Robust and Reversible Watermark Embedding and Extraction Method Based on Moment Clustering and Normalization Optimization

Abstract

This invention relates to the field of digital watermarking technology and discloses a robust and reversible watermark embedding and extraction method based on moment clustering and normalization optimization. The method includes: calculating the PCET moments of the original image; selecting moments of optimal order and degree selected through a clustering algorithm as the watermark embedding carrier; performing robust watermark embedding using a quantized watermarking method and performing an inverse transformation to obtain a robust watermark image; calculating the difference between the robust watermark image and the original image, performing normalization coefficient optimization based on embedding simulation, and embedding the calculated image difference as reversible information into the outer part of the inscribed circle of the image; when the image is not attacked, extracting the watermark information of the unattacked image and restoring the original image; when the image is attacked, extracting the watermark information of the attacked image. This invention solves the problems of insufficient watermark robustness and significant image distortion in existing technologies, and has the characteristics of improving watermark robustness and reducing image distortion.

Description

Technical Field

[0001] This invention relates to the field of digital watermarking technology, and more specifically, to a robust and reversible watermark embedding and extraction method based on moment clustering and normalization optimization. Background Technology

[0002] Digital watermarking technology falls under the category of information hiding, focusing on copyright protection for multimedia information. It is an invisible information pattern embedded in a signal carrier, such as images, audio, or video. Significant progress has been made in the robustness of digital image watermarking in recent years, but it still suffers from insufficient robustness against geometric attacks such as rotation, scaling, and translation, as well as insufficient embedding capacity. Robust reversible watermarking, on the other hand, allows for the correct extraction and complete recovery of the embedded watermark information when the carrier image is unaffected, and even when the carrier image is subjected to a certain degree of attack, the watermark information can still be extracted correctly without loss.

[0003] A robust and reversible watermarking technique is proposed. It calculates the PCET moments of an image, performs quantized watermark embedding based on the PCET moments, and determines whether the image has been attacked by the distortion information generated during the quantized watermark embedding process. When the image is determined not to be attacked, the watermark information is extracted using the PCET moments of the image and the original image is restored. When the image is determined to be attacked, the PCET moments of the attacked image with watermark information are calculated, and the watermark information is extracted using the PCET moments of the image with watermark information.

[0004] However, the aforementioned techniques do not consider the varying robustness of PCET moments of different orders and degrees to different signal processing and geometric deformation attacks during watermark embedding, resulting in insufficient robustness of watermark embedding and high bit error rate in watermark extraction. Existing methods also suffer from excessive auxiliary information used in reversible watermark embedding, leading to excessive image distortion. Therefore, how to invent a robust watermark embedding and extraction method that can consider the robustness differences of geometric moments of different orders and degrees, and a reversible watermark embedding and extraction method with low distortion, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To overcome the two shortcomings of the above-mentioned technologies—insufficient robustness and large distortion of robust reversible watermark images—this invention provides a robust reversible watermark embedding and extraction method based on moment clustering and normalization optimization, which has the characteristics of improving watermark robustness and reducing image distortion.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: A robust and reversible watermark embedding method based on moment clustering and normalization optimization includes the following steps: S1: Obtain the original image And calculate the original image of Step Secondary PCET moments ; S2: Choose the order and degree to satisfy the optimal set of orders. and the set of optimal times PCET moments As a watermark embedding carrier; S3: PCET moment Perform quantized watermark embedding to obtain PCET moments with robust watermarks. ; S4: Calculate PCET moments and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. ; S5: Modify robust watermark difference moments Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. ,in, For watermark information; S6: For the robust watermarked image Perform pixel overflow detection and record overflow information. ; S7: The robust watermark difference moment and overflow information Embedded into robust watermarked images In the process, an image containing a robust reversible watermark is obtained. ;in, This is reversible watermark information; S8: Will include images with robust reversible watermarks The least significant bit of the first few pixels is replaced with 0, and a hash value is generated. Replace images containing robust reversible watermarks with hash values. The least significant bits of the first few pixels are used to obtain the robust reversible watermark image. Robust and reversible watermark embedding is achieved.

