CN116993567A - Frequency domain blind watermarking method based on Hadamard transform and teaching optimization algorithm - Google Patents
Frequency domain blind watermarking method based on Hadamard transform and teaching optimization algorithm Download PDFInfo
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Abstract
In order to better protect the copyright of the color image, a high-efficiency color image watermarking algorithm based on Hadamard transformation and teaching optimization algorithm is provided. In the watermark embedding stage, different watermark embedding strategies are adopted in the 4 multiplied by 4 blocks according to the influence degree of the high and low bits of the watermark on pixels and considering the energy concentration characteristic of the Hadamard matrix. In order to enhance the robustness of the watermark algorithm, a voting system is designed for the high 4-bit watermark information. Meanwhile, the low 4 bits of watermark information are compressed by adopting a serial ordered binary digital system, so that the invisibility and the embedding capacity of watermark images are improved. When the watermark is required to be extracted, the inverse process of the ordered binary digital system transformation is optimized and arranged, so that the watermark extraction time is shortened. Finally, the parameters of the watermark algorithm are optimized by using the teaching algorithm, and the operation time of the algorithm is saved while the invisibility and the robustness of the algorithm are both considered. Compared with other algorithms, the algorithm has the advantages of greatly improving the robustness, the running time, the watermark embedding capacity, the security, the invisibility and the like.
Description
Technical Field
The invention belongs to the technical field of information security, and relates to rapid copyright protection of a large-capacity color digital image.
Background
Since the 21 st century, human society has entered the information age, and the dissemination of various information has not been limited to paper media. Emerging multimedia technologies offer great convenience to people, however, the development of things tends to be twofold. While people enjoy the age to develop bonus, various infringement piracy technologies on the internet are also layered endlessly. In order to cope with the current problem, digital watermarking technology has been developed, which is a technology of hiding information in digital media. Digital watermarking technology has been relatively mature through decades of development. However, the existing watermarking algorithm still has the defects of small embedding capacity, poor invisibility and poor robustness. Therefore, to better protect the copyrights of images, new and efficient watermarking algorithms are urgently needed. Color image watermarking schemes based on Hadamard transform and teaching and learning optimization algorithms have been invented to meet this need.
Disclosure of Invention
The invention aims to provide a blind watermarking algorithm based on Hadamard transformation and a teaching optimization algorithm, which is characterized by being realized through a specific watermarking embedding process and an extracting process, wherein the watermarking embedding process is described as follows:
the first step: the number of pixels is one24-bit color image digital watermarkingDividing into 3 layered watermark images according to the sequence of three primary colors of red, green and blueThe method comprises the steps of carrying out a first treatment on the surface of the Key-based processing of each layered watermark imageAffine transformation encryption of (a); the encrypted layered watermark imageThe pixels represented by each decimal number in (a) are represented by 8-bit binary numbers; the first four digits of every 8 digits binary numbers are sequentially connected to form a length ofIs a layered watermark bit sequence of (1)Simultaneously taking the last four bits of every 8 bits binary numbers to connect in turn to form a length ofIs a layered watermark bit sequence of (1)Then, according to the formula (1)Compression processing using permuted ordered binaries to obtain sequencesThe length after compression isAt this time, the total length of the processed layered watermark sequenceIs that,Respectively representing three layers of red, green and blue, wherein floor is a downward rounding function, and mod is a remainder function;
（1）
wherein ,in order to obtain the binary sequence after compression,for the sequence number in the binary sequence,expressed in the original binary sequence positionWhere the value, C (deg.) is a function of the number of combinations,representing the length of the binary sequence,；
