CN112907435B - High-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping - Google Patents
High-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping Download PDFInfo
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Abstract
The invention discloses a high-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping, which expands the range of an image to be coded in a space domain according to the principle and characteristics of calculation holography, encrypts the watermark by using an improved Burch coding algorithm and generates a holographic watermark image. And the holographic watermark image is subjected to interval mapping, and the compressed numerical value is subjected to data interval mapping, so that the safety of the image watermark system is further improved. Secondly, converting the RGB color carrier image into YUV color space, selecting Y component to perform secondary discrete wavelet transformation, blocking low-frequency component, and performing Schur decomposition on each sub-block. And finally, selecting the first row and the first column of the upper triangular matrix as the position for embedding the holographic watermark, and dynamically selecting proper embedding strength. Performing Schur reconstruction and wavelet inverse transformation on the upper triangular matrix embedded with watermark information, and converting YUV space into RGB color space to obtain an image containing watermark information.
Description
Technical Field
The invention belongs to the technical fields of computer holographic technology, information security and copyright protection, and particularly relates to a high-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping.
Background
Along with the rapid popularization of network technology and computer technology, the channel for people to acquire information (take images, audio and video) is more convenient, and a richer carrier is provided for information transmission and storage. However, the easy propagation and convenience of digital media often occur such as theft and infringement of digital information. Meanwhile, the demands of people on information and the awareness of copyright protection are increasingly enhanced. Therefore, research into copyright protection of digital images is of great importance.
The existing digital watermarking technology is mainly divided into three main types of robust watermarking [Roop Singh,Alaknanda Ashok,Mukesh Saraswat.Optimised robust watermarking technique using CKGSA in DCT-SVD domain.2020,14(10):2052-2063.]、 blind watermarking [Soumitra Roy,Arup Kumar Pal.A blind DCT based color watermarking algorithm for embedding multiple watermarks.2017,72:149-161.] and zero watermarking [ hot spring, sunfeng, wang Shuxun ] the concept and application of zero watermarking [ J ]. Electronic journal, 2003 (02): 214-216 ]. The basic idea of the robust watermark is to embed part of the information (such as the maximum singular value) of the copyright information into the invisible domain of the carrier image, which has good robustness to conventional attacks, but the complete copyright watermark can be extracted by providing part of the watermark information in the authentication stage. The zero watermark technology is to generate unique zero watermark information by performing exclusive OR operation on the characteristic information of the carrier image and the copyright watermark, and then use the zero watermark to extract the copyright information when copyright disputes occur. In order to solve the problem of complicated authentication of the robust watermark, soumitra et al propose a blind watermark algorithm, the copyright information is fully embedded into the carrier image in a quantization mode, the robustness is good for the conventional operation of the image, any information of the original copyright information is not required to be provided in the authentication process, and the blind extraction process is realized. The blind watermarking technology can embed copyright information into a carrier image completely, and does not need any information of original copyright in the authentication process, so that the blind watermarking technology is widely applied to copyright protection of digital information. If literature [Guo Q,Chen G X,Luo J,et al.A Blind Watermarking Algorithm Using DWT and DCT Techniques for Color Image[J].Applied Mechanics and Materials,2015,731:179-182.] combines DWT and DCT to embed watermark information into intermediate frequency blocks of carrier image, firstly converting color image into Lab space, then DWT for L component to obtain intermediate frequency coefficient, and partitioning intermediate frequency coefficient, finally embedding watermark information into DCT coefficient of sub-block. Since the DCT coefficients are more sensitive to image rotation, the robustness against rotation attacks is poor. Document [Soumitra Roy,Arup Kumar Pal.A blind DCT based color watermarking algorithm for embedding multiple watermarks.2017,72:149-161.] thus embeds multiple watermarks in the blue and green components of a color image and replaces the DCT coefficients of the intermediate frequency block with repetition codes to improve the robustness of the algorithm. In watermark embedding DCT coefficient, although the transparency can be well protected and the robustness is improved, the DCT coefficient has larger change when the geometric position of the image is changed, so the robustness to geometric attack is poor.
