A fusion domain blind watermarking method based on graph transformation and particle swarm optimization algorithm

Abstract

This invention combines the advantages of high speed in spatial domain digital watermarking algorithms and high robustness in frequency domain digital watermarking algorithms, disclosing a fusion-domain blind watermarking method based on graph transform and particle swarm optimization (PSO) algorithm. Based on the data correlation-removing properties of graph transform and the optimal solution-obtaining properties of PSO, this invention first obtains the first frequency domain coefficients of the image patch after graph transform in the spatial domain. Then, these coefficients are used in the spatial domain to complete the embedding and blind extraction of the digital watermark. Finally, PSO is used for optimization to select the optimal quantization step size. This invention can embed a color image digital watermark into a color host image, possessing not only good watermark concealment and strong robustness, but also good real-time performance and security. It solves the problem of slow operation speed in large-capacity color image digital watermarking and is suitable for fast, efficient, and secure digital media copyright protection.

Description

Technical Field

[0001] This invention belongs to the field of information security technology and relates to rapid copyright protection for large-capacity color digital images. Background Technology

[0002] With the advent of the digital, networked, and information-based era, the transmission volume of digital multimedia information such as color digital images is growing exponentially. In the increasingly complex network environment, a series of digital infringement issues, such as piracy and tampering, have also emerged. Therefore, related copyright protection issues have gradually attracted widespread attention from scholars both domestically and internationally. On the one hand, copyright protection markers tend to be aesthetically pleasing, practical, and information-rich color images; on the other hand, with the widespread adoption of mobile terminal devices and the gradual upgrading of hardware configurations, people increasingly pursue faster and more efficient work, while single-frequency domain watermarking algorithms with long running times are insufficient to meet application needs. Therefore, it is necessary to further improve the running speed of information-rich digital watermarking algorithms. Furthermore, depending on the working domain of the carrier image, digital watermarking algorithms also include simple and efficient spatial domain digital watermarking algorithms, but they suffer from weak robustness. Therefore, combining the advantages of both spatial and frequency domain digital watermarking algorithms, and designing a high-real-time, high-security color image digital watermarking method while ensuring watermark invisibility and algorithm robustness, has become one of the key and challenging aspects of current digital watermarking technology research. Summary of the Invention

[0003] The purpose of this invention is to provide a fusion-domain blind watermarking method based on graph transformation and particle swarm optimization algorithm. Its key feature is that it is achieved through specific watermark embedding and extraction processes, the watermark embedding process of which is described below:

[0004] Step 1: First, divide a 24-bit color image digital watermark W with N×N pixels into three layered watermark images W according to the order of the three primary colors: red, green, and blue. i Then, each layered watermark image is processed based on the key Ka. i , Kb i Kc i The fractional-order Chen-style chaotic mapping is encrypted; finally, the encrypted layered watermark image W is... i Each decimal number in the graph represents a pixel, which is then concatenated to form a length of 8N. 2 Layered watermark bit sequence SW i The key Ka i Kb i Kc i The values ​​are randomly generated by the asymmetric encryption algorithm RSA, where i = 1, 2, 3 represent the red, green, and blue layers, respectively.

[0005] Step 2: Divide a color carrier image C with an M×M pixel count into three layered carrier images C1, according to the order of the three primary colors: red, green, and blue. i Simultaneously, each layered carrier image C i Divide the image into m×m non-overlapping blocks; based on the layered watermark bit sequence SW i Length 8N 2 Using key-based Kd i The MD5 hash pseudo-random scrambling algorithm generates a non-repeating sequence of selected blocks in the layered carrier image C. i Image patches at appropriate locations are selected to randomize the embedding position, thereby improving the robustness of the watermark against shearing attacks, where 8N 2 <=(M×M) / (m×m), i=1,2,3 represent the red, green and blue layers respectively;

[0006] Step 3: Select an image block B, and calculate its first frequency domain coefficient G after graph transformation directly in the spatial domain according to formula (1). 1,1 ;

[0007]