and a second step of: the number of pixels is oneIs a color carrier image of (a)Divided into 3 layered carrier images in the order of three primary colors of red, green and blueThe method comprises the steps of carrying out a first treatment on the surface of the At the same time, each layered carrier imageThe number of the divided pixels isIs a non-overlapping image block of (1); from layered watermark bit sequencesIs the total length of (2)Using keysThe MD5 hash pseudo-random scrambling algorithm of (1) generates a non-repeated block selection sequence in the layered carrier imageIs selected in (a)Image blocks, in front ofBlocks for embeddingThereafterBlocks for embedding, wherein ，Respectively representing three layers of red, green and blue, wherein floor is a downward rounding function, and mod is a remainder function;
and a third step of: before choosingSelecting one image block from the blocks according to the sequence of the blocksAccording to the formula (2), forHadamard transformation is carried out to obtain a transformed coefficient block matrix；
（2）
wherein ,is thatA rank Hadamard matrix;
fourth step: hierarchical watermark bit sequenceIn the method, a bit of watermark information to be embedded is taken out according to the sequenceWill beRepeated embedding into coefficient block matrixFirst three coefficients of the first line of (a)Calculating quantized frequency domain coefficients according to the embedded watermark information and formulas (3) and (4)，，=1, 2, 3 represent red, green, blue three layers, respectively;
（3）
wherein mod (-) is a remainder function, round (-) is a rounding function, xor (-) is an exclusive-or function,representing a judgment threshold value in the quantization process;
（4）
wherein ,is the quantization step length;
fifth step: will beUpdate to its transformed coefficient blockCorresponding positions in the matrix to obtain a coefficient block matrix after watermark embedding，=1, 2, 3, then the inverse transform of the hadamard matrix is achieved by equation (5), resulting in a watermarked image block；
（5）
wherein ,is thatA rank Hadamard matrix;
sixth step: image block containing water markUpdate to its in-hierarchical carrier imageCorresponding positions in (a), wherein=1, 2, 3 represent red, green, blue three layers, respectively;
seventh step: at the selected restSelecting one image block from the blocks according to the sequence of the blocksAccording to formula (6), forHadamard transformation is carried out to obtain a transformed coefficient block matrixFloor () is a downward rounding function, mod () is a remainder function;
（6）
wherein ,is thatA rank Hadamard matrix;
eighth step: hierarchical watermark bit sequenceIn the method, a bit of watermark information to be embedded is taken out according to the sequenceWill beEmbedded in a matrix of coefficient blocksFirst coefficient of first lineIn which quantized frequency domain coefficients are calculated according to the embedded watermark information and formulas (7) and (8)，=1, 2, 3 represent red, green, blue three layers, respectively;
（7）
wherein mod (-) is a remainder function, round (-) is a rounding function, xor (-) is an exclusive-or function,representing a judgment threshold value in the quantization process;
（8）
wherein ,is the quantization step length;
ninth step: will beUpdate to its transformed coefficient blockCorresponding positions in the matrix to obtain a coefficient block matrix after watermark embeddingThen through formula (9), realizing inverse transformation of Hadamard matrix to obtain image block containing watermark；
（9）
wherein ,is thatA rank Hadamard matrix;
tenth step: image block containing water markUpdate to its in-hierarchical carrier imageCorresponding positions in (a), wherein=1, 2, 3 represent red, green, blue three layers, respectively;
eleventh step: repeating the third to tenth steps until all watermark information is embedded, thereby obtaining layered carrier image containing watermarkThe method comprises the steps of carrying out a first treatment on the surface of the Finally, the layered carrier image containing the watermark is subjected toRecombining and obtaining the number of pixels asIs a water-printed image of (a)；
Twelfth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, error rate and the like, and selecting the optimal quantization step by using a teaching optimization algorithm；
The watermark extraction process is described as follows:
the first step: the number of pixels is set to beIs a water-printed image of (a)Dividing into 3 layered watermark-containing imagesAnd each layered watermark-containing imageFurther divided into a number of pixelsIn which=1, 2, 3 represent red, green, blue three layers, respectively;
and a second step of: layered aqueous print imageIn using the key-based mentioned in the watermark embedding processSelecting image blocks by MD5 hash pseudo-random scrambling algorithm of (2), whereinRespectively representing red, green and blue layers;
and a third step of: before choosingSelecting one image block from the blocks according to the sequence of the blocksAccording to the formula (10), forHadamard transformation is carried out to obtain a transformed coefficient block matrix；
（10）
wherein ,is thatA rank Hadamard matrix;
fourth step: optimum quantization step size selected by teaching optimization algorithmExtracting a coefficient block matrix according to the formulas (11), (12)Watermark contained in the document；
