CN115510404A - Fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm - Google Patents
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Abstract
The invention discloses a fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm by combining the advantages of high operation speed of a space domain digital watermarking algorithm and high robustness of the frequency domain digital watermarking algorithm. According to the characteristics of data correlation removal of image transformation and the characteristics of an optimal solution obtained by combining a particle swarm optimization algorithm, a first frequency domain coefficient of an image block after image transformation is obtained in a space domain, then the coefficient is utilized to complete embedding and blind extraction of a digital watermark in the space domain, and finally the particle swarm optimization algorithm is utilized to optimize so as to select an optimal quantization step. The invention can embed the color image digital watermark into the color host image, not only has better watermark concealment and stronger robustness, but also has better real-time property and safety, solves the problem of low running speed of the large-capacity color image digital watermark, and is suitable for the occasion of quickly, efficiently and safely carrying out digital media copyright protection.
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
With the advent of the era of digitization, networking and informatization, the transmission quantity of digital multimedia information such as color digital images and the like is exponentially increased, and a series of digital infringement problems such as piracy, tampering and the like are generated under the increasingly complex network background, so that the related copyright protection problem is gradually concerned by scholars at home and abroad. On the one hand, copyright protected logos tend to be color images that are aesthetically practical and have a high information content; on the other hand, with the wide popularization of mobile terminal devices and the gradual upgrade of hardware configuration, people seek faster and more efficient working efficiency, and a single frequency domain watermarking algorithm with longer running time is difficult to meet the application requirements of people. Therefore, there is a need to further increase the operating speed of information volume digital watermarking algorithms. In addition, the digital watermarking algorithm also comprises a simple and efficient spatial domain digital watermarking algorithm according to different working domains of the carrier image, but the digital watermarking algorithm has the defect of weak robustness. Therefore, by combining the respective advantages of the spatial domain digital watermarking algorithm and the frequency domain digital watermarking algorithm, on the basis of ensuring the invisibility of the watermark and the robustness of the algorithm, the method for designing the color image digital watermarking with high real-time performance and high safety becomes one of the key points and difficulties of the current digital watermarking technical research.
Disclosure of Invention
The invention aims to provide a fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm, which is characterized by being realized by a specific watermark embedding process and an extracting process, wherein the watermark embedding process is described as follows:
the first step is as follows: firstly, a frame is counted asN×N24-bit color image digital watermarkWDividing into 3 layered watermark images according to the sequence of red, green and blue three primary colorsW i (ii) a Then, each layered watermark image is subjected to key-based watermarkingKa i ，Kb i ，Kc i The fractional order Chen type chaotic mapping is encrypted; finally, the encrypted layered watermark image is processedW i ’Each decimal number in the decimal system is represented by 8-bit binary number and is connected in sequence to form a length of 8N 2 Hierarchical watermark bit sequence ofSW i Wherein the secret keyKa i ，Kb i ，Kc i Is randomly generated by the asymmetric cryptographic algorithm RSA,i=1, 2, 3 pointsRespectively showing three layers of red, green and blue;
the second step is that: one pixel is counted asM×MColor carrier image ofCDividing into 3 layered carrier images according to the sequence of red, green and blue three primary colorsC i (ii) a Simultaneously, each layered carrier image is putC i Divided into pixels ofm×mThe non-overlapping image blocks of (1); based on a hierarchical watermark bit sequenceSW i Length 8 ofN 2 Using a key-basedKd i The MD5 Hash pseudorandom scrambling algorithm generates non-repetitive block selection sequences in the layered carrier imageC i To achieve the embedding position randomization and thus improve the robustness of the watermark against shearing attacks, wherein 8N 2 <=(M×M)/(m×m)，i=1, 2, 3 respectively represent red, green, blue three layers;