For this purpose, literature [Araghi T K,Manaf A A,Araghi S K.A Secure Blind Discrete Wavelet Transform based Watermarking Scheme Using Two-level Singular Value Decomposition[J].Expert Systems with Applications,2018,112(DEC.):208-228.] and literature [Xu H,Kang X,Wang Y,et al.Exploring robust and blind watermarking approach of colour images in DWT-DCT-SVD domain for copyright protection[J].International journal of electronic security and digital forensics,2018,10(1):79-96.] perform singular value decomposition on DWT high-frequency information of each sub-block of an image, and embed watermark information in a singular value matrix of a sub-block of a carrier image. The singular value decomposition has rotation invariance and stability, and has great improvement on the robust performance. Singular value decomposition, while solving the problem of DCT energy sensitivity, often results in local missing of the watermark image extracted for a cut attack due to the maximum singular value of embedding the watermark into the sub-blocks. Document [A R T,B A K,C D T.Hybrid and blind watermarking scheme in DCuT–RDWT domain[J].Journal of Information Security and Applications,2019,46:231-249.] and document [ [1] Guo Pengfei, feng Lin, sun Saiyu ] new-type gray image blind detection digital watermarking algorithm [ J ]. Computer engineering and science, 2019, 41 (01): 104-112 ] firstly, redundant discrete wavelet transform RDWT is carried out on a carrier image, the approximate low frequency domain of the carrier image is extracted, then the low frequency information is segmented, schur decomposition is carried out on each sub-block, and watermark information embedding is completed by modifying the maximum energy value of an upper triangular matrix. The algorithm shows strong robustness to geometric attacks due to the time-shift invariance of RDWT and the jitter immunity of Schur decomposition. Document [Qiao L Y,Kim J W.A Zero-watermarking Scheme based on LPM and Holographic[J].International Journal of Security and Its Applications,2014,8(6):89-100.] generates a hologram of a carrier image through a holographic technique and polar coordinate transformation, and the hologram has the characteristic of being not torn, so that zero watermark generation can resist a large-amplitude rotation attack, but has poor robustness in the aspect of shearing attack. Document [Yu C,Li X,Chen X,Li J.An Adaptive and Secure Holographic Image Watermarking Scheme.Entropy.2019;21(5):460] proposes a binary holographic encryption algorithm for generating a holographic watermark, adaptively selecting an embedding location by calculating entropy and edge entropy, and finally embedding the holographic image into a low frequency domain of a carrier image by Schur decomposition. The holographic encryption algorithm has a larger encryption space, is beneficial to improving the safety of information, and can well balance the robustness and the transparency by using the edge entropy. The method has strong robustness to filter attack, JPEG compression, fuzzy operation and image shielding, but the copyright watermark extracted under noise attack contains more noise points.
In the traditional blind watermark algorithm, the resistance performance to shearing attack and rotation attack is poor, and the extracted copyright watermark is in a missing phenomenon, mainly in the blind watermark embedding process, the whole carrier image is embedded in a quantization mode, and although the transparency and the robustness are improved, when the geometric pixels of the image change, the complete copyright watermark is difficult to extract in the original position. The current blind watermarking method also has the following defects:
(1) The existing blind watermarking algorithm cannot resist large-angle shearing attacks and rotation attacks, and noise points are more when copyrighted images are extracted.
(2) The existing blind men use a single encryption method to scramble copyright information, so that the security is more and the key space is small.
Disclosure of Invention
Based on the defects of the digital watermarking in the prior art, the technical problem solved by the invention is to provide a high-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping, the blind watermarking overcomes the false alarm rate problem in the zero watermark authentication process, the holographic technology solves the problem of poor robustness of the blind watermarking to shearing attack, and copyright protection of digital information can be realized.
The high-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping comprises copyright watermarking embedding and copyright authentication:
the copyright watermark embedding comprises the following steps:
1.1, H is set as a color carrier image, the size of MxNx 3,W is a watermark image, the size of P x Q is set as a watermark image, holographic encryption is carried out on the watermark image W, fourier holographic encryption is carried out on a binary copyright image with the size of P x Q, and improved Burch coding is carried out on the Fourier holographic image, so that a hologram BW with the size of 2P x 2Q is obtained;
1.2, preprocessing a holographic image, and mapping a data interval of the obtained holographic image BW to obtain an image BW 1;
1.3 converting the RGB Carrier image H into YUV color space to obtain three components H Y、HU、HV, and performing wavelet decomposition twice on the luminance component H Y to obtain a size of A low frequency coefficient LL;
1.4, 4×4 non-overlapping partitioning is performed on the low-frequency coefficient LL, each sub-block is marked as b i,j, and Schur decomposition is performed on each sub-block to obtain a unitary matrix U i,j and an upper triangular matrix T i,j;
1.5 embedding the elements in the pre-processed hologram BW 1 in the upper triangular matrix T i,j;
1.6, performing inverse Schur transformation and inverse wavelet transformation on T ' i,j (1, 1) after watermark information is embedded to obtain a brightness component H ' Y after the watermark information is embedded, and transforming to an RGB color space according to a U component H U and a V component H V obtained in the step 1.3 to obtain a carrier image H ' embedded with the watermark;
The copyright authentication includes the following steps:
2.1 extracting SURF characteristic points from the carrier image H 'att after being attacked, matching the characteristic points in the K 1 key with the characteristic points of the carrier image H' att, selecting three pairs of non-coincident and non-collinear matching points to generate an affine matrix, and carrying out affine transformation on the carrier image H 'att to obtain a corrected carrier image H' att;
2.2 transforming the color image H 'att of the RGB color space into the YUV color space, taking the brightness component Y att thereof to carry out wavelet transformation twice, and taking the transformed low-frequency coefficient LL';
2.3, carrying out non-overlapping 4 × to 4 blocks of the low-frequency coefficient LL ', carrying out Schur matrix decomposition on the obtained sub-block b ' i,j in sequence to obtain an upper triangular matrix T ' i,j;
2.4, taking the element T 'i,j (1, 1) of the first row and the first column of the upper triangular matrix T' i,j, and extracting watermark information;
2.5, carrying out interval inverse mapping on the holographic coding matrix BW 'and carrying out holographic reproduction process to obtain a binary watermark image W'.
Optionally, in step 1.5, the embedding method is as follows:
Where Δ=mod (T i,j (1, 1), q), mod is a modulo operation, T i,j (1, 1) is the first row and first column element of the upper triangular matrix T i,j, and q is the watermark embedding strength.
Optionally, in step 2.4, watermark information is extracted as follows:
Where Δ '=mod (T "i,j (1, 1), q), mod is a modulo operation, T" i,j (1, 1) is the first column element of the first row of the upper triangular matrix T "i,j, q is the watermark embedding strength, and BW' is the extracted holographic encoding matrix.
By the above, the high robust holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping of the invention expands the range of the image to be coded in the space domain according to the principle and characteristics of calculation holography, encrypts the watermark by using the improved Burch coding algorithm, and generates a holographic watermark image. And (3) carrying out interval mapping on the holographic watermark image, compressing random discrete decimal of the [0,1] interval into 4 numerical values, and embedding less information on the basis of retaining data. And the compressed numerical value is subjected to data interval mapping, so that the safety of the image watermarking system is further improved. Secondly, converting the RGB color carrier image into YUV color space, selecting Y component to perform secondary discrete wavelet transformation, blocking low-frequency component, and performing Schur decomposition on each sub-block. And finally, selecting the first row and the first column of the upper triangular matrix as the position for embedding the holographic watermark, and dynamically selecting proper embedding strength. Performing Schur reconstruction and wavelet inverse transformation on the upper triangular matrix embedded with watermark information, and converting YUV space into RGB color space to obtain an image containing watermark information.