（11）
wherein ,information representing the extracted watermark, mod (i.e.) being a remainder function, fix (i.e.) being a rounding function in the near zero direction,=1, 2, 3；
（12）
wherein ,representation ofThe mid-watermark is the number of '1',representation ofThe number of mid-watermarks is '0',representing the final extracted watermark value;
fifth step: at the selected restSelecting one image block from the blocks according to the sequence of the blocksAccording to formula (13), forHadamard transformation is carried out to obtain a transformed coefficient block matrix；
（13）
wherein ,is thatA rank Hadamard matrix;
sixth step: optimum quantization step size selected by teaching optimization algorithmExtracting a coefficient block matrix according to formula (14)Watermark contained in the document；
（14）
wherein ,information representing the extracted watermark, mod (.) being a remainder function, fix (.) being a near zero rounding function;
seventh step: repeatedly executing the third step to the sixth step of the process to obtain the binary watermark bit sequence of each layer
And (3) withWatermark information using improved reverse permutation ordered binary algorithm simultaneouslyRecovering; then according to the segmentation process of 8-bit binary information, the methodEvery 4 bits of binary information in (a)Every 4 bits of binary information in a set of decimal-converted pixel values, wherein=1, 2, 3 represent red, green, blue three layers, respectively;
eighth step: performing key-based on the transformed encrypted layered watermark imageDecryption operation of inverse affine transformation and obtaining an extracted layered watermark image, wherein =1, 2, 3 represent red, green, blue three layers, respectively;
ninth step: combining layered watermark imagesObtaining a complete extracted watermark, wherein =1, 2, 3 represent three layers of red, green, and blue, respectively.
According to the influence degree of different positions on watermark pixels, watermark information is embedded by different methods; under the condition of keeping the embedded information unchanged, the embedded amount is reduced, and the real-time performance of the algorithm is improved; meanwhile, the parameters of the watermark algorithm are optimized by using an artificial intelligent algorithm, so that the time required for optimization is reduced, the effect of the algorithm is improved, and the algorithm meets the requirements of invisibility, robustness, instantaneity, safety and watermark capacity.
Drawings
To prove the effectiveness of the present invention, two 24-bit standard images of pixel size 512×512 as shown in fig. 1 (a) and 1 (b) were selected as carrier images, and two 24-bit color images of pixel size 32×32 as shown in fig. 2 were used as digital watermarks, respectively, for verification.
Fig. 3 (a) and 3 (b) are watermark images obtained by sequentially embedding the watermarks shown in fig. 2 (a) and 2 (b) into the carrier images in fig. 1 (a) and 1 (b), respectively, wherein the structural similarity SSIM values are 0.958 and 0.966 in sequence, and the peak signal-to-noise ratio PSNR values are 40.036dB and 40.041dB in sequence; fig. 4 (a) and 4 (b) are watermarks extracted from fig. 3 (a) and 3 (b) in order, and normalized cross-correlation coefficient NC values thereof are 1.000 and 1.000, respectively; fig. 5 (a), 5 (b), 5 (c), 5 (d), 5 (e), and 5 (f) show the watermark image shown in fig. 3 (a) sequentially subjected to JPEG (70), JPEG2000 (4:1), median filtering (3×3), gaussian low pass filtering (3×3), salt and pepper noise (0.2%), scaling (400%), and rotation (15) 。 ) The normalized cross-correlation coefficient NC values of the watermarks extracted after the attack are respectively 0.969, 1.000, 0.923, 0.984, 1.000, 0.994 and 0.993; fig. 6 (a), 6 (b), 6 (c), 6 (d), 6 (e), and 6 (f) show the watermark image shown in fig. 3 (b) sequentially subjected to JPEG (70), JPEG2000 (4:1), median filtering (3×3), gaussian lowPass filtering (3 x 3), salt and pepper noise (0.2%), scaling (400%), rotation (15) 。 ) The normalized cross-correlation coefficient NC values of the watermarks extracted after the attack are respectively 0.932, 1.000, 0.860, 0.989, 0.999, 0.989 and 0.996.
The algorithm runs on a platform 1.00GHZ CPU, 16.00GB RAM, win 11 and MATLAB (R2021 a) for nearly ten thousand times, the average embedding time of the digital watermark is 0.3121 seconds, the average extracting time is 0.1341 seconds, and the total time is 0.4462 seconds.
In summary, the embedded color image digital watermark has better invisibility, and meets the invisibility requirement of a watermark algorithm; meanwhile, the color image digital watermark extracted from various attacked images has better authenticability and higher NC value, which indicates that the method has stronger robustness; in addition, the average running total time of the algorithm is less than 1 second, and the requirement of rapid copyright protection of multimedia big data is met.