the third step: selecting an image blockBAnd directly calculating the first frequency domain coefficient after graph transformation in the spatial domain according to the formula (1)G 1,1 ；
Wherein the content of the first and second substances,mis an image blockBThe number of the side length pixels of (a),B(x, y) Representing image blocksBFirst, thexGo to the firstyPixel values of the columns;
the fourth step: from hierarchical watermark bit sequencesSW i In which one bit of watermark information to be embedded is taken out in sequencewCalculating the first quantized frequency domain coefficient according to the embedded watermark information and the formulas (2), (3) and (4)G * 1,1 ；
Where mod () is a remainder function, abs () is an absolute value function,Tin order to quantize the step size,δis the scaling factor that is used to scale the image,i=1, 2, 3 respectively represent red, green, blue three layers;
the fifth step: using the formulas (5) and (6), the variation of the first frequency domain coefficient before and after quantization is determinedchangeAmplification ofmMultiplied evenly distributed to the image blockBAll the pixels of the image block can obtain the image block containing the watermarkB * ；
Wherein the content of the first and second substances,
and is the amount of change in the first frequency domain coefficient,mis an image blockBThe number of side length pixels, round (.) is a rounding function,deltfis the average modifier of the pixel values,B * (x, y) Representing blocks containing watermarkB * First, thexGo to the firstyPixel values of the columns;
and a sixth step: considering that the pixel value range is between 0 and 255, the simple addition and subtraction of the pixel value can cause the pixel out-of-range phenomenon, so that the extraction of the watermark bit is wrong, the scheme is optimized, and the pixel value is adjustedB(x, y) The modification of (b) is discussed in three cases, namely:
(1) When there is no overflow, i.e. if
Modifying the pixel at the corresponding position according to the formula (6);
wherein abs (. Eta.) is an absolute value function, min (. Eta.) is a minimum function, max (. Eta.) is a maximum function, round (. Eta.) is a rounding function,deltfis the average modifier of the pixel values;
(2) When an underflow condition occurs, i.e.
If, if
Then will be
The average is assigned to the minimum pixel value as shown in equation (7);
wherein, min (.) is a function of taking the minimum value,B(m 1 , n 1 ) Is composed ofBIs determined by the minimum pixel value of (c), (ii) (m 1 , n 1 ) Round (.) is a rounding function where the minimum pixel value is located,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num1 is the number of minimum pixel values; otherwise, the pixel of the corresponding position is modified according to the formula (8);
where round (.) is a rounding function,deltfis the average modifier of the pixel values,Tis a quantization step size;
(3) When an overflow condition occurs, i.e.
If it is determined that
Then will be
The average is assigned to the maximum pixel value as shown in equation (9):
wherein max (. Eta.) is a function of taking the maximum value, round (. Eta.) is a function of rounding off the integer,B(m 2 ,n 2 ) In order to be the maximum pixel value of the pixel, (ii) (m 2 , n 2 ) Is the position where the maximum pixel value is located,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num2 is the number of maximum pixel values; otherwise, the pixel modification of the corresponding position is as shown in equation (10)
Where round (.) is a rounding function,deltfis the average modifier of the pixel values,Tis a quantization step size;
the seventh step: image block containing watermarkB * Updated to its on-layer carrier imageC i In a corresponding position in (b), whereini=1, 2, 3 respectively represent red, green, blue three layers;
eighth step: repeating the third to seventh steps until all watermark information is embedded, thereby obtaining a layered carrier image containing watermarkC i * (ii) a Finally, the layered carrier image containing the watermark is processedC i * Recombining and obtaining pixelsThe number isM×MAqueous printed image ofC * ；
The ninth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross correlation coefficient, bit error rate and the like, and selecting the optimal quantization step length by utilizing a particle swarm optimization algorithmT opt ；