[0008] Where m is the side length and number of pixels of image block B, and B(x,y) represents the pixel value of the x-th row and y-th column of image block B;

[0009] Step 4: From the layered watermark bit sequence SW i One bit of watermark information w to be embedded is extracted in sequence. Based on the embedded watermark information and formulas (2), (3) and (4), the first frequency domain coefficient G after quantization is calculated. * 1,1 ;

[0010]

[0011] Where mod(.) is the modulo function, abs(.) is the absolute value function, T is the quantization step size, δ is the scaling factor, and i = 1, 2, 3 represent the red, green, and blue layers, respectively;

[0012] Step 5: Using formulas (5) and (6), amplify the change in the first frequency domain coefficient before and after quantization by a factor of m and distribute it evenly across all pixels of image block B to obtain the watermarked image block B. * ;

[0013]

[0014] B * (x,y)=round(B(x,y)+deltf) (6)

[0015] in, And this is the change in the first frequency domain coefficient, m is the side length and number of pixels of image patch B, round(.) is the rounding function, deltf is the average modification of pixel values, and B * (x,y) represents the watermarked image block B. * The pixel value in the x-th row and y-th column;

[0016] Step 6: Considering that the pixel value range is between 0 and 255, simply adding or subtracting pixel values ​​will cause pixel out-of-bounds errors, leading to incorrect watermark extraction. Therefore, the solution is optimized by discussing the modification of pixel value B(x,y) in the following three cases:

[0017] (1) When there is no overflow, that is, if ((abs(deltf)<min(B)) or (deltf>0 and (min(B)<deltf))) and (max(B)<255-deltf), then the pixels at the corresponding positions are modified according to formula (6);

[0018] B * (x,y)=round(B(x,y)+deltf) (6)

[0019] Where abs(.) is the absolute value function, min(.) is the minimum value function, max(.) is the maximum value function, round(.) is the rounding function, and deltf is the average modification amount of the pixel value;

[0020] (2) When an underflow occurs, i.e. (deltf < 0) and (min(B) < abs(deltf)), if Then Distribute the values ​​evenly to the smallest pixel value, as shown in formula (7);

[0021]

[0022] Wherein, min(.) is the minimum value function, B(m1,n1) is the minimum pixel value of B, (m1,n1) is the position of the minimum pixel value, round(.) is the rounding function, deltf is the average modification amount of the pixel value, T is the quantization step size, and num1 is the number of minimum pixel values; otherwise, the pixels at the corresponding positions are modified according to formula (8).

[0023]

[0024] Where, round(.) is the rounding function, deltf is the average modification of pixel values, and T is the quantization step size;

[0025] (3) When an overflow occurs, i.e., deltf > 0 and (max(B) + deltf > 255), if Then The values ​​are evenly distributed across the largest pixel value, as shown in formula (9):

[0026]

[0027] Where max(.) is the maximum value function, round(.) is the rounding function, B(m2,n2) is the maximum pixel value, (m2,n2) is the position of the maximum pixel value, deltf is the average modification of the pixel value, T is the quantization step size, and num2 is the number of maximum pixel values; otherwise, the pixel modification at the corresponding position is as shown in formula (10).

[0028]

[0029] Where, round(.) is the rounding function, deltf is the average modification of pixel values, and T is the quantization step size;

[0030] Step 7: Remove watermarked image block B * Update it to its layered carrier image C i The corresponding positions in the text, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0031] Step 8: Repeat steps 3 through 7 of this process until all watermark information has been embedded, thus obtaining the watermarked layered carrier image C. i * Finally, the watermarked layered carrier image C i * Reassemble and obtain a watermarked image C with an M×M pixel count. * ;

[0032] Step 9: Taking into account peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, and bit error rate, the optimal quantization step size T is selected using the particle swarm optimization algorithm. opt ;

[0033] Step 10: Use the Cantor pairing function shown in formula (11) to pair and encrypt the important parameters in the above steps to generate a large integer key. The important parameters include the optimal quantization step size T. opt Image block size (m);

[0034]

[0035] Where Ψ is a non-negative large integer generated by the Cantor pairing function CantorPair, and a and b are the two numbers to be paired, with the initial value of a being T. opt The initial value of b is m;

[0036] The watermark extraction process is described as follows:

[0037] Step 1: Use the inverse Cantor pairing function shown in formulas (12) and (13) to decrypt the large integer Ψ and obtain the important parameters after decryption;

[0038] b * =ψ-β (12)

[0039] a * =μ-b * (13)

[0040] in, floor(.) is the floor function, sqrt(.) is the absolute value function, and a * The final value is the optimal quantization step size T. opt b * The final value is the image patch size m;

[0041] Step 2: Extract the watermarked image C with a pixel count of M×M. * Divided into 3 layered watermarked images C i * And each layer of watermarked image C i * The image is further divided into non-overlapping image blocks with m×m pixels, where i = 1, 2, 3 represent the red, green, and blue layers, respectively.

[0042] Step 3: In the layered watermarked image C i * In the process of embedding watermarks, the key Kd mentioned above is used. i The MD5 hash pseudo-random scrambling algorithm is used to select image patches;

[0043] Step 4: Select a watermarked image block B * The first frequency domain coefficient G obtained by graph transformation can be directly calculated in the spatial domain using formula (14). * 1,1 ;

[0044]

[0045] Where m is the watermarked image block B * The number of pixels on the side, B * (x,y) represents the watermarked image block B. * The pixel value in the x-th row and y-th column;

[0046] Step 5: Using formula (15) and the optimal quantization step size T selected by the particle swarm optimization algorithm opt Extract watermarked image patch B * The watermark contained in it * ;

[0047]

[0048] Among them, G * 1,1 For watermarked image block B * The first frequency domain coefficient obtained after graph transformation, mod(.) is the remainder function;

[0049] Step 6: Repeat steps 4 and 5 of this process to extract the binary watermark bit sequence SW for each layer. i Then, each group of 8 bits of binary information is converted into a decimal pixel value, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0050] Step 7: Perform key-based watermarking on the converted encrypted layered watermark image. i , Kb i Kc i Fractional-order Chen-style chaotic decryption operation and obtaining the extracted layered watermark image W i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0051] Step 8: Combine the extracted layered watermark images W i * The final watermarked image W is formed. * , where i = 1, 2, 3 represent the red, green, and blue layers respectively.

[0052] This method utilizes the data correlation-removing properties of graph transform to complete the embedding and blind extraction of color digital watermarks by obtaining the first frequency domain coefficient through a fast spatial calculation method and the distribution law of the coefficient change in spatial pixels. The optimal quantization step size is determined in the spatial domain using a particle swarm optimization algorithm. This method has good invisibility, strong robustness, high real-time performance, and security. Attached Figure Description

[0053] Figure 1 (a) Figure 1 (b) are two original color carrier images.

[0054] Figure 2 (a) Figure 2 (b) are two original color watermark images.

[0055] Figure 3 (a) Figure 3 (b) is to respectively... Figure 2 (a) Embedded into carrier image Figure 1 (a) Figure 2 (b) Embedded into carrier image Figure 1 (b) The structural similarity (SSIM) values ​​of the watermarked images obtained after the watermarking are 0.954 and 0.973, respectively, and the peak signal-to-noise ratio (PSNR) values ​​are 40.050 dB and 40.660 dB, respectively.

[0056] Figure 4 (a) Figure 4 (b) is sequentially from Figure 3 (a) Figure 3 The watermarks extracted in (b) have normalized cross-correlation coefficient (NC) values ​​of 1.000 and 1.000, respectively.

[0057] Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) is to Figure 3 The watermarks extracted from the watermarked image shown in (a) after being subjected to attacks such as JPEG (70), JPEG2000 (4:1), salt and pepper noise (0.6%), median filtering (3×3), scaling (400%), and cropping (12.5%) are 1.000, 1.000, 0.964, 0.999, 1.000, and 0.877, respectively.

[0058] Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) is to Figure 3 (b) shows the watermarks extracted after being subjected to attacks such as JPEG (70), JPEG2000 (4:1), salt and pepper noise (0.6%), median filtering (3×3), scaling (400%), and cropping (12.5%). The normalized cross-correlation coefficients (NC) of the watermarked image are 1.000, 1.000, 0.966, 0.996, 1.000, and 0.877, respectively. Detailed Implementation

[0059] The purpose of this invention is to provide a fusion-domain blind watermarking method based on graph transformation and particle swarm optimization algorithm. Its key feature is that it is achieved through specific watermark embedding and extraction processes, the watermark embedding process of which is described below:

[0060] Step 1: First, divide a 24-bit color image digital watermark W with a pixel count of 32×32 into three layered watermark images W according to the order of the three primary colors: red, green, and blue. i Then, each layered watermark image is processed based on the key Ka. i , Kb i Kc i The fractional-order Chen-style chaotic mapping is encrypted; finally, the encrypted layered watermark image W is... i Each decimal number in the array represents a pixel using an 8-bit binary number (e.g., the decimal number 156 can be converted to the binary number 10011100), and these bits are concatenated to form a length of 8×32. 2 =8192 layered watermark bit sequence SW i The key Ka i , Kb i Kc i The values ​​are randomly generated by the asymmetric encryption algorithm RSA, where i = 1, 2, 3 represent the red, green, and blue layers, respectively.

[0061] Step 2: Divide a 512×512 pixel color carrier image C into three layered carrier images C1 according to the order of the three primary colors: red, green, and blue. i Simultaneously, each layered carrier image C i Divide the image into 4×4 pixel blocks; based on the layered watermark bit sequence SW i Length 8×32 2 =8192, using key-based Kd i The MD5 hash pseudo-random scrambling algorithm generates a non-repeating sequence of selected blocks in the layered carrier image C. i Image patches at appropriate locations are selected to randomize the embedding position, thereby improving the robustness of the watermark against shearing attacks. Among these, 8×32... 2 <(512×512) / (4×4), i=1,2,3 represent the red, green and blue layers respectively;

[0062] Step 3: Select an image block B, and calculate its first frequency domain coefficient G after graph transformation directly in the spatial domain according to formula (1). 1,1 ;

[0063]

[0064] Where m is the side length and number of pixels of image patch B, and B(x,y) represents the pixel value of image patch B at row x and column y; here, let the selected image patch... If m = 4, then we get G 1,1 =892;

[0065] Step 4: From the layered watermark bit sequence SW i One bit of watermark information w to be embedded is extracted in sequence. Based on the embedded watermark information and formulas (2), (3) and (4), the first frequency domain coefficient G after quantization is calculated. * 1,1 ;

[0066]

[0067] Where mod(.) is the modulo function, abs(.) is the absolute value function, T is the quantization step size, δ is the scaling factor, and i = 1, 2, 3 represent the red, green, and blue layers respectively; here, let G 1,1 =892, w='1', T=46, δ=0.25, then we get G upper =908.5, G lower =862.5, G * 1,1 =908.5;

[0068] Step 5: Using formulas (5) and (6), amplify the change in the first frequency domain coefficient before and after quantization by a factor of m and distribute it evenly across all pixels of image block B to obtain the watermarked image block B. * ;

[0069]

[0070] B * (x,y)=round(B(x,y)+deltf) (6)

[0071] in, And this is the change in the first frequency domain coefficient, m is the side length and number of pixels of image block B, deltf is the average modification of pixel values, and round(.) is the rounding function; here, let G 1,1 =892, G * 1,1 =908.5, m=4, then change=16.5, deltf=4.125, containing the watermarked image block.

