimensional interleaving to obtain an interleaved square matrix S with watermark information; Perform geometric correction on the carrier image using the Radon transform, and perform J-level NSCT transform on the corrected carrier image to obtain the low-pass subband coefficients L J and the subband coefficients in each direction; For the low-pass subband coefficients L J perform a DCT transformation to obtain the coefficients L D ; establishing the relationship between NSCT coefficients and determinants, and embedding the interleaved square matrix S with watermark information therein; calculating the value of the determinant according to the following formula: Among them, A 1 = d J,0 , A 2 = d J,1 , A 3 = d J,2 , A 4 = d J,3 ; d J,0 , d J,1 , d J,2 , d J,3 are subband coefficients in the J-level direction; From A 1 (i,j) and the relationship of det(i,j), the watermark is embedded as follows: if S(i,j) = 1 and A 1 (i,j) ≥ det(i,j) then L w (i,j) = L D (i,j) × (1 - α), Lg(i,j) = 0; if S(i,j) = 1 and A 1 (i,j) < det(i,j) then L w (i, j) = L D (i, j) × (1 + α), Lg(i, j) = 1; if S(i,j) = 0 and A 1 (i,j) ≥ det(i,j) then L w (i, j) = L D (i, j) × (1 - α), Lg(i, j) = 1; if S(i,j) = 0 and A 1 (i,j) < det(i,j) then L w (i,j) = L D (i,j) × (1 + α), Lg(i,j) = 0; Among them, L w is L after the modification coefficient D , L g is the logo matrix after watermark embedding, and α is the embedding strength; perform the inverse DCT on L w to obtain the restored NSCT low-pass subband coefficients, and then perform NSCT reconstruction with the directional subband coefficients to obtain the image with the embedded watermark.

Images