Detailed Description
The invention aims to provide a blind watermarking algorithm based on Hadamard transformation and a teaching optimization algorithm, which is characterized by being realized through a specific watermarking embedding process and an extracting process, wherein the watermarking embedding process is described as follows:
the first step: digital watermarking a 24-bit color image with 32×32 pixelsDividing into 3 layered watermark images according to the sequence of three primary colors of red, green and blueThe method comprises the steps of carrying out a first treatment on the surface of the Key-based processing of each layered watermark imageAffine transformation encryption of (a); the encrypted layered watermark imageEach decimal number representing a pixel is represented by an 8-bit binary number (e.g., decimal number 156 may be converted to binaryNumber 10011100); the first four bits of every 8 bits binary numbers are sequentially connected to form a length of 4 multiplied by 32 2 Hierarchical watermark bit sequence=4096Simultaneously, the last four bits of every 8-bit binary number are sequentially connected to form a length of 4 multiplied by 32 2 Hierarchical watermark bit sequence=4096Then, according to the formula (1)Compression processing using permuted ordered binaries to obtain sequencesThe compressed length is 3272+6=3278, and the total length of the processed layered watermark sequence is the same as that of the compressed lengthIs that,Respectively representing red, green and blue layers;
（1）
wherein ,in order to obtain the binary sequence after compression,for the sequence number in the binary sequence,expressed in the original binary sequence positionWhere the value, C (deg.) is a function of the number of combinations,representing the length of the binary sequence,(e.g., convert 864 to binary 1101100000,from the slave=0 is added up to=9 is 4 whenWhen=9, the whole 864 indicatesCan be calculated as 202, 202 can be converted into 8-bit binary 11001010);
and a second step of: a color carrier image with 512×512 pixelsDivided into 3 layered carrier images in the order of three primary colors of red, green and blueThe method comprises the steps of carrying out a first treatment on the surface of the At the same time, each layered carrier imageDividing non-overlapping image blocks with the number of pixels of 4 multiplied by 4; from layered watermark bit sequences4096+3272+6=7374, with key-basedMD5 hash pseudoness of (c)Random scrambling algorithm to generate non-repeated block selection sequence in layered carrier image4096+3272+6=7374 image blocks, the first 4096 blocks of which are used for embeddingAfter which 3272+6=3278 blocks are used for embeddingWherein 4096+3272+6<(512×512)/(4×4)，Respectively representing three layers of red, green and blue, wherein floor is a downward rounding function, and mod is a remainder function;
and a third step of: selecting one image block from the first 4096 blocks according to the sequence of the blocksAccording to the formula (2), forHadamard transformation is carried out to obtain a transformed coefficient block matrix；
（2）
wherein ,is thatA rank Hadamard matrix; here, a selected image block is set，Then obtain；
Fourth step: hierarchical watermark bit sequenceIn the method, a bit of watermark information to be embedded is taken out according to the sequenceWill beRepeated embedding into coefficient block matrixFirst three coefficients of the first line of (a)Calculating quantized frequency domain coefficients according to the embedded watermark information and formulas (3) and (4)，，=1, 2, 3 represent red, green, blue three layers, respectively;
（3）
wherein mod (-) is a remainder function, round (-) is a rounding function, xor (-) is an exclusive-or function,represents the judgment threshold in the quantization process, and is set here=900，=890，=879，=‘1’；
（4）
wherein ,to quantize the step size, here, one can obtain=916.9333，= 916.9333，=916.9333；
Fifth step: will beUpdate to its transformed coefficient blockCorresponding positions in the matrix to obtain a coefficient block matrix after watermark embedding，=1, 2, 3, then the inverse transform of the hadamard matrix is achieved by equation (5), resulting in a watermarked image block；
（5）
wherein ,is thatA Hadamard matrix, where；
Sixth step: updating blocks of a watermark-containing image to its layered carrier imageCorresponding positions in (a), wherein=1, 2, 3 represent red, green, blue three layers, respectively;
seventh step: selecting one image block from the selected remaining 3272+6=3278 blocks according to the sequence of the blocksAccording to formula (6), forHadamard transformation is carried out to obtain a transformed coefficient block matrixFloor () is a downward rounding function, mod () is a remainder function;
（6）
wherein ,is thatA rank Hadamard matrix; here, a selected diagram is setImage block matrix，Then obtain；