In addition, the invention selects the improved Boqi code to carry out holographic encryption on the copyright watermark, and reduces the embedded information quantity by utilizing interval mapping based on normal distribution, thereby ensuring the precision of extracting holographic information. Selecting YUV space, HSV space and Lab space as three basic color spaces for constructing color zero watermark, selecting DWT as image frequency domain transformation tool to obtain low frequency domain information of carrier image, schur decomposing maximum characteristic value for extracting carrier image, and dynamically selecting embedding strength; under the conventional attack, the invention has stronger robustness and stability. Compared with the prior art, the invention has the following beneficial effects:
(1) The holographic image is generated by utilizing the improved Bosch coding, so that the problem of twin image overlapping in the traditional holographic technology can be solved, and meanwhile, the holographic image is used as watermark information, so that the influence of shearing attack on the watermark image can be effectively resisted.
(2) The interval mapping based on normal distribution can reduce the embedded information amount, thereby ensuring the transparency and the robustness of the carrier image.
(3) By utilizing schur decomposition, the robustness of each sub-block against geometric attacks and the speed of matrix decomposition can be improved.
(4) The holographic blind watermark can improve the safety of the traditional blind watermark and solve the problem of poor robustness under scale attack.
The foregoing description is only an overview of the present invention, and is intended to be implemented in accordance with the teachings of the present invention, as well as to provide further clarity and understanding of the above and other objects, features and advantages of the present invention, as described in the following detailed description of the preferred embodiments, taken in conjunction with the accompanying drawings.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings of the embodiments will be briefly described below.
FIG. 1 is a diagram of a copyright watermark embedding process;
Fig. 2 is a diagram of a copyright authentication process.
Detailed Description
The following detailed description of the invention, taken in conjunction with the accompanying drawings, illustrates the principles of the invention by way of example and by way of a further explanation of the principles of the invention, and its features and advantages will be apparent from the detailed description. In the drawings to which reference is made, the same or similar components in different drawings are denoted by the same reference numerals.
The digital holographic technology is to utilize computer coding, numerical calculation and other methods to generate holographic image, which records all the information of the amplitude and phase of the image, and the map has the characteristics of being not torn and locally recoverable and global, so that any part of the holographic image is cut and attacked to have certain resistance. Therefore, the holographic technology is utilized to carry out holographic encryption on the watermark image, and the generated holographic image has the characteristics of safety and shearing resistance. The invention improves the Boqi coding, and embeds the pixel points of the original image into a full zero matrix which is four times larger than the original image so as to realize the separation of the original image and the conjugate image. The method comprises the following specific steps:
Step1: and (5) extension coding. Since the calculated holographic images of the Fourier holographic codes are restored to have aliasing among twin images, the Bosch codes are improved in order to realize conjugate separation of the holographic images. Writing the pixel points of the original image into an all-zero matrix with pixel values larger than those of the original image, so as to achieve the off-axis effect. Then, an accurate off-axis image is obtained through a holographic reconstruction optical system, and when the all-zero matrix is four times that of the original image, the original image and the conjugate image can be completely separated. The number of pixels of an original image O (x, y) is set as M multiplied by N, an origin coordinate is taken as an image center, the coding range of the O (x, y) is enlarged, the O (x, y) is written into an all-zero matrix with the pixels of 2M multiplied by 2N, an image O 1 (x, y) to be coded is obtained, and the image O 1 (x, y) is expressed as a matrix
Step2: holographic encryption. O 1 (x, y) is used for obtaining a holographic image function H (u, v) on an optical off-axis holographic surface through interference of object light waves and reference light waves
Wherein O 1 (u, v) represents an object light wave; a (u, v) represents the complex amplitude of the object light wave; r (u, v) represents an off-axis planar reference light wave; j2 pi alpha x is the object light wave, the spatial frequency alpha = sin theta/lambda of the reference light wave, lambda is the reference light wave wavelength,Is the phase information of the reference light wave. According to the Bosch coding method, a new holographic function is constructed, i.e
Where K is a constant such that H (u, v) is a non-negative real number for all u, v.