The tenth step: pairing and encrypting the important parameters in the steps by using a Comptor pairing function shown in formula (11) to generate a large integer key, wherein the important parameters comprise the optimal quantization step sizeT opt Image block sizem；
Wherein the content of the first and second substances,Ψas a function of the Comtor pairingCantorPairThe generated non-negative large integer is not negative,aandbrespectively two numbers to be paired,ais initially ofT opt ，bIs initially ofm；
The watermark extraction process is described as follows:
the first step is as follows: using inverse Cortor pairing function shown in formulas (12) and (13) to pair large integersΨDecrypting to obtain decrypted important parameters;
wherein the content of the first and second substances,
，
floor (.) is a floor rounding function, sqrt: (For a function of the absolute value,a * is the optimal quantization stepT opt ，b * The final value of (a) is the image block sizem；
The second step is that: the number of pixels is equal toM×MOf (2) a water-marked imageC * Divided into 3 layers containing watermark imagesC i * And each layer is provided with a watermark imageC i * Further divided into a number of pixelsm×mOf non-overlapping image blocks, whereini=1, 2, 3 respectively represent red, green, blue three layers;
the third step: in-layer water-printed imageC i * By using the key-based key mentioned in the above watermark embedding processKd i Selecting an image block by using an MD5 Hash pseudorandom scrambling algorithm;
the fourth step: selecting a block containing watermarkB * The first frequency domain coefficient obtained by graph transformation is directly calculated in the space domain by using the formula (14)G * 1,1 ；
Wherein the content of the first and second substances,mis a water-marked image blockB * The number of the side length pixels of (a),B * (x, y) Water-bearing image blockB * In the first placexGo to the firstyPixel values of the columns;
the fifth step: the optimal quantization step size selected by using the formula (15) and the particle swarm optimization algorithmT opt Extracting the block containing the watermarkB * Watermark contained thereinw * ；
Wherein the content of the first and second substances,G * 1,1 for containing watermark image blocksB * A first frequency domain coefficient obtained by map transformation, mod (.) is a residue taking function;
and a sixth step: repeatedly executing the fourth step and the fifth step of the process, and extracting the binary watermark bit sequence of each layerSW i ’Then each 8-bit binary information is converted into a decimal pixel value as a group, whereini=1, 2, 3 respectively represent red, green, blue three layers;
the seventh step: key-based execution of transformed encrypted layered watermark imagesKa i ，Kb i ，Kc i Fractional order Chen type chaotic decryption operation and acquisition of extracted layered watermark imageW i * In whichi=1, 2, 3 respectively represent red, green, blue three layers;
eighth step: combining extracted layered watermark imagesW i * Forming a final extracted watermark imageW * Whereini=1, 2, 3 represents red, green, blue trilayer, respectively.
The method utilizes the characteristic of removing data correlation by graph transformation, completes the embedding and blind extraction of the color digital watermark by a space domain fast calculation method for obtaining a first frequency domain coefficient and the distribution rule of the coefficient variable quantity in space domain pixels, and determines the optimal quantization step size in the space domain by using a particle swarm optimization algorithm; the method has the advantages of good invisibility, strong robustness, high real-time performance and high safety.
Drawings
Fig. 1 (a) and 1 (b) show two original color carrier images.
Fig. 2 (a) and 2 (b) show two original color watermark images.
Fig. 3 (a) and 3 (b) show watermark images obtained by embedding fig. 2 (a) into the carrier image fig. 1 (a) and fig. 2 (b) into the carrier image fig. 1 (b), respectively, and the structural similarity SSIM values are 0.954 and 0.973 in this order, and the peak signal-to-noise ratio PSNR values are 40.050dB and 40.660dB in this order.
Fig. 4 (a) and 4 (b) show watermarks extracted from fig. 3 (a) and 3 (b) in this order, and normalized cross-correlation coefficients NC thereof are 1.000 and 1.000, respectively.
Fig. 5 (a), 5 (b), 5 (c), 5 (d), 5 (e), and 5 (f) show watermarks extracted after the watermark-containing image shown in fig. 3 (a) is subjected to attacks such as JPEG (70), JPEG2000 (4).
Fig. 6 (a), 6 (b), 6 (c), 6 (d), 6 (e), and 6 (f) are watermarks extracted after the watermark image shown in fig. 3 (b) is subjected to attacks such as JPEG (70), JPEG2000 (4).
Detailed Description
The invention aims to provide a fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm, which is characterized by being realized by a specific watermark embedding process and an extracting process, wherein the watermark embedding process is described as follows:
the first step is as follows: firstly, a 24-bit color image digital watermark with 32 x 32 pixels is appliedWDividing into 3 layered watermark images according to the sequence of red, green and blue three primary colorsW i (ii) a Then, each layered watermark image is subjected to key-based watermarkingKa i ，Kb i ，Kc i The fractional order Chen type chaotic mapping is encrypted; finally, the encrypted layered watermark image is processedW i ’Each decimal number represented pixel in (a) is represented by an 8-bit binary number (e.g., decimal number 156 may be converted to binary number 10011100) and connected in sequence to form a length of 8 x 32 2 =8192 layered watermark bit sequenceSW i Wherein the secret keyKa i ，Kb i ，Kc i By asymmetric encryptionThe algorithm RSA is generated randomly and,i=1, 2, 3 respectively represent red, green, blue three layers;
the second step is that: a color carrier image with 512 x 512 pixels is formedCDividing into 3 layered carrier images according to the sequence of red, green and blue three primary colorsC i (ii) a Simultaneously, each layered carrier image is putC i Dividing the image into image blocks with the pixel number of 4 multiplied by 4; based on a hierarchical watermark bit sequenceSW i Length of 8X 32 2 =8192, using a key-based keyKd i The MD5 Hash pseudo-random scrambling algorithm generates non-repeated block selection sequences on the layered carrier imagesC i The image blocks at proper positions are selected to realize the randomization of the embedding positions, thereby improving the robustness of the watermark against the shearing attack, wherein 8 is multiplied by 32 2 <(512×512)/(4×4)，i=1, 2, 3 respectively represent red, green, blue three layers;
the third step: selecting an image blockBAnd directly calculating the first frequency domain coefficient after graph transformation in the space domain according to the formula (1)G 1,1 ；
Wherein, the first and the second end of the pipe are connected with each other,mis an image blockBThe number of the side length pixels of (a),B(x, y) Representing image blocksBFirst, thexGo to the firstyPixel values of the columns; here, the selected image block is set
，m=4, then obtainG 1,1 =892；
The fourth step: from a hierarchical watermark bit sequenceSW i In which one bit of watermark information to be embedded is taken out in sequencewCalculating the first quantized frequency domain coefficient according to the embedded watermark information and the formulas (2), (3) and (4)G * 1,1 ；
Wherein mod () is a remainder function, abs () is an absolute value function,Tin order to quantize the step size,δis the scaling factor that is used to scale the image,i=1, 2, 3 represents red, green, blue trilayer respectively; here, letG 1,1 =892，w=’1’，T=46，δ=0.25, thenG upper =908.5，G lower =862.5，G * 1,1 =908.5；
The fifth step: using the formulas (5) and (6), the variation of the first frequency domain coefficient before and after quantization is adjustedchangeAmplification ofmIs uniformly distributed to the image blockBAll the pixels of the image block can obtain the image block containing the watermarkB * ；
Wherein the content of the first and second substances,
and is the amount of change in the first frequency domain coefficient,mis an image blockBThe number of the side length pixels of (a),deltfround (.) is a rounding function for the average modifier of pixel values; here, letG 1,1 =892，G * 1,1 =908.5，m=4, then obtainchange=16.5，deltf=4.125, water print image block
；
And a sixth step: considering that the pixel value range is between 0 and 255, the simple addition and subtraction of the pixel value can cause the pixel out-of-range phenomenon, so that the extraction of the watermark bit is wrong, the scheme is optimized, and the pixel value is adjustedB(x, y) The modifications of (c) are discussed in three cases:
(1) When there is no overflow, i.e. if
Modifying the pixel at the corresponding position according to the formula (6);
wherein abs (. Eta.) is an absolute value function, min (. Eta.) is a minimum function, max (. Eta.) is a maximum function, round (. Eta.) is a rounding function,deltfis the average modifier of the pixel values;
(2) When an underflow condition occurs, i.e.