[0007] Preferably, in step S1, the original image is acquired. And calculate the original image of Step Secondary PCET moments The specific steps are as follows: Based on size The original image With the center of the circle as the center and K as a positive integer, construct the original image. The inscribed circle is used to construct PCET moment basis functions. Using the inscribed circle as the unit circle, according to the PCET moment basis function... Calculate the nth-order m-th PCET moment of the pixels within the unit circle. The specific expression is:

[0008] Among them, PCET basis functions It is a complete orthogonal basis on the unit circle. This represents the x-th x-coordinate of the original image I. Represents the original image The y-th ordinate, This represents the step size of the x-coordinate of the unit circle in the original image I. Represents the original image The step size of the ordinate in the unit circle. Represents the pixels within the unit circle.

[0009] Furthermore, in step S2, the matrix to be embedded with watermark information is also... The simulation attack experiment was conducted, and the PCET moments with the strongest robustness were selected by clustering algorithm. The specific steps are as follows: S201: Randomly select from the BOWS2 database Zhang Image ; S202: Calculate the image of Step Secondary PCET moments ; S203: Regarding the PCET moment Attack simulation experiments were conducted, using AWGN, JPEG compression, and JPEG2000 compression to analyze images. Perform a simulated attack to obtain the PCET moments of the attacked image. That is,

[0010] in, Let be the order of the PCET moments. Let be the order of the PCET moments. Indicates that the variance is Gaussian noise simulation attack, Indicates the compression rate JPEG compression simulation attack Indicates the compression rate A JPEG2000 compression simulation attack; S204: Calculate the difference values ​​of the moments of order and degree for each image in the dataset. and will Step The corresponding difference values ​​form the difference vector. ; S205: For the difference vector The difference value in the middle is used min-max The normalization process is performed to obtain the normalized difference vector. Then normalize the difference vector The AFCM clustering algorithm was used to determine the number of classifications. Classification, AFCM clustering algorithm The specific expression is as follows:

[0011] ,

[0012] ,

[0013] ,

[0014] in, Represents the number of clusters, Indicates the total number of data. For the corresponding vectors and clusters The probability of belonging, Represents clustering parameters, Represents the vector to be classified. Indicates the cluster center; S206: Accumulate and calculate the normalized difference vector for each class after classification. difference This yields the set of orders corresponding to the minimum accumulated difference value. and number set .

[0015] Furthermore, in step S3, the PCET moment... Perform quantized watermark embedding to obtain PCET moments with robust watermarks. The specific steps are as follows: S301: Based on whether the embedded watermark information is '0' or '1', find the nearest '0 interval' or '1 interval' where the carrier is located, and move it a corresponding distance. The specific expression is:

[0016] in, To quantize the step size, The jitter value. For embedding the first The order of the PCET moment of the watermark bits. For embedding the first The number of times the PCET moment of each watermark bit, For the first The bit value corresponding to each watermark bit; S302: PCET matrix with robust watermark Restored to PCET moments The specific expression is: .

[0017] Furthermore, in step S4, the PCET moment is calculated. and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. The specific steps are as follows: S401: Calculate the robust watermark difference between the embedded robust watermark PCET moment and the original PCET moment. ; S402: Randomly select from the database Zhang images as a dataset Perform the S3 operation on the image; S403: Calculate the dataset Robust watermark difference between the PCET moments of the image with embedded robust watermark and the original PCET moments. And robust watermark difference for each image. Normalization coefficients The reversible information was embedded in the simulation and normalized experiment to obtain normalized reversible information. ; S404: For the above dataset Normalized reversible information The simulation embedding experiment was performed, and S5-S7 operations were executed on it to obtain a set of simulated images with robust reversible information. ; S405: Calculate the dataset and robust reversible information simulation image set PSNR, and simulation image set of robust reversible information An attack simulation experiment was conducted, and the watermark extraction error rate was calculated. The optimal normalization parameters are obtained. ; S406: Robust watermark difference Use the optimal normalization parameters Normalization is performed to obtain robust watermark difference moments. .

[0018] Furthermore, in step S5, the robust watermark difference moment is... Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. The specific expression is: ; in, L Indicates the length of the robust watermark information.

[0019] A robust and reversible watermark extraction method based on moment clustering and normalization optimization includes the following specific steps: Obtaining a robust reversible watermark image and robust watermarked images The robust reversible watermark image and robust watermarked images The robust and reversible watermark embedding method based on moment clustering and normalization optimization described above is used to generate the watermark. S21: Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the image containing the robust reversible watermark. hash value And use the reversible watermarking method to create a robust reversible watermark image. Restored to an image containing a robust reversible watermark. ; S22: Extract robust watermark image The former S The least significant bit of each pixel is extracted, and the extracted result replaces the image containing the robust reversible watermark. forward S After retrieving the least significant bit of each pixel, an image containing a robust reversible watermark is generated. hash value ; S23: Compare hash values and hash value If the hash value equal to hash value If the robust and reversible watermarked image has not been attacked, proceed to step S24; if the hash value... Not equal to hash value If the robust reversible watermark image is attacked, proceed to step S25. S24: Extract unattacked images containing robust reversible watermarks The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I ; S25: Extract the attacked image containing a robust reversible watermark. The watermark information.

[0020] In step S24, the unattacked image containing the robust reversible watermark is extracted. The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I， The specific steps are as follows: S2401: Extract unattacked images containing robust reversible watermarks The former S The least significant bit of each pixel is used to extract the robust reversible watermark from the unaffected image. Restore to robust watermark image And extract the watermark information Robust watermark difference moments ; S2402: Calculating Robust Watermarked Images PCET moments ; S2403: PCET moment Watermark information is extracted using a quantized watermarking method. Its expression is as follows:

[0021]

[0022]

[0023] in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, For quantization step size, This is the jitter value; S2404: For the robust watermark difference Use normalization parameters Perform the inverse operation of normalization Robust watermark difference moment ; For the robust watermark difference Performing PCET inverse moment transform and rounding operations yields the original image with the watermark removed. Its expression is as follows:

[0024] in, L Indicates the length of the robust watermark information.

[0025] In step S25, the attacked image containing the robust reversible watermark is extracted. The watermark information, the specific steps are as follows: Calculate the attacked image containing a robust reversible watermark. PCET moments , and for PCET moments Watermark information is extracted using a quantized watermarking method. w 1. Its expression is as follows:

[0026]

[0027]

[0028] in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, This is for quantization step size.

[0029] Furthermore, the reversible watermark is obtained through prediction error expansion and histogram shifting techniques, specifically including the following steps: The diamond pattern prediction scheme divides all pixels in the image into two intersecting sets, called the cross set and the point set, respectively. The cross set is used to embed information, and the point set is used to calculate the predicted value. Among them, the center pixel The predicted value is obtained by using the pixels around it ( The mean of the values ​​is calculated by using the center pixel. The prediction error of a pixel is obtained by subtracting the actual value from the predicted value; similarly, the prediction error of all cross-set pixels is obtained. Calculate the local variance of all fork set pixels and sort them in ascending order to obtain the robust watermark difference moments. Overflow information The prediction error sequence of the least significant bits of the first S pixels of the image; The robust watermark difference moment is obtained by using the histogram translation method. Overflow information With the image front S The least significant bit of each pixel is embedded into the sorted prediction error sequence to obtain a reversible watermark. The beneficial effects of this invention are as follows: This invention discloses a robust reversible watermark embedding and extraction method based on moment clustering and normalization optimization. Addressing the robustness differences of PCET moments at different orders and degrees, this invention selects moments with better robustness as the watermark embedding carrier, enhancing robustness. When calculating reversible information, this invention uses optimal parameters for normalization to reduce the amount of reversible information data, thereby reducing the distortion of the robust reversible watermark image. This invention enables robust reversible watermark images to achieve stronger robustness against conventional signal attacks and geometric transformation attacks while maintaining lower image distortion. Therefore, this invention solves the problems of insufficient watermark robustness and significant image distortion in existing technologies, and features improved watermark robustness and reduced image distortion. Attached Figure Description

[0030] Figure 1 This is a flowchart of the robust reversible watermark embedding method based on moment clustering and normalization optimization of the present invention.

[0031] Figure 2 This is a flowchart of the robust reversible watermark extraction method based on moment clustering and normalization optimization of the present invention. Detailed Implementation

[0032] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] Example 1 like Figure 1 As shown, the robust reversible watermark embedding method based on moment clustering and normalization optimization includes the following steps: S1: Obtain the original image And calculate the original image of Step Secondary PCET moments ; S2: Choose the order and degree to satisfy the optimal set of orders. and the set of optimal times PCET moments As a watermark embedding carrier; S3: PCET moment Perform quantized watermark embedding to obