Statistical image watermarking method based on non-Gaussian mixture HMT (Hidden Markov Transform)

Abstract

The invention discloses a statistical image digital watermarking method based on a non-Gaussian mixture HMT (Hidden Markov Transform), which comprises the following steps of: firstly, implementing secondary non-subsampled shearlet transform (NSST) decomposition on a host image to obtain high-frequency sub-bands of two scales in multiple directions, selecting the high-frequency sub-band with the highest energy on the second scale as a target sub-band of an experiment, and partitioning the target sub-band; secondly, selecting a high-entropy block, calculating by utilizing fast polar coordinate linear regular transformation (FPLCT) to obtain an amplitude matrix, embedding watermark information by utilizing a multiplicative method, and obtaining a watermark-containing image which is as large as the original image through inverse transformation of the FPLCT and NSST; then, obtaining a BSM-HMT mixed probability density function according to BSM mixed distribution and HMT, performing statistical modeling based on the BSM-HMT mixed probability density function, and inputting the organized training samples into an Aitken-ECM algorithm for parameter estimation; and finally, according to a maximum likelihood criterion, an ML decoder with a good effect is constructed and is used for extracting watermark information.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital image watermarking, and relates to a method for embedding and extracting digital watermark information in an image, and in particular to a statistical image watermarking method based on a non-Gaussian mixture HMT. Background Art

[0002] As life becomes more and more digital and digital resources develop rapidly, it is very convenient for people to obtain information such as images, audio and video. At the same time, many unavoidable problems are hidden, one of which is the copyright protection of image information. Many digital images can be easily obtained, which leads to problems such as unauthorized tampering of information and blurred copyright. In order to ensure that multimedia signals, especially digital image signals, are not tampered with privately or copied or disseminated without permission, digital image watermarking technology that can effectively protect copyright is considered to be a very effective solution with powerful functional support.

[0003] Digital watermarking technology includes an effective method, that is, adding specified digital information, that is, watermark, to the host image to hide it in the image, and then confirming whether the image is safe by detecting or extracting the watermark information. There are three important indicators for judging the feasibility of digital image watermarking methods: robustness, imperceptibility, and watermark capacity. Robustness means that the ability to extract the watermark is not affected after the image watermark is subjected to conventional attacks or geometric attacks; imperceptibility means that there is no visible difference between the original image and the image after adding the watermark; watermark capacity represents the length of the watermark sequence allowed to be added to the host image. Although these three standards are all very important, there is a restrictive relationship between them. Therefore, the most urgent goal in the field of digital image watermarking is to achieve a balance between the above three attributes.

[0004] The digital image watermarking algorithm based on statistical modeling can be divided into three parts: watermark embedding, watermark detection and watermark extraction. Whether the watermark information can be accurately extracted has become the focus of research, and the construction method of the decoder is also constantly updated. However, so far, the decoder construction proposed by most researchers still has some shortcomings, such as not taking into account the strong correlation between coefficients and the low accuracy of parameter estimation. Summary of the invention

[0005] In view of the existing problems in the field of digital watermarking technology, the present invention proposes a statistical image watermarking method based on non-Gaussian mixture HMT.

[0006] The technical solution of the present invention is: a statistical image watermarking method based on non-Gaussian mixture HMT, which is carried out according to the following steps:

[0007] A statistical image watermarking method based on non-Gaussian mixture HMT is characterized by following the following steps:

[0008] Convention: P represents the host image; P' represents the watermarked image; D represents the low-frequency subband obtained after the host image is decomposed; H1 and H2 represent the high-frequency subbands of the first and second scales obtained after the host image is decomposed; H'1 and H'2 represent the high-frequency subbands of the first and second scales obtained after the watermarked image is decomposed; L is the length of the watermark information; x i represents the original NSST-FPLCT amplitude coefficient; y i Represents the amplitude coefficient of NSST-FPLCT containing watermark; ω l is the watermark information to be embedded, λ is the watermark embedding strength; ij It refers to the amplitude without watermark information at the i-th position of the j-th scale; y ij It refers to the amplitude of the watermark information at the i-th position at the j-th scale; Indicates the amplitude x ij The probability when the state is m and satisfies represents the state transition probability from the parent scale ρ(j) to the child scale j in the i-th tree, where the hidden state is transferred from ρ(m) to m; represents the shape parameter in the m state; Indicates that when x ij The scale parameter when the hidden state is m; H0 represents the assumption when the watermark information -1 is embedded in the subband; H1 represents the assumption when the watermark information +1 is embedded in the subband;

[0009] a. Initial Setup

[0010] Get the host image P of size M×N and initialize the variables;

[0011] b. Watermark Embedding

[0012] b.1 A two-level NSST (non-subsampled shearlet transform) operation is performed on a host image P of size M×N. Specifically, the image is first decomposed into multiple scales according to NSLP (non-subsampled pyramid filter bank). While ensuring translation invariance, a low-frequency subband D and high-frequency subbands H1 and H2 of the first and second scales are generated. Then, SF (shearing filter) is used to realize the multi-directionality of subband decomposition. Then, the high-frequency subbands of each scale are decomposed in terms of direction. Each image will obtain eight directions of the first scale and four directions of the second scale, for a total of 12 high-frequency components of the same size of M×N.

[0013] b.2 In the high-frequency sub-band obtained by decomposition, select the sub-band image with the maximum energy on the second scale as the carrier image for embedding the watermark, divide the sub-band image into blocks of K×K size, ensure that the blocks do not overlap, and calculate the entropy value of each block respectively. Based on the length L of the watermark to be embedded, select the first L target blocks with higher entropy values, and record the position of each block;

[0014] b.3 Perform 3rd-order FPLCT (Fast Polar Coordinate Linear Canonical Transform) decomposition on the selected L target blocks respectively to obtain the NSST-FPLCT amplitude domain. For each block, after 3rd-order FPLCT calculation, the dimension of the block becomes 7×7;

[0015] b.4 Embed a one-bit watermark of 1 or -1 into each block accordingly, and perform the watermark information embedding operation according to the multiplicative embedding rule of the watermark:

[0016] y i =(1+λω l )x i ;

[0017] b.5 Perform 3rd-order FPLCT reconstruction on the L target blocks containing watermark information, and the dimension of the target block changes from 7×7 to K×K, and then puts it back to its original position in the target subband;

[0018] b.6 Apply NSST inverse transform to all coefficients in the target subband, and finally obtain the image P' with hidden watermark information;

[0019] c.BSM (Birnbaum-Saunders Mixture)-HMT (Hidden Markov Tree) Statistical Modeling

[0020] c.1 Perform [2,3] NSST decomposition on the obtained watermarked image P'. Specifically, the image is first decomposed into multiple scales according to NSLP to obtain a low frequency D and high frequencies H'1 and H'2 at two scales. Then, H'1 and H'2 are decomposed into multiple directions using SF to obtain high frequency sub-bands in eight directions at one scale and four directions at two scales.

[0021] c.2 Select the high-frequency sub-bands with the largest variance of the second scale and the first scale respectively, implement the block operation according to the strategy of "same size and non-overlapping", sort the obtained entropy values ​​of each block in descending order, and select the first L high entropy blocks for watermark information extraction;

[0022] c.3 Perform 3rd-order FPLCT calculation on the selected L high entropy blocks, and obtain a 7×7 NSST-FPLCT amplitude coefficient matrix for each block;

[0023] c.4 According to the target position definition, select from the amplitude domain at each scale NSST-FPLCT amplitude coefficients are selected, and a BSM-HMT hybrid model is constructed for statistical modeling, where BSM is used to capture the non-Gaussian distribution characteristics of the amplitude and HMT is used to capture the scale correlation of the amplitude. The probability density function of the BSM-HMT is defined as:

[0024]

[0025] d. Aitken-ECM parameter estimation

[0026] The training samples of the same position block in the same scale and different direction subbands are bound to form a group of training samples. Using the inter-tree binding idea, the training samples of two scales are considered and organized into a training sample set and sent to the Aitken-ECM parameter estimation algorithm to calculate the parameter set of the BSM-HMT model for use by the decoder.

[0027] e. Construct ML decoder to extract watermark

[0028] e.1 adopts the blind watermark extraction method and regards the watermark extraction problem as a binary hypothesis testing problem, which has:

[0029]

[0030] e.2 According to the maximum likelihood criterion and calculating the log-likelihood ratio, the decoder is constructed as:

[0031]

[0032] in:

[0033] And f Y (y i |H0)=f X (y i ), f X (x) represents the probability density function of the model used;

[0034] The e.3 decoder adopts a blind watermark extraction method. The watermarked image maintains the same statistical distribution characteristics as the original image. The BSM-HMT model is used to represent the amplitude distribution characteristics of the watermarked image. The ML detector based on BSM-HMT is constructed as follows:

[0035]

[0036] e.4 Define the watermark position discriminant, that is, the lth watermark position in the image is extracted according to the following decision expression:

[0037]

[0038] The present invention firstly performs a two-level non-subsampled shearlet transform (NSST) on the host image to obtain high-frequency subbands in two scales and multiple directions, selects the high-frequency subband with the highest energy on the second scale as the target subband and divides it into blocks; secondly, selects a high entropy block and then uses the fast polar coordinate linear canonical transform (FPLCT) to calculate to obtain an amplitude matrix, embeds the watermark information using the multiplicative method, and obtains a watermarked image of the same size as the original image through the inverse transform of FPLCT and NSST; then, according to the BSM mixed distribution and HMT, the probability density function of the BSM-HMT mixture is obtained, and statistical modeling is performed based on this, and the organized training samples are input into the Aitken-ECM algorithm for parameter estimation; finally, according to the maximum likelihood criterion, a good ML decoder is constructed for extracting watermark information. The experimental results show that the present invention fully considers the non-Gaussian distribution characteristics of the amplitude coefficient and the correlation between scales, uses the non-Gaussian mixed HMT for statistical modeling, and has made great progress in the accuracy of watermark extraction by the decoder.

[0039] Compared with the existing technology, the solution of the present invention has the following improved characteristics:

[0040] Firstly, a method of organically combining non-subsampled shearlet transform (NSST) and fast polar coordinate linear canonical transform (FPLCT) is proposed to construct a new robust research object, namely, NSST-FPLCT coefficient amplitude.

[0041] Second, a statistical model based on BSM-HMT is constructed to describe the marginal distribution characteristics of the amplitude coefficient while fully considering the non-Gaussian distribution characteristics and the strong correlation between scales;

[0042] Thirdly, the Aitken-ECM with superior performance is introduced, and the Aitken-ECM and Baum-Welch algorithms are combined to achieve effective estimation of the parameters of the model of the present invention, while achieving a lower time complexity characteristic. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a histogram of the non-Gaussian characteristic results of the amplitude coefficient according to an embodiment of the present invention.

[0044] Figure 2 This is a BSM-HMT fitting result diagram of an embodiment of the present invention.

[0045] Figure 3 This is a watermarked image result image after a 512-bit watermark is embedded in a grayscale image according to an embodiment of the present invention.

[0046] Figure 4 This is a result diagram showing a 20-fold difference between a 512-bit watermarked image and the original grayscale image according to an embodiment of the present invention.

[0047] Figure 5 This is a graph showing the results of extracting a 2048-bit watermark under multiple single attacks according to an embodiment of the present invention.

[0048] Figure 6 This is a flow chart of watermark embedding according to an embodiment of the present invention.

[0049] Figure 7 This is a flow chart of watermark extraction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The method of the present invention includes four stages: multiplicative embedding of watermark information, BSM-HMT hybrid statistical modeling, Aitken-ECM parameter estimation, and construction of an ML decoder for extracting watermarks. The specific operation process is as follows Figure 6 , 7 As shown, follow the steps below:

[0051] Convention: P represents the host image; P' represents the watermarked image; D represents the low-frequency subband obtained after the host image is decomposed; H1 and H2 represent the high-frequency subbands of the first and second scales obtained after the host image is decomposed; H'1 and H'2 represent the high-frequency subbands of the first and second scales obtained after the watermarked image is decomposed; L is the length of the watermark information; x i represents the original NSST-FPLCT amplitude coefficient; y i Represents the amplitude coefficient of NSST-FPLCT containing watermark; ω l is the watermark information to be embedded, λ is the watermark embedding strength; ij It refers to the amplitude without watermark information at the i-th position of the j-th scale; y ij It refers to the amplitude of the watermark information at the i-th position at the j-th scale; Indicates the amplitude x ij The probability when the state is m and satisfies represents the state transition probability from the parent scale ρ(j) to the child scale j in the i-th tree, where the hidden state is transferred from ρ(m) to m; represents the shape parameter in the m state; Indicates that when x ij The scale parameter when the hidden state is m; H0 represents the assumption when the watermark information -1 is embedded in the subband; H1 represents the assumption when the watermark information +1 is embedded in the subband;

[0052] a. Initial Setup

[0053] Get the host image P of size M×N and initialize the variables;

[0054] b. Watermark Embedding

[0055] b.1 A two-level NSST (non-subsampled shearlet transform) operation is performed on a host image P of size M×N. Specifically, the image is first decomposed into multiple scales according to NSLP (non-subsampled pyramid filter bank). While ensuring translation invariance, a low-frequency subband D and high-frequency subbands H1 and H2 of the first and second scales are generated. Then, SF (shearing filter) is used to realize the multi-directionality of subband decomposition. Then, the high-frequency subbands of each scale are decomposed in terms of direction. Each image will obtain eight directions of the first scale and four directions of the second scale, for a total of 12 high-frequency components of the same size of M×N.

[0056] b.2 In the high-frequency sub-band obtained by decomposition, select the sub-band image with the maximum energy on the second scale as the carrier image for embedding the watermark, divide the sub-band image into blocks of K×K size, ensure that the blocks do not overlap, and calculate the entropy value of each block respectively. Based on the length L of the watermark to be embedded, select the first L target blocks with higher entropy values, and record the position of each block;

[0057] b.3 Perform 3rd-order FPLCT (Fast Polar Coordinate Linear Canonical Transform) decomposition on the selected L target blocks respectively to obtain the NSST-FPLCT amplitude domain. For each block, after 3rd-order FPLCT calculation, the dimension of the block becomes 7×7;

[0058] b.4 Embed a one-bit watermark of 1 or -1 into each block accordingly, and perform the watermark information embedding operation according to the multiplicative embedding rule of the watermark:

[0059] y i =(1+λω l )x i ;

[0060] b.5 Perform 3rd-order FPLCT reconstruction on the L target blocks containing watermark information, and the dimension of the target block changes from 7×7 to K×K, and then puts it back to its original position in the target subband;

[0061] b.6 Apply NSST inverse transform to all coefficients in the target subband, and finally obtain the image P' with hidden watermark information;

[0062] c. BSM (Birnbaum-Saunders Mixture)-HMT (Hidden Markov Tree) Statistical Modeling

[0063] c.1 Perform [2,3] NSST decomposition on the obtained watermarked image P'. Specifically, the image is first decomposed into multiple scales according to NSLP to obtain a low frequency D and high frequencies H'1 and H'2 at two scales. Then, H'1 and H'2 are decomposed into multiple directions using SF to obtain high frequency sub-bands in eight directions at one scale and four directions at two scales.

[0064] c.2 Select the high-frequency sub-bands with the largest variance of the second scale and the first scale respectively, implement the block operation according to the strategy of "same size and non-overlapping", sort the obtained entropy values ​​of each block in descending order, and select the first L high entropy blocks for watermark information extraction;

[0065] c.3 Perform 3rd-order FPLCT calculation on the selected L high entropy blocks, and obtain a 7×7 NSST-FPLCT amplitude coefficient matrix for each block;

[0066] c.4 According to the target position definition, select from the amplitude domain at each scale NSST-FPLCT amplitude coefficients are selected, and a BSM-HMT hybrid model is constructed for statistical modeling, where BSM is used to capture the non-Gaussian distribution characteristics of the amplitude and HMT is used to capture the scale correlation of the amplitude. The probability density function of the BSM-HMT is defined as:

[0067]

[0068] d. Aitken-ECM parameter estimation

[0069] The training samples of the same position block in the same scale and different direction subbands are bound to form a group of training samples. Using the inter-tree binding idea, the training samples of two scales are considered and organized into a training sample set and sent to the Aitken-ECM parameter estimation algorithm to calculate the parameter set of the BSM-HMT model for use by the decoder.

[0070] e. Construct ML decoder to extract watermark

[0071] e.1 adopts the blind watermark extraction method and regards the watermark extraction problem as a binary hypothesis testing problem, which has:

[0072]

[0073] e.2 According to the maximum likelihood criterion and calculating the log-likelihood ratio, the decoder is constructed as:

[0074]

[0075] in:

[0076] And f Y (y i |H0)=f X (y i ), f X (x) represents the probability density function of the model used;

[0077] The e.3 decoder adopts a blind watermark extraction method. The watermarked image maintains the same statistical distribution characteristics as the original image. The BSM-HMT model is used to represent the amplitude distribution characteristics of the watermarked image. The ML detector based on BSM-HMT is constructed as follows:

[0078]

[0079] e.4 Define the watermark position discriminant, that is, the lth watermark position in the image is extracted according to the following decision expression:

[0080]

[0081] Experimental test and parameter setting:

[0082] The implementation environment of this experiment is Matlab R2016a. All the test images used in the experiment are grayscale images with a size of 512×512, and they are all public images that can be searched and downloaded through the Internet.

[0083] The histogram of the non-Gaussian characteristic result of the amplitude coefficient of the embodiment of the present invention is as follows: Figure 1 shown.

[0084] The BSM-HMT fitting results of the embodiment of the present invention are shown in FIG. Figure 2 shown.

[0085] The watermarked image result after the grayscale image of the embodiment of the present invention is embedded with a 512-bit watermark is shown in the figure below: Figure 3 shown.

[0086] Figure 3 (a) Mandrill original image; (b) Peppers original image; (c) Lena original image; (d) Mandrill with 512 bits watermark; (e) Peppers with 512 bits watermark; (f) Lena with 512 bits watermark.

[0087] The result of the 512-bit watermark image and the original grayscale image with a difference of 20 times is shown in the figure below. Figure 4 shown.

[0088] Figure 4 (a) Mandrill - 20 times difference; (b) Peppers - 20 times difference; (c) Lena - 20 times difference.

[0089] The effect diagram of extracting 2048 bits watermark under several common attacks in the embodiment of the present invention is as follows: Figure 5 shown.

[0090] Figure 5(a) JPEG compression; (b) rotation; (c) salt and pepper noise; (d) shearing.

[0091] Figure 5 The following are the prior art references:

[0092] Comparative Literature:

[0093] coefficients and bounded generalized Gaussian mixtures-based HMT.SignalProcessing, 2022,192:108371.

Claims

1. A statistical image watermarking method based on non-Gaussian mixture HMT, which is characterized by following the following steps: Convention: P represents the host image; P' represents the watermarked image; D represents the low-frequency subband obtained after the host image is decomposed; H1 and H2 represent the high-frequency subbands of the first and second scales obtained after the host image is decomposed; H'1 and H'2 represent the high-frequency subbands of the first and second scales obtained after the watermarked image is decomposed; L is the length of the watermark information; x i represents the original NSST-FPLCT amplitude coefficient; y i Represents the amplitude coefficient of NSST-FPLCT containing watermark; is the watermark information to be embedded, λ is the watermark embedding strength; ij It refers to the amplitude without watermark information at the i-th position of the j-th scale; y ij It refers to the amplitude of the watermark information at the i-th position at the j-th scale; Indicates the amplitude x ij The probability when the state is m and satisfies represents the state transition probability from the parent scale ρ(j) to the child scale j in the i-th tree, where the hidden state is transferred from ρ(m) to m; represents the shape parameter in the m state; Indicates that when x ij The scale parameter when the hidden state is m; H0 represents the assumption when the watermark information -1 is embedded in the subband; H1 represents the assumption when the watermark information +1 is embedded in the subband; a. Initial Setup Get the host image P of size M×N and initialize the variables; b. Watermark Embedding b.1 Perform a two-level NSST operation on the host image P of size M×N. Specifically, the image is first decomposed into multiple scales according to NSLP. While ensuring translation invariance, a low-frequency subband D and high-frequency subbands H1 and H2 of the first and second scales are generated. SF is then used to achieve multi-directional decomposition of the subbands. The high-frequency subbands of each scale are then decomposed in terms of direction. Each image will obtain eight directions of the first scale and four directions of the second scale, for a total of 12 high-frequency components of the same size of M×N. b.2 In the high-frequency sub-band obtained by decomposition, select the sub-band image with the maximum energy on the second scale as the carrier image for embedding the watermark, divide the sub-band image into blocks of K×K size, ensure that the blocks do not overlap, and calculate the entropy value of each block respectively. Based on the length L of the watermark to be embedded, select the first L target blocks with higher entropy values, and record the position of each block; b.3 Perform 3rd-order FPLCT decomposition on the selected L target blocks respectively to obtain the NSST-FPLCT amplitude domain. For each block, after 3rd-order FPLCT calculation, the dimension of the block becomes 7×7; b.4 Embed a one-bit watermark of 1 or -1 into each block accordingly, and perform the watermark information embedding operation according to the multiplicative embedding rule of the watermark: yi=(1+λωl)xi; b.5 Perform 3rd-order FPLCT reconstruction on the L target blocks containing watermark information, and the dimension of the target block changes from 7×7 to K×K, and then puts it back to its original position in the target subband; b.6 Apply NSST inverse transform to all coefficients in the target subband, and finally obtain the image P' with hidden watermark information; c.BSM-HMT statistical modeling c.1 Perform [2,3] NSST decomposition on the obtained watermarked image P'. Specifically, the image is first decomposed into multiple scales according to NSLP to obtain a low frequency D and high frequencies H'1 and H'2 at two scales. Then, H'1 and H'2 are decomposed into multiple directions using SF to obtain high frequency sub-bands in eight directions at one scale and four directions at two scales. c.2 Select the high-frequency subbands with the largest variance of the second scale and the first scale respectively, implement the block operation according to the strategy of "same size and non-overlapping", sort the obtained entropy values ​​of each block in descending order, and select the first L high entropy blocks for watermark information extraction; c.3 Perform 3rd-order FPLCT calculation on the selected L high entropy blocks, and obtain a 7×7 NSST-FPLCT amplitude coefficient matrix for each block; c.4 According to the target position definition, select from the amplitude domain at each scale NSST-FPLCT amplitude coefficients are selected, and a BSM-HMT hybrid model is constructed for statistical modeling, where BSM is used to capture the non-Gaussian distribution characteristics of the amplitude and HMT is used to capture the scale correlation of the amplitude. The probability density function of the BSM-HMT is defined as: d. Aitken-ECM parameter estimation The training samples of the same position block in the same scale and different direction subbands are bound to form a group of training samples. Using the inter-tree binding idea, the training samples of two scales are considered and organized into a training sample set and sent to the Aitken-ECM parameter estimation algorithm to calculate the parameter set of the BSM-HMT model for use by the decoder. e. Construct ML decoder to extract watermark e.1 adopts the blind watermark extraction method and regards the watermark extraction problem as a binary hypothesis testing problem, which has: e.2 According to the maximum likelihood criterion and calculating the log-likelihood ratio, the decoder is constructed as: in: And f Y (y i |H0)=f X (y i ), f X (x) represents the probability density function of the model used; The e.3 decoder adopts a blind watermark extraction method. The watermarked image maintains the same statistical distribution characteristics as the original image. The BSM-HMT model is used to represent the amplitude distribution characteristics of the watermarked image. The ML detector based on BSM-HMT is constructed as follows: e.4 Define the watermark position discriminant, that is, the lth watermark position in the image is extracted according to the following decision expression:

Images