If it is determined that
Then will be
The average is assigned to the minimum pixel value as shown in equation (7):
wherein, min (.) is a minimum function,B(m 1 , n 1 ) Is composed ofBIs determined by the minimum pixel value of (c), (ii) (m 1 , n 1 ) Round (.) is a rounding function for the location of the minimum pixel value,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num1 is the number of minimum pixel values; otherwise, the pixel of the corresponding position is modified according to the formula (8);
wherein round (.) is a rounding function,deltfis the average modifier of the pixel values, Tis the quantization step size;
(3) When an overflow condition occurs, i.e.
If, if
Then will be
The average is assigned to the maximum pixel value as shown in equation (9):
wherein max (. Eta.) is a function of taking the maximum value, round (. Eta.) is a function of rounding off the integer,B(m 2 , n 2 ) In order to be the maximum pixel value of the pixel, (ii) (m 2 ,n 2 ) Is the position where the maximum pixel value is located,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num2 is the number of maximum pixel values; otherwise, the pixel modification of the corresponding position is as shown in equation (10)
Wherein round (.) is a rounding function,deltfis likeThe average modifier of the values of the elements, Tis the quantization step size; here, the selected image block
，T=46，deltf=4.125, no overflow problem exists in each pixel value of the image block after calculation, and the image block containing water printing can be obtained in the case of (1)
；
The seventh step: image block containing watermarkB * Update to its on-layer carrier imageC i In a corresponding position in (b), whereini=1, 2, 3 represents red, green, blue trilayer respectively;
eighth step: repeating the third to seventh steps until all watermark information is embedded, thereby obtaining a layered carrier image containing watermarkC i * (ii) a Finally, the layered carrier image containing the watermark is processedC i * Recombined and obtained water-containing printed image with 512 x 512 pixelsC * ；
The ninth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross correlation coefficient, bit error rate and the like, and selecting the optimal quantization step length by utilizing a particle swarm optimization algorithmT opt (ii) a Here, the selected optimal quantization step size is setT opt =46；
The tenth step: pairing and encrypting the important parameters in the steps by using a Comtor pairing function shown in formula (11) to generate a large integer key, wherein the important parameters comprise an optimal quantization step sizeT opt Image block sizem；
Wherein, the first and the second end of the pipe are connected with each other,Ψas a function of the Comtor pairingCantorPairThe generated non-negative large integer is not negative,aandbare respectively ready to be preparedTwo numbers of pairs;ais initially ofT opt ，bIs initially ofm(ii) a Here, leta=T opt =46，b=m=4, then obtainΨ=1279；
The watermark extraction process is described as follows:
the first step is as follows: using inverse Cortor pairing function shown in formulas (12) and (13) to pair large integersΨDecrypting to obtain decrypted important parameters;
wherein, the first and the second end of the pipe are connected with each other,
，
floor (.) is a floor function, sqrt (.) is an absolute value function,a * is the optimal quantization stepT opt ，b * The final value of (a) is the image block sizem(ii) a Here, letΨ=1279, then get
，
，b * =4，a * =46；
The second step: the water-containing print image with the number of pixels of 512 x 512C * Divided into 3 layered images containing watermarksC i * And each layer is provided with a watermark imageC i * Is further divided intoNon-overlapping image blocks of 4 x 4 pixels, whereini=1, 2, 3 represents red, green, blue trilayer respectively;
the third step: in layered water-bearing printed imageC i * By using the key-based key mentioned in the above watermark embedding processKd i Selecting an image block by using the MD5 Hash pseudorandom scrambling algorithm;
the fourth step: selecting a block of a watermarked imageB * The first frequency domain coefficient obtained by graph transformation is directly calculated in the space domain by using the formula (14)G * 1,1 ；