The encoded and expanded image O 1 (x, y) is fourier transformed by a lens under horizontal light illumination to obtain a holographic image H (u, v). Under the irradiation of parallel light, a hologram reproduction image g (ζ, η) subjected to inverse fourier transform is then obtained on the back focal plane.
Step3: and (3) performing Fourier inverse transformation on the coded hologram H (u, v) in a decryption process to obtain a holographic reproduction image g (xi, eta).
g(ξ，η)＝ifft(H(u,v))
Wherein g (ζ, η) has a pixel size of M 'x N', and the coordinate rangeThe hologram g (ζ, eta) after decoding realizes the conjugate separation of the twin image, which is respectively composed of three parts of 0-1 matrix delta (ζ, eta), original image O and conjugate image O'.
g(ξ，η)＝Kδ(ξ，η)+O1(ξ-α,η)+O1[-(ξ+η),η]
Wherein the method comprises the steps of
Therefore, the holograms generated after the improved bosch coding do not have aliasing between twin images.
The invention combines the proposed off-axis Fourier holographic technology based on the improved Buch coding to process the copyrighted image so as to improve the security and the robustness of watermark information. The Fourier holographic image coded by the improved Burch is formed by discontinuous and randomly distributed numerical values of [0,1], and the holographic image is directly embedded into the carrier image as watermark information, so that the problems of excessive embedded information and incapability of guaranteeing extraction accuracy are faced. In order to solve the problem, the invention provides a data threshold compression algorithm based on normal distribution.
Step1: and (5) normal fitting. According to the distribution of the data values in the holographic matrix and the occurrence frequency, normal distribution can be fitted by calculating the mean value and standard deviation of the data. The data distribution X obeys the probability distribution of the position parameter μ, the scale parameter σ, and the following formula is a probability density function of the data distribution.
Wherein μ is the mean and σ is the standard deviation.
F (x) is point-symmetrical about x=μ, and reaches a maximum at x=μ. As can be seen from the nature of the probability density function, the more frequently the value of f (x) appears near the μ -point, the greater the probability that the random variable x takes a value near the μ -point, and there is no random variable that obeys the normal distribution N (μ, σ 2).
p(μ-σ≤x≤μ+σ)≈0.688
p(μ-2σ≤x≤μ+2σ)≈0.955
p(μ-3σ≤x≤μ+3σ)≈0.997
From the above equation, the probability of the random variable being between [ mu-sigma, mu+sigma ] exceeds 2/3, and the probability of the random variable being between [ mu-2 sigma, mu+2 sigma ] is 0.955, so that it is considered that the random variable is substantially free from information loss in this range.
Step2: and (5) parameter selection. In order to preserve as much as possible the information of the holographic image embedded in the carrier image and to embed fewer information bits, the information bits are compressed before embedding the information. The embedded interval range is [ mu-beta sigma, mu+beta sigma ] (0.9 < beta < 2.1), the parameter beta takes a value on the interval [0.9,2.1] (the probability of the data falling on the area is large), the step size is increased by 0.01, and the holographic watermark is subjected to data compression in a dot taking mode of three equally divided intervals, so that the compressed and encoded holographic matrix only has2, 3 or 4 numerical values.
Experiments prove that when the holographic matrix is compressed to 4 numerical values, the NC value of holographic recovery can reach local optimum at the position where the parameter beta is slightly larger than 1.92. Further optimization of the parameter β is performed, in interval [1.92,1.93], in increments of 0.0001 steps. When the beta epsilon 1.9204,1.9217 is selected to be embedded with information, the information can be recovered perfectly, namely the NC value is 1.0000.
Step3, data compression. When β ε [1.9204,1.9217], [ μ - βσ, μ+βσ ] is divided into five equal parts, the interval division points are used as compression values, and the compression values are used for replacing numerical values in the holographic matrix, and the replacement mode is shown in the following formula. Wherein a 1～a4 is a numerical value corresponding to 4 demarcation points, and the data of the holographic image matrix is composed of four data values of the demarcation points, so that the compression of the data is realized. The data compression scheme is as follows.