Eighth step: hierarchical watermark bit sequenceIn the method, a bit of watermark information to be embedded is taken out according to the sequenceWill beEmbedded in a matrix of coefficient blocksFirst coefficient of first lineIn which quantized frequency domain coefficients are calculated according to the embedded watermark information and formulas (7) and (8)，=1, 2, 3 respectively represent red, green, blue three layers, here, set=895，=‘1’；
（7）
Wherein mod (-) is a remainder function and round (-) is a rounding functionThe xor (x.) is an exclusive-or function,representing a judgment threshold value in the quantization process;
（8）
wherein ,to quantize the step size, here, one can obtain=916.9333；
Ninth step: will beUpdate to its transformed coefficient blockCorresponding positions in the matrix to obtain a coefficient block matrix after watermark embeddingThen through formula (9), realizing inverse transformation of Hadamard matrix to obtain image block containing watermark；
（9）
wherein ,is thatA Hadamard matrix, where；
Tenth step: will beImage block containing watermarkUpdate to its in-hierarchical carrier imageCorresponding positions in (a), wherein=1, 2, 3 represent red, green, blue three layers, respectively;
eleventh step: repeating the third to tenth steps until all watermark information is embedded, thereby obtaining layered carrier image containing watermarkThe method comprises the steps of carrying out a first treatment on the surface of the Finally, the layered carrier image containing the watermark is subjected toRecombining and obtaining a water-containing print image with 512×512 pixels；
Twelfth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, error rate and the like, and selecting the optimal quantization step by using a teaching optimization algorithm；
The watermark extraction process is described as follows:
the first step: a water-containing print image with 512×512 pixelsDividing into 3 layered watermark-containing imagesAnd each layered watermark-containing imageFurther dividing the number of pixels into 4×4 non-weightsStacking image blocks, wherein=1, 2, 3 represent red, green, blue three layers, respectively;
and a second step of: layered aqueous print imageIn using the key-based mentioned in the watermark embedding processSelecting image blocks by MD5 hash pseudo-random scrambling algorithm of (2), whereinRespectively representing red, green and blue layers;
and a third step of: selecting one image block from the first 4096 blocks according to the sequence of the blocksAccording to the formula (10), forCarrying out Hadamard transformation to obtain a transformed coefficient block matrix;
（10）
wherein ,is thatThe Hadamard matrix is selected to obtain the image block containing watermark，Then obtain=916.9332，=916.9332，=916.9332；
Fourth step: optimum quantization step size selected by teaching optimization algorithmExtracting a coefficient block matrix according to the formulas (11), (12)Watermark contained in the document；
（11）
wherein ,information representing the extracted watermark, mod (i.e.) being a remainder function, fix (i.e.) being a rounding function in the near zero direction,=1, 2, 3, where, one can obtain=1，=1，=1；
（12）
wherein ,representation ofThe mid-watermark is the number of '1',representation ofThe number of mid-watermarks is '0',representing the final extracted watermark value, where it is available=3，=0，=1；
Fifth step: selecting one image block from the selected remaining 3272+6=3278 blocks according to the sequence of the blocksAccording to formula (13), forHadamard transformation is carried out to obtain a transformed coefficient block matrix；
（13）
wherein ,is thatThe Hadamard matrix is selected to obtain the image block containing watermark，Then obtain=916.9332；
Sixth step: optimum quantization step size selected by teaching optimization algorithm=52.9, extracting the coefficient block matrix according to equation (14)Watermark contained in the document；
（14）
wherein ,information representing the extracted watermark mod (i.e., mod) is a remainder function, fix (i.e., fix) is a near zero rounding function, where it is available=1；
Seventh step: repeatedly executing the third step to the sixth step of the process to obtain the binary watermark bit sequence of each layer
And (3) withWatermark information using improved reverse permutation ordered binary algorithm simultaneouslyRecovering; then according to the segmentation process of 8-bit binary information, the methodEvery 4 bits of binary information in (a)Every 4 bits of binary information in a set of decimal-converted pixel values, wherein=1, 2, 3 represent red, green, blue three layers, respectively;
eighth step: performing key-based on the transformed encrypted layered watermark imageDecryption operation of inverse affine transformation and obtaining an extracted layered watermark image, wherein =1, 2, 3 represent red, green, blue three layers, respectively;
ninth step: combining layered watermark imagesObtaining a complete extracted watermark, wherein =1, 2, 3 represent three layers of red, green, and blue, respectively.