[0072] Step 6: Considering that the pixel value range is between 0 and 255, simply adding or subtracting pixel values ​​will cause pixel out-of-bounds errors, leading to incorrect watermark extraction. Therefore, the solution is optimized by discussing the modification of pixel value B(x,y) in the following three cases:

[0073] (1) When there is no overflow, that is, if ((abs(deltf)<min(B)) or (deltf>0 and (min(B)<deltf))) and (max(B)<255-deltf), then the pixels at the corresponding positions are modified according to formula (6);

[0074] B * (x,y)=round(B(x,y)+deltf); (6)

[0075] Where abs(.) is the absolute value function, min(.) is the minimum value function, max(.) is the maximum value function, round(.) is the rounding function, and deltf is the average modification amount of the pixel value;

[0076] (2) When an underflow occurs, i.e. (deltf < 0) and (min(B) < abs(deltf)), if Then The values ​​are evenly distributed across the smallest pixel value, as shown in formula (7):

[0077]

[0078] Wherein, min(.) is the minimum value function, B(m1,n1) is the minimum pixel value of B, (m1,n1) is the position of the minimum pixel value, round(.) is the rounding function, deltf is the average modification amount of the pixel value, T is the quantization step size, and num1 is the number of minimum pixel values; otherwise, the pixels at the corresponding positions are modified according to formula (8).

[0079]

[0080] Where, round(.) is the rounding function, deltf is the average modification of pixel values, and T is the quantization step size;

[0081] (3) When an overflow occurs, i.e., deltf > 0 and (max(B) + deltf > 255), if Then The values ​​are evenly distributed across the largest pixel value, as shown in formula (9):

[0082]

[0083] Where max(.) is the maximum value function, round(.) is the rounding function, B(m2,n2) is the maximum pixel value, (m2,n2) is the position of the maximum pixel value, deltf is the average modification of the pixel value, T is the quantization step size, and num2 is the number of maximum pixel values; otherwise, the pixel modification at the corresponding position is as shown in formula (10).

[0084]

[0085] Where `round(.)` is the rounding function, `deltf` is the average modification of pixel values, and `T` is the quantization step size; here, the selected image patch... T = 46, deltf = 4.125. Calculations show that there is no overflow problem for any pixel value in this image block, which falls under case (1). Therefore, the watermarked image block can be obtained.

[0086] Step 7: Remove watermarked image block B * Update it to its layered carrier image C i The corresponding positions in the text, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0087] Step 8: Repeat steps 3 through 7 of this process until all watermark information has been embedded, thus obtaining the watermarked layered carrier image C. i * Finally, the watermarked layered carrier image C i * Reassemble and obtain a watermarked image C with a pixel count of 512×512. * ;

[0088] Step 9: Taking into account peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, and bit error rate, the optimal quantization step size T is selected using the particle swarm optimization algorithm. opt Here, let the selected optimal quantization step size T be... opt =46;

[0089] Step 10: Use the Cantor pairing function shown in formula (11) to pair and encrypt the important parameters in the above steps to generate a large integer key. The important parameters include the optimal quantization step size T. opt Image block size (m);

[0090]

[0091] Where Ψ is a non-negative large integer generated by the Cantor pairing function CantorPair, and a and b are the two numbers to be paired; the initial value of a is T. opt The initial value of b is m; here, let a = Topt =46, b=m=4, then we get Ψ=1279;

[0092] The watermark extraction process is described as follows:

[0093] Step 1: Use the inverse Cantor pairing function shown in formulas (12) and (13) to decrypt the large integer Ψ and obtain the important parameters after decryption;

[0094] b * =ψ-β (12)

[0095] a * =μ-b * (13)

[0096] in, floor(.) is the floor function, sqrt(.) is the absolute value function, and a * The final value is the optimal quantization step size T. opt b * The final value is the image patch size m; here, let Ψ = 1279, then we get μ = 50, β = 1275, b * =4, a * =46;

[0097] Step 2: Extract the watermarked image C with a pixel count of 512×512. * Divided into 3 layered watermarked images C i * And each layer of watermarked image C i * The image is further divided into non-overlapping image blocks of 4×4 pixels, where i = 1, 2, 3 represent the red, green, and blue layers, respectively.

[0098] Step 3: In the layered watermarked image C i * In the process of embedding watermarks, the key Kd mentioned above is used. i The MD5 hash pseudo-random scrambling algorithm is used to select image patches;

[0099] Step 4: Select a watermarked image block B * The first frequency domain coefficient G obtained by graph transformation can be directly calculated in the spatial domain using formula (14). * 1,1 ;

[0100]

[0101] Where m is the watermarked image block B * The number of pixels on the side, B * (x,y) represents the watermarked image block B.* The pixel value in the x-th row and y-th column; here, let's assume we select to obtain the watermarked image block. If m = 4, then G can be obtained. * 1,1 =908;

[0102] Step 5: Using formula (15) and the optimal quantization step size T selected by the particle swarm optimization algorithm opt Extract watermarked image patch B * The watermark contained in it * ;

[0103]

[0104] Among them, G * 1,1 For watermarked image block B * The first frequency domain coefficient obtained after graph transformation, mod(.) is the remainder function, and i = 1, 2, 3 represent the red, green, and blue layers respectively; here, let the optimal quantization step size T be... opt =46, so we can get w * ='1';

[0105] Step 6: Repeat steps 4 and 5 of this process to extract the binary watermark bit sequence SW for each layer. i Then, each group of 8 bits of binary information is converted into a decimal pixel value, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0106] Step 7: Perform key-based watermarking on the converted encrypted layered watermark image. i , Kb i Kc i Fractional-order Chen-style chaotic decryption operation and obtaining the extracted layered watermark image W i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0107] Step 8: Combine the extracted layered watermark images W i * The final watermarked image W is formed. * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0108] This method utilizes the data correlation-removing properties of graph transform to complete the embedding and blind extraction of color digital watermarks by obtaining the first frequency domain coefficient through a fast spatial calculation method and the distribution law of the coefficient change in spatial pixels. The optimal quantization step size is determined in the spatial domain using a particle swarm optimization algorithm. This method has good invisibility, strong robustness, high real-time performance, and security.

[0109] Validation of the invention

[0110] To demonstrate the effectiveness of this invention, the following were selected: Figure 1 (a) Figure 1 (b) shows two 24-bit standard images with a pixel size of 512×512 as carrier images, and respectively use the following... Figure 2 The two 24-bit color images with a pixel size of 32×32 shown are used as digital watermarks for verification.

[0111] Figure 3 (a) Figure 3 (b) is to respectively... Figure 2 (a) Figure 2 (b) The watermark shown is sequentially embedded into the carrier image. Figure 1 (a) Figure 1 (b) The structural similarity (SSIM) values ​​of the watermarked images obtained after the watermarking are 0.954 and 0.973, respectively, and the peak signal-to-noise ratio (PSNR) values ​​are 40.050 dB and 40.660 dB, respectively. Figure 4 (a) Figure 4 (b) is sequentially from Figure 3 (a) Figure 3 The watermarks extracted in (b) have normalized cross-correlation coefficient (NC) values ​​of 1.000 and 1.000, respectively. Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) Figure 5 (f) is to Figure 3 (a) shows the watermarks extracted from the watermarked image after being subjected to attacks such as JPEG (70), JPEG2000 (4:1), salt and pepper noise (0.6%), median filtering (3×3), scaling (400%), and cropping (12.5%). The normalized cross-correlation coefficients (NC) values ​​are 1.000, 1.000, 0.964, 0.999, 1.000, and 0.877, respectively. Figure 6 (a) Figure 6 (b) Figure 6 (c) Figure 6 (d) Figure 6 (e) Figure 6 (f) is to Figure 3(b) shows the watermarks extracted after being subjected to attacks such as JPEG (70), JPEG2000 (4:1), salt and pepper noise (0.6%), median filtering (3×3), scaling (400%), and cropping (12.5%). The normalized cross-correlation coefficients (NC) of the watermarked image are 1.000, 1.000, 0.966, 0.996, 1.000, and 0.877, respectively.

[0112] The algorithm has been run nearly 10,000 times on a platform with a 2.00GHz CPU, 16.00GB RAM, Win 10, and MATLAB (R2021b). Its average embedding time for digital watermarks is 0.7284 seconds, the average extraction time is 0.1374 seconds, and the total time is 0.8658 seconds.

[0113] In summary, the embedded color image digital watermark has good invisibility, meeting the invisibility requirement of watermarking algorithms. Meanwhile, the color image digital watermarks extracted from various attacked images have good identifiability and high NC values, indicating that the method has strong robustness. Furthermore, the algorithm's average total running time is less than 1 second, meeting the needs of rapid copyright protection for multimedia big data.

Claims

1. A fusion-domain blind watermarking method based on graph transformation and particle swarm optimization algorithm, characterized in that... This is achieved through specific watermark embedding and extraction processes. The watermark embedding process is described as follows: Step 1: First, divide a 24-bit color image digital watermark W with N×N pixels into three layered watermark images W according to the order of the three primary colors: red, green, and blue. i Then, each layered watermark image is processed based on the key Ka. i Kb i Kc i The fractional-order Chen-style chaotic mapping is encrypted; finally, the encrypted layered watermark image W is... i Each decimal number in the graph represents a pixel, which is then concatenated to form a length of 8N. 2 Layered watermark bit sequence SW i The key Ka i Kb i Kc i The values ​​are randomly generated by the asymmetric encryption algorithm RSA, where i = 1, 2, 3 represent the red, green, and blue layers, respectively. Step 2: Divide a color carrier image C with an M×M pixel count into three layered carrier images C1, according to the order of the three primary colors: red, green, and blue. i Simultaneously, each layered carrier image C i Divide the image into m×m non-overlapping blocks; based on the layered watermark bit sequence SW i Length 8N 2 Using key-based Kd i The MD5 hash pseudo-random scrambling algorithm generates a non-repeating sequence of selected blocks in the layered carrier image C. i Image patches at appropriate locations are selected to randomize the embedding position, thereby improving the robustness of the watermark against shearing attacks, where 8N 2 <=(M×M) / (m×m), i=1,2,3 represent the red, green and blue layers respectively; Step 3: Select an image block B, and calculate its first frequency domain coefficient G after graph transformation directly in the spatial domain according to formula (1). 1,1 ; Where m is the side length and number of pixels of image block B, and B(x,y) represents the pixel value of the x-th row and y-th column of image block B; Step 4: From the layered watermark bit sequence SW i One bit of watermark information w to be embedded is extracted in sequence. Based on the embedded watermark information and formulas (2), (3) and (4), the first frequency domain coefficient G after quantization is calculated. * 1,1 ; Where mod(.) is the modulo function, abs(.) is the absolute value function, T is the quantization step size, δ is the scaling factor, and i = 1, 2, 3 represent the red, green, and blue layers, respectively; Step 5: Using formulas (5) and (6), amplify the change in the first frequency domain coefficient before and after quantization by a factor of m and distribute it evenly across all pixels of image block B to obtain the watermarked image block B. * ; B * (x,y)=round(B(x,y)+deltf) (6) in, And this is the change in the first frequency domain coefficient, m is the side length and number of pixels of image patch B, round(.) is the rounding function, deltf is the average modification of pixel values, and B * (x,y) represents the watermarked image block B. * The pixel value in the x-th row and y-th column; Step 6: Considering that the pixel value range is between 0 and 255, simply adding or subtracting pixel values ​​will cause pixel out-of-bounds errors, leading to incorrect watermark extraction. Therefore, the solution is optimized by discussing the modification of pixel value B(x,y) in the following three cases: (1) When there is no overflow, that is, if ((abs(deltf)<min(B)) or (deltf>0 and (min(B)<deltf))) and (max(B)<255-deltf), then the pixels at the corresponding positions are modified according to formula (6); B * (x,y)=round(B(x,y)+deltf) (6) Where abs(.) is the absolute value function, min(.) is the minimum value function, max(.) is the maximum value function, round(.) is the rounding function, and deltf is the average modification amount of the pixel value; (2) When an underflow occurs, i.e. (deltf < 0) and (min(B) < abs(deltf)), if Then Distribute the values ​​evenly to the smallest pixel value, as shown in formula (7); Wherein, min(.) is the minimum value function, B(m1,n1) is the minimum pixel value of B, (m1,n1) is the position of the minimum pixel value, round(.) is the rounding function, deltf is the average modification amount of the pixel value, T is the quantization step size, and num1 is the number of minimum pixel values; otherwise, the pixels at the corresponding positions are modified according to formula (8). Where, round(.) is the rounding function, deltf is the average modification of pixel values, and T is the quantization step size; (3) When an overflow occurs, i.e., deltf > 0 and (max(B) + deltf > 255), if Then The values ​​are evenly distributed across the largest pixel value, as shown in formula (9): Where max(.) is the maximum value function, round(.) is the rounding function, B(m2,n2) is the maximum pixel value, (m2,n2) is the position of the maximum pixel value, deltf is the average modification of the pixel value, T is the quantization step size, and num2 is the number of maximum pixel values; otherwise, the pixel modification at the corresponding position is as shown in formula (10). Where, round(.) is the rounding function, deltf is the average modification of pixel values, and T is the quantization step size; Step 7: Remove watermarked image block B * Update it to its layered carrier image C i The corresponding positions in the text, where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 8: Repeat steps 3 through 7 of this process until all watermark information has been embedded, thus obtaining the watermarked layered carrier image C. i * Finally, the watermarked layered carrier image C i * Reassemble and obtain a watermarked image C with an M×M pixel count. * ; Step 9: Taking into account peak signal-to-noise ratio, structural similarity, normalized cross-correlation coefficient, and bit error rate, the optimal quantization step size T is selected using the particle swarm optimization algorithm. opt ; Step 10: Use the Cantor pairing function shown in formula (11) to pair and encrypt the important parameters in the above steps to generate a large integer key. The important parameters include the optimal quantization step size T. opt Image block size (m); Where Ψ is a non-negative large integer generated by the Cantor pairing function CantorPair, and a and b are the two numbers to be paired, with the initial value of a being T. opt The initial value of b is m; The watermark extraction process is described as follows: Step 1: Use the inverse Cantor pairing function shown in formulas (12) and (13) to decrypt the large integer Ψ and obtain the important parameters after decryption; b * =ψ-β (12) a * =μ-b * (13) in, floor(.) is the floor function, sqrt(.) is the absolute value function, and a * The final value is the optimal quantization step size T. opt b * The final value is the image patch size m; Step 2: Extract the watermarked image C with a pixel count of M×M. * Divided into 3 layered watermarked images C i * And each layer of watermarked image C i * The image is further divided into non-overlapping image blocks with m×m pixels, where i = 1, 2, 3 represent the red, green, and blue layers, respectively. Step 3: In the layered watermarked image C i * In the process of embedding watermarks, the key Kd mentioned above is used. i The MD5 hash pseudo-random scrambling algorithm is used to select image patches; Step 4: Select a watermarked image block B * The first frequency domain coefficient G obtained by graph transformation can be directly calculated in the spatial domain using formula (14). * 1,1 ; Where m is the watermarked image block B * The number of pixels on the side, B * (x,y) represents the watermarked image block B. * The pixel value in the x-th row and y-th column; Step 5: Using formula (15) and the optimal quantization step size T selected by the particle swarm optimization algorithm opt Extract watermarked image patch B * The watermark contained in it * ; Among them, G * 1,1 For watermarked image block B * The first frequency domain coefficient obtained after graph transformation, mod(.) is the remainder function; Step 6: Repeat steps 4 and 5 of this process to extract the binary watermark bit sequence SW for each layer. i Then, each group of 8 bits of binary information is converted into a decimal pixel value, where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 7: Perform key-based watermarking on the converted encrypted layered watermark image. i Kb i Kc i Fractional-order Chen-style chaotic decryption operation and obtaining the extracted layered watermark image W i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 8: Combine the extracted layered watermark images W i * The final watermarked image W is formed. * , where i = 1, 2, 3 represent the red, green, and blue layers respectively.

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