Step4, data mapping. After the data compression is carried out on the whole interval, the data value mapping is carried out, the decimal values inconvenient to calculate and read are mapped one by one, each group of mapping consists of the original numerical value and the mapping numerical value, the operation further encrypts watermark information, meanwhile, the calculation time is saved, and the extracted information cannot be restored to a watermark image on the premise of not knowing the mapping relation. In the mapping process, a 1 is mapped to 1, a 2 is mapped to 2, a 3 is mapped to 3, and a 4 is mapped to 4. And carrying out reverse mapping again when the hologram is restored and the image is extracted. When one bit of data mapping is wrong, the holographic image cannot be correctly recovered, and the security of watermark information is further improved.
Carrying out schur decomposition on the sub-blocks after the secondary blocking, extracting the singular value of each sub-block, and constructing a characteristic matrix of the carrier image, so as to improve the robustness of the carrier image after being attacked, wherein schur decomposition can be expressed as the product of three matrixes, and the decomposition mode is shown as the following formula:
I＝QUQ'
wherein U is an upper triangular matrix, Q is a unitary matrix, and Q' is a transposed matrix of Q.
The invention adopts normalized correlation coefficient (Normalization correlation, NC value) to measure the similarity between the extracted watermark and the original watermark, and the calculation method is shown in the following formula respectively:
wherein w, w' represent the original watermark and the extracted watermark, respectively, wherein NC e 0,1, when nc=1, indicates that the two watermark images are identical, and when nc=0, indicates that the two watermarks are uncorrelated.
For objective evaluation of the performance of the algorithm, the change between the watermarked carrier image and the original carrier image is measured by peak signal to noise ratio (PSNR). The calculation method comprises the following steps:
Wherein M, N is the image size, f (i, j), g (i, j) are the pixel points of the original image and the target image respectively, M max is the maximum value of the pixel values in the image, the higher the peak signal-to-noise ratio PSNR value is, the closer the target image is to the original image, and when the PSNR value is more than 30dB, the target image and the original image have no obvious difference in the human eye observation effect.
The invention relates to a high-robustness holographic watermarking algorithm based on improved Boqi coding and data interval mapping, which comprises a watermarking embedding process and a copyright authentication step:
1. the specific steps of the watermark embedding process comprise the following contents:
In the watermark embedding stage, the brightness component information of the color image is subjected to frequency domain transformation, blocking and Schur decomposition, and then the preprocessed watermark information is embedded into the maximum singular value of the sub-block. Let H be the color carrier image, the size M x N x3,W be the watermark image, the size P x Q, the specific steps are as follows:
Step 1: the watermark image W is holographically encrypted. And carrying out Fourier holographic encryption on the binary copyright image with the size of P multiplied by Q, and carrying out improved Burch encoding on the Fourier holographic image to obtain a hologram BW with the size of 2P multiplied by 2Q.
Step 2: holographic image preprocessing. And performing interval mapping and sub-block mapping operation on the obtained holographic image BW to obtain an image BW 1.
Step 3: converting RGB carrier image H into YUV color space to obtain three components H Y、HU、HV, and performing wavelet decomposition twice on brightness component H Y to obtain size ofLow frequency coefficient LL.
Step 4: 4×4 non-overlapping partitioning is performed on the low-frequency coefficient LL, each sub-block is denoted by b i,j, and Schur decomposition is performed on each sub-block to obtain a unitary matrix U i,j and an upper triangular matrix T i,j, as shown in the following formula:
[Ui,j,Ti,j]＝Schur(bi,j)
Wherein the method comprises the steps of
Step 5: the elements in the hologram BW 1 after the pre-processing are embedded in the upper triangular matrix T i,j by the following formula:
Where Δ=mod (T i,j (1, 1), q), mod is a modulo operation, T i,j (1, 1) is the first row and first column element of the upper triangular matrix T i,j, and q is the watermark embedding strength.