According to the influence degree of different positions on watermark pixels, watermark information is embedded by different methods; under the condition of keeping the embedded information unchanged, the embedded amount is reduced, and the real-time performance of the algorithm is improved; meanwhile, the parameters of the watermark algorithm are optimized by using an artificial intelligent algorithm, so that the time required for optimization is reduced, the effect of the algorithm is improved, and the algorithm meets the requirements of invisibility, robustness, instantaneity, safety and watermark capacity.
Claims (1)
1. The blind watermarking algorithm based on Hadamard transformation and teaching optimization algorithm is characterized by being realized through a specific watermarking embedding process and an extraction process, wherein the watermarking embedding process is described as follows:
the first step: the number of pixels is one24-bit color image digital watermark->Dividing into 3 layered watermark images according to the sequence of three primary colors of red, green and blue>The method comprises the steps of carrying out a first treatment on the surface of the Each layered watermark image is subjected to a key-based +.>Affine transformation encryption of (a); the encrypted layered watermark image ++>The pixels represented by each decimal number in (a) are represented by 8-bit binary numbers; the first four digits of every 8 digits binary numbers are sequentially connected to form a length of +.>Is->Simultaneously, the last four digits of every 8 digits binary numbers are sequentially connected to form a length of +.>Is->Then, according to formula (1)/(I)>Compression treatment using permutation ordered binary system to obtain the sequence +.>The length after compression isAt this time, the total length of the processed layered watermark sequence +.>Is that,/>Respectively representing three layers of red, green and blue, wherein floor is a downward rounding function, and mod is a remainder function;
（1）
wherein ,for the binary sequence obtained after compression, +.>For sequence numbers in the binary sequence, +.>Expressed in the original binary sequence position +.>The value at C (-) is a function of the number of combinations, ">Representing the length of the binary sequence, < >>；
And a second step of: the number of pixels is oneColor carrier image->Dividing into 3 layered carrier images according to the order of three primary colors of red, green and blue>The method comprises the steps of carrying out a first treatment on the surface of the At the same time, each layered carrier image +.>The number of the divided pixels is +.>Is a non-overlapping image block of (1); according to the layered watermark bit sequence->Is>Using keysThe MD5 hash pseudo-random scrambling algorithm of (2) generates a non-repeated block selection sequence in the layered carrier image +.>Is selected in (a)Image blocks, before->The blocks are used for embedding->ThereafterThe blocks are used for embedding->, wherein ，/>Respectively representing three layers of red, green and blue, wherein floor is a downward rounding function, and mod is a remainder function;
and a third step of: before choosingIn the blocks, an image block is selected according to the sequence of the blocks>According to the formula (2), forHadamard transform is carried out to obtain a transformed coefficient block matrix +.>；
（2）
wherein ,is->A rank Hadamard matrix;
fourth step: hierarchical watermark bit sequenceIn which a bit of watermark information to be embedded is taken out in succession>Will->Repeated embedding into coefficient block matrix>The first three coefficients of the first row +.>Calculating quantized frequency domain coefficients according to the embedded watermark information and formulas (3) and (4)>，/>，/>=1, 2, 3 represent red, green, blue three layers, respectively;
（3）
wherein mod (-) is a remainder function, round (-) is a rounding function, xor (-) is an exclusive-or function,representing a judgment threshold value in the quantization process;
（4）
wherein ,is the quantization step length;
fifth step: will beUpdate to its transformed coefficient block +.>Corresponding positions in (a) to obtain a matrix of coefficient blocks after embedding the watermark +.>，/>=1, 2, 3, then the inverse transformation of the hadamard matrix is achieved by equation (5), resulting in a watermarked image block +.>；
（5）
wherein ,is->A rank Hadamard matrix;
sixth step: image block containing water markUpdate to its layered carrier image +.>Corresponding position in (a)/(b)>=1, 2, 3 represent red, green, blue three layers, respectively;
seventh step: at the selected restIn the blocks, an image block is selected according to the sequence of the blocks>According to formula (6), for->Hadamard transform is carried out to obtain a transformed coefficient block matrix +.>Floor () is a downward rounding function, mod () is a remainder function;
（6）
wherein ,is->A rank Hadamard matrix;
eighth step: hierarchical watermark bit sequenceIn which a bit of watermark information to be embedded is taken out in succession>Will->Embedded in coefficient block matrix->First coefficient of first line->In which quantized frequency domain coefficients are calculated based on the embedded watermark information and formulas (7) and (8)>，/>=1, 2, 3 represent red, green, blue three layers, respectively;
（7）
wherein mod (-) is a remainder function, round (-) is a rounding function, xor (-) is an exclusive-or function,representing a judgment threshold value in the quantization process;
（8）
wherein ,is the quantization step length;
ninth step: will beUpdate to its transformed coefficient block +.>Corresponding positions in (a) to obtain a matrix of coefficient blocks after embedding the watermark +.>Then, through the formula (9), the inverse transformation of the Hadamard matrix is realized, and the image block containing the watermark is obtained>；
（9）
wherein ,is->A rank Hadamard matrix;
tenth step: image block containing water markUpdate to its layered carrier image +.>Corresponding position in (a)/(b)>=1, 2, 3 represent red, green, blue three layers, respectively;
eleventh step: repeating the third to tenth steps until all watermark information is embedded, thereby obtaining layered carrier image containing watermarkThe method comprises the steps of carrying out a first treatment on the surface of the Finally, the layered carrier image with watermark is +.>Recombination and obtaining the number of pixels +.>Is->；
Twelfth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, error rate and the like, and selecting the optimal quantization step by using a teaching optimization algorithm；
The watermark extraction process is described as follows:
the first step: the number of pixels is set to beIs->Division into 3 layered watermark-containing images>And each layered watermark-containing image +.>The number of the further divided pixels is +.>Is a non-overlapping image block of (1), wherein->=1, 2, 3 represent red, green, blue three layers, respectively;
and a second step of: layered aqueous print imageIn using the key-based +.>Selecting image blocks by MD5 hash pseudo-random scrambling algorithm of (2), wherein +.>Respectively representing red, green and blue layers;
and a third step of: before choosingIn the blocks, an image block is selected according to the sequence of the blocks>According to formula (10), for->Hadamard transform is carried out to obtain a transformed coefficient block matrix +.>；
（10）
wherein ,is->A rank Hadamard matrix;
fourth step: optimum quantization step size selected by teaching optimization algorithmExtracting the coefficient block matrix ++according to the formula (11), (12)>Watermark->；
（11）
wherein ,information representing the extracted watermark mod (& gt) is a remainder function, fix (& gt) is a rounding function in a direction close to zero, & lt/h>=1, 2, 3；
（12）
wherein ,representation->The watermark is the number '1'>Representation->The number of watermark '0' in +.>Representing the final extracted watermark value;
fifth step: at the selected restIn the blocks, an image block is selected according to the sequence of the blocks>According to formula (13), for->Hadamard transform is carried out to obtain a transformed coefficient block matrix +.>；
（13）
wherein ,is->A rank Hadamard matrix;
sixth step: optimum quantization step size selected by teaching optimization algorithmExtracting a coefficient block matrix according to formula (14)Watermark->；
（14）
wherein ,information representing the extracted watermark, mod (.) being a remainder function, fix (.) being a near zero rounding function;
seventh step: repeatedly executing the third step to the sixth step of the process to obtain the binary watermark bit sequence of each layer
And->Watermark information is simultaneously +.>Recovering; then according to the segmentation process of 8-bit binary information +.>Every 4 bits of binary information and +.>Every 4 bits of binary information in (1) is converted into a set of pixel values converted into decimal, wherein +.>=1, 2, 3 represent red, green, blue three layers, respectively;
eighth step: performing key-based on the transformed encrypted layered watermark imageDecryption operation of inverse affine transformation and obtaining an extracted layered watermark image +.>, wherein />=1, 2, 3 represent red, green, blue three layers, respectively;
ninth step: combining layered watermark imagesObtaining the complete extracted watermark->, wherein />=1, 2, 3 represent three layers of red, green, and blue, respectively.
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