Wherein the content of the first and second substances,mis a block containing watermarkB * The number of the side length pixels of (a),B * (x, y) Water-bearing image blockB * In the first placexGo to the firstyPixel values of the columns; here, it is designed to select image blocks containing watermarks
，m=4, thenG * 1,1 =908；
The fifth step: the optimal quantization step size selected by using the formula (15) and the particle swarm optimization algorithmT opt Extracting the block containing the watermarkB * Watermark contained thereinw * ；
Wherein, the first and the second end of the pipe are connected with each other,G * 1,1 for water-containing printed image blocksB * The first frequency domain coefficient obtained by the map transform, mod () is a residue taking function,i=1, 2, 3 represents red, green, blue trilayer respectively; here, an optimal quantization step size is setT opt =46, availablew * =’1’；
And a sixth step: repeatedly executing the fourth step and the fifth step of the process, and extracting the binary watermark bit sequence of each layerSW i ’Then each 8-bit binary information is converted into a decimal pixel value as a group, whereini=1, 2, 3 respectively represent red, green, blue three layers;
the seventh step: performing key-based encryption of transformed encrypted layered watermark imagesKa i ，Kb i ，Kc i Fractional order Chen type chaotic decryption operation and acquisition of extracted layered watermark imageW i * In whichi=1, 2, 3 respectively represent red, green, blue three layers;
eighth step: combining extracted layered watermark imagesW i * Forming a final extracted watermark imageW * In whichi=1, 2, 3 represents red, green, blue trilayer respectively;
the method utilizes the characteristic of removing data correlation by graph transformation, completes the embedding and blind extraction of the color digital watermark by a space domain fast calculation method for obtaining a first frequency domain coefficient and the distribution rule of the coefficient variable quantity in space domain pixels, and determines the optimal quantization step size in the space domain by using a particle swarm optimization algorithm; the method has the advantages of good invisibility, strong robustness, high real-time performance and high safety.
Validation of the invention
In order to prove the effectiveness of the invention, two 24-bit standard images with the pixel size of 512 × 512 as shown in fig. 1 (a) and 1 (b) are selected as carrier images, and two 24-bit color images with the pixel size of 32 × 32 as shown in fig. 2 are respectively used as digital watermarks for verification.
Fig. 3 (a) and 3 (b) are watermark-containing images obtained by embedding the watermarks shown in fig. 2 (a) and 2 (b) into the carrier images such as fig. 1 (a) and 1 (b), respectively, and the structural similarity SSIM values are 0.954 and 0.973, respectively, and the peak signal-to-noise ratio PSNR values are 40.050dB and 40.660dB, respectively; fig. 4 (a) and 4 (b) show watermarks extracted from fig. 3 (a) and 3 (b) in sequence, and normalized cross-correlation coefficients NC of the watermarks are 1.000 and 1.000, respectively; fig. 5 (a), 5 (b), 5 (c), 5 (d), 5 (e), and 5 (f) are watermarks extracted after the watermark image shown in fig. 3 (a) is subjected to attacks such as JPEG (70), JPEG2000 (4); fig. 6 (a), 6 (b), 6 (c), 6 (d), 6 (e), and 6 (f) show watermarks extracted after the watermark-containing image shown in fig. 3 (b) is subjected to attacks such as JPEG (70), JPEG2000 (4).
The algorithm is run on platforms 2.00GHZ CPU, 16.00GB RAM, win 10 and MATLAB (R2021 b) for nearly ten thousand times, the average embedding time of the digital watermark is 0.7284 seconds, the average extraction time is 0.1374 seconds, and the total time is 0.8658 seconds.
In conclusion, the embedded digital watermark of the color image has better invisibility, and the invisibility requirement of a watermark algorithm is met; meanwhile, the color image digital watermarks extracted from various attacked images have good identifiability and high NC values, which shows that the method has strong robustness; in addition, the average running total time of the algorithm is less than 1 second, and the requirement of the multimedia big data on quick copyright protection is met.
Claims (1)
1. A fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm is characterized in that the method is realized through a specific watermark embedding process and an extraction process, and the watermark embedding process is described as follows:
the first step is as follows: firstly, a frame is counted asN×N24-bit color image digital watermarkWDividing into 3 layered watermark images according to the sequence of red, green and blue three primary colorsW i (ii) a However, the device is not limited to the specific type of the deviceThen, each layered watermark image is subjected to key-based watermarkingKa i ，Kb i ，Kc i The fractional order Chen type chaotic mapping is encrypted; finally, the encrypted layered watermark image is processedW i ’Each decimal number in the decimal system is represented by 8-bit binary number and is connected in sequence to form a length of 8N 2 Hierarchical watermark bit sequence ofSW i Wherein the secret keyKa i ，Kb i ，Kc i Is randomly generated by the asymmetric cryptographic algorithm RSA,i=1, 2, 3 represents red, green, blue trilayer respectively;
the second step: one pixel is counted asM×MColor carrier image ofCDividing into 3 layered carrier images according to the sequence of red, green and blue three primary colorsC i (ii) a Simultaneously, each layered carrier imageC i Divided into pixels ofm×mThe non-overlapping image blocks of (1); based on a hierarchical watermark bit sequenceSW i Length 8 ofN 2 Using a key-based keyKd i The MD5 Hash pseudorandom scrambling algorithm generates non-repetitive block selection sequences in the layered carrier imageC i To realize the randomization of the embedding position, and 8, to improve the robustness of the watermark against shearing attackN 2 <=(M×M)/(m×m)，i=1, 2, 3 respectively represent red, green, blue three layers;
the third step: selecting an image blockBAnd directly calculating the first frequency domain coefficient after graph transformation in the space domain according to the formula (1)G 1,1 ；
Wherein the content of the first and second substances,mis an image blockBThe number of the side length pixels of (a),B(x, y) Representing image blocksBFirst, thexGo to the firstyPixel values of the columns;
the fourth step: from a hierarchical watermark bit sequenceSW i In which one bit of watermark information to be embedded is taken out in sequencewCalculating the first quantized frequency domain coefficient according to the embedded watermark information and the formulas (2), (3) and (4)G * 1,1 ；
Where mod () is a remainder function, abs () is an absolute value function,Tin order to quantize the step size,δis the scaling factor that is used to scale the image,i=1, 2, 3 respectively represent red, green, blue three layers;
the fifth step: using the formulas (5) and (6), the variation of the first frequency domain coefficient before and after quantization is determinedchangeAmplification ofmMultiplied evenly distributed to the image blockBAll the pixels of the image block can obtain the image block containing the watermarkB * ；
Wherein the content of the first and second substances,
and is the amount of change in the first frequency domain coefficient,mfor image blocksBThe number of side length pixels, round (.) is a rounding function,deltfis the average modifier of the pixel values,B * (x, y) Representing blocks containing watermarkB * First, thexGo to the firstyPixel values of the columns;
and a sixth step: considering that the pixel value range is between 0 and 255, the simple addition and subtraction of the pixel value can cause the pixel out-of-range phenomenon, so that the extraction of the watermark bit is wrong, the scheme is optimized, and the pixel value is adjustedB(x, y) The modifications of (c) are discussed in three cases:
(1) When there is no overflow, i.e. if
Modifying the pixel at the corresponding position according to the formula (6);
wherein abs (. Eta.) is an absolute value function, min (. Eta.) is a minimum function, max (. Eta.) is a maximum function, round (. Eta.) is a rounding function,deltfis the average modifier of the pixel values;
(2) When underflow conditions occur, i.e.
If it is determined that
Then will be
The average is assigned to the minimum pixel value as shown in equation (7);
wherein, min (.) is a minimum function,B(m 1 , n 1 ) Is composed ofBMinimum pixel value of (a), (b), (c)m 1 , n 1 ) Round (.) is a rounding function where the minimum pixel value is located,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num1 is the number of minimum pixel values; otherwise, the pixel of the corresponding position is modified according to the formula (8);
wherein round (.) is a rounding function,deltfis the average modifier of the pixel values,Tis a quantization step size;
(3) When an overflow condition occurs, i.e.