Step 6: and (3) performing inverse Schur transformation and inverse wavelet transformation on the T 'i,j (1, 1) embedded with the watermark information to obtain a brightness component H' Y embedded with the watermark information, and transforming the brightness component H 'Y into an RGB color space according to the U component H U and the V component H V obtained in the step (3) to obtain a carrier image H' embedded with the watermark.
The watermark extraction process is the inverse of watermark embedding. In the watermark information extraction process, watermark information can be extracted only by extracting characteristic points of the carrier image after attack and a user key K 1, so that the carrier image after attack is H' att, and the watermark extraction comprises the following specific steps:
Step 1: extracting SURF feature points from the carrier image H 'att after being attacked, matching the feature points in the K 1 key with the feature points of the carrier image H' att, selecting three pairs of non-coincident and non-collinear matching points, generating an affine matrix, and carrying out affine transformation on the carrier image H 'att to obtain a corrected carrier image H' att.
Step 2: the color image H 'att of the RGB color space is transformed into the YUV color space, the brightness component Y att is taken to perform wavelet transformation twice, and the transformed low-frequency coefficient LL' is taken.
Step 3: non-overlapping 4×4 blocking is performed on the low-frequency coefficient LL ', the obtained sub-blocks b' i,j are sequentially subjected to Schur matrix decomposition, and an upper triangular matrix T "i,j is obtained, wherein the following formula is shown:
[～,T”i,j]＝Schur(b'i,j)
Wherein,
Step 4: the element T "i,j (1, 1) of the first row and first column of the upper triangular matrix T" i,j is taken, and watermark information is extracted as follows.
Where Δ '=mod (T "i,j (1, 1), q), mod is a modulo operation, T" i,j (1, 1) is the first column element of the first row of the upper triangular matrix T "i,j, q is the watermark embedding strength, and BW' is the extracted holographic encoding matrix.
Step 5: and performing interval inverse mapping on the holographic coding matrix BW 'and performing holographic reproduction to obtain a binary watermark image W'.
TABLE 1
TABLE 2
The present invention employs a number of methods for experiments, where a set of experimental results are presented. As shown in tables 1 and 2.
Claims (3)
1. The high-robustness holographic blind watermarking algorithm based on improved Bosch coding and data interval mapping is characterized by comprising copyright watermarking embedding and copyright authentication:
the copyright watermark embedding comprises the following steps:
1.1, H is set as a color carrier image, the size of MxNx 3,W is a watermark image, the size of P x Q is set as a watermark image, holographic encryption is carried out on the watermark image W, fourier holographic encryption is carried out on a binary copyright image with the size of P x Q, and improved Burch coding is carried out on the Fourier holographic image, so that a hologram BW with the size of 2P x 2Q is obtained;
1.2, preprocessing a holographic image, and mapping a data interval of the obtained holographic image BW to obtain an image BW 1;
1.3 converting the RGB Carrier image H into YUV color space to obtain three components H Y、HU、HV, and performing wavelet decomposition twice on the luminance component H Y to obtain a size of A low frequency coefficient LL;
1.4, 4×4 non-overlapping partitioning is performed on the low-frequency coefficient LL, each sub-block is marked as b i,j, and Schur decomposition is performed on each sub-block to obtain a unitary matrix U i,j and an upper triangular matrix T i,j;
1.5 embedding the elements in the pre-processed hologram BW 1 in the upper triangular matrix T i,j;
1.6, performing inverse Schur transformation and inverse wavelet transformation on T ' i,j (1, 1) after watermark information is embedded to obtain a brightness component H ' Y after the watermark information is embedded, and transforming to an RGB color space according to a U component H U and a V component H V obtained in the step 1.3 to obtain a carrier image H ' embedded with the watermark;
The copyright authentication includes the following steps:
2.1 extracting SURF characteristic points from the carrier image H 'att after being attacked, matching the characteristic points in the K 1 key with the characteristic points of the carrier image H' att, selecting three pairs of non-coincident and non-collinear matching points to generate an affine matrix, and carrying out affine transformation on the carrier image H 'att to obtain a corrected carrier image H' att;
2.2 transforming the color image H 'att of the RGB color space into the YUV color space, taking the brightness component Y att thereof to carry out wavelet transformation twice, and taking the transformed low-frequency coefficient LL';
2.3 non-overlapping 4×4 blocking is carried out on the low-frequency coefficient LL ', the obtained sub-blocks b ' i,j are subjected to Schur matrix decomposition in sequence, and an upper triangular matrix T ' i,j is obtained;
2.4, taking the element T 'i,j (1, 1) of the first row and the first column of the upper triangular matrix T' i,j, and extracting watermark information;
2.5, performing interval inverse mapping on the holographic encoding matrix BW 'and performing holographic reproduction process to obtain a binary watermark image W';
Processing a copyright image based on an off-axis Fourier holographic technology of improved Buch coding to improve the safety and robustness of watermark information, wherein the Fourier holographic image of the improved Burch coding consists of discontinuous random distribution values of [0,1], and the holographic image is directly embedded into a carrier image as watermark information, so that a data threshold compression algorithm based on normal distribution is provided;
Step1: fitting normally, namely fitting normal distribution according to distribution and occurrence frequency of data values in a holographic matrix by calculating mean value and standard deviation of data, wherein the data distribution X obeys a position parameter mu, the scale parameter is probability distribution of sigma, and the following formula is probability density function of the data distribution;
Wherein μ is the mean and σ is the standard deviation;
f (x) is point symmetric about x=μ, and reaches a maximum at x=μ;
Step2: parameter selection, namely compressing information bits before embedding information, selecting the embedded interval range as [ mu-beta sigma, mu+beta sigma ] (0.9 < beta < 2.1), taking the value of the parameter beta on the interval [0.9,2.1], increasing the value by 0.01 step length, and carrying out data compression on the holographic watermark in a point taking mode of three equal intervals, so that the compressed and encoded holographic matrix only has 2, 3 or 4 numerical values;
step3, data compression, when beta is epsilon [1.9204,1.9217], carrying out five equal divisions on [ mu-beta sigma, mu+beta sigma ], taking interval dividing points as compression values, and replacing numerical values in the holographic matrix by the compression values; wherein a 1～a4 is a numerical value corresponding to 4 demarcation points, the data of the holographic image matrix is composed of four data values of the demarcation points, the data compression is realized, and the data compression mode is as follows:
Step4, data mapping, namely performing data value mapping after data compression on the whole interval, performing one-to-one mapping on decimal values inconvenient to calculate and read, wherein each group of mapping consists of an original numerical value and a mapping numerical value, and in the mapping process, a 1 is mapped to 1, a 2 is mapped to 2, a 3 is mapped to 3 and a 4 is mapped to 4; when the hologram is restored and the image is extracted, reverse mapping is performed again;
And carrying out schur decomposition on the sub-blocks after the secondary blocking, extracting the singular value of each sub-block, and constructing a characteristic matrix of the carrier image, so that the robustness of the carrier image after being attacked is improved, and the schur decomposition can be expressed as the product of three matrices.
2. The highly robust holographic blind watermarking algorithm based on improved bosch coding and data interval mapping according to claim 1, wherein in step 1.5 the embedding method is as follows:
Where Δ=mod (T i,j (1, 1), q), mod is a modulo operation, T i,j (1, 1) is the first row and first column element of the upper triangular matrix T i,j, and q is the watermark embedding strength.
3. The highly robust holographic blind watermarking algorithm based on improved bosch coding and data interval mapping according to claim 1, wherein in step 2.4, the watermark information is extracted as follows:
Where Δ '=mod (T "i,j (1, 1), q), mod is a modulo operation, T" i,j (1, 1) is the first column element of the first row of the upper triangular matrix T "i,j, q is the watermark embedding strength, and BW' is the extracted holographic encoding matrix.
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