If, if
Then will be
The average is assigned to the maximum pixel value as shown in equation (9):
wherein max (. Eta.) is a function of taking the maximum value, round (. Eta.) is a function of rounding off the integer,B(m 2 ,n 2 ) Is the maximum pixel value: (a)m 2 , n 2 ) Is the position where the maximum pixel value is located,deltfis the average modifier of the pixel values,Tin order to quantize the step size,num2 is the number of maximum pixel values; otherwise, the pixel of the corresponding position is modified as the formula(10) Shown in (a)
Where round (.) is a rounding function,deltfis the average modifier of the pixel values,Tis the quantization step size;
the seventh step: image block containing watermarkB * Update to its on-layer carrier imageC i In a corresponding position in (b), whereini=1, 2, 3 represents red, green, blue trilayer respectively;
eighth step: repeating the third to seventh steps until all watermark information is embedded, thereby obtaining a layered carrier image containing watermarkC i * (ii) a Finally, the layered carrier image containing the watermark is processedC i * Recombining and obtaining a pixel number ofM×MAqueous printed image ofC * ；
The ninth step: comprehensively considering the measurement indexes such as peak signal-to-noise ratio, structural similarity, normalized cross correlation coefficient, bit error rate and the like, and selecting the optimal quantization step length by utilizing a particle swarm optimization algorithmT opt ；
The tenth step: pairing and encrypting the important parameters in the steps by using a Comtor pairing function shown in formula (11) to generate a large integer key, wherein the important parameters comprise an optimal quantization step sizeT opt Image block sizem；
Wherein the content of the first and second substances,Ψas a function of the Comtor pairingCantorPairThe generated non-negative large integer is not negative,aandbrespectively two numbers to be paired, and respectively,ais initially ofT opt ，bIs at an initial value ofm；
The watermark extraction process is described as follows:
the first step is as follows: pairing large integers by using the inverse Cortoler pairing functions shown in equations (12) and (13)ΨDecrypting to obtain decrypted important parameters;
wherein the content of the first and second substances,
，
floor (.) is a floor function, sqrt (.) is an absolute value function,a * is the optimal quantization stepT opt ，b * Is the image block sizem；
The second step is that: the number of pixels is equal toM×MAqueous printed image ofC * Divided into 3 layers containing watermark imagesC i * And each layer is provided with a watermarkC i * Further divided into a number of pixelsm×mOf non-overlapping image blocks, whereini=1, 2, 3 respectively represent red, green, blue three layers;
the third step: in-layer water-printed imageC i * By using the key-based key mentioned in the above watermark embedding processKd i Selecting an image block by using the MD5 Hash pseudorandom scrambling algorithm;
the fourth step: selecting a block containing watermarkB * The first frequency domain coefficient obtained by graph transformation is directly calculated in the space domain by using the formula (14)G * 1,1 ；
Wherein the content of the first and second substances,mis a water-marked image blockB * The number of the side length pixels of (a),B * (x, y) Water marked image blockB * In the first placexGo to the firstyPixel values of the columns;
the fifth step: the optimal quantization step size selected by using the formula (15) and the particle swarm optimization algorithmT opt Extracting block containing watermarkB * Watermark contained thereinw * ；
Wherein, the first and the second end of the pipe are connected with each other,G * 1,1 for containing watermark image blocksB * A first frequency domain coefficient obtained by map transformation, mod (.) is a residue taking function;
and a sixth step: repeatedly executing the fourth step and the fifth step of the process, and extracting the binary watermark bit sequence of each layerSW i ’Then converting each 8-bit binary information into a set of decimal pixel values, whereini=1, 2, 3 represents red, green, blue trilayer respectively;
the seventh step: performing key-based encryption of transformed encrypted layered watermark imagesKa i ，Kb i ，Kc i Fractional order Chen type chaotic decryption operation and acquisition of extracted layered watermark imageW i * Whereini=1, 2, 3 respectively represent red, green, blue three layers;
the eighth step: combining extracted layered watermark imagesW i * Forming a final extracted watermark imageW * Whereini=1, 2, 3 denotes red, green, blue, respectivelyAnd (3) a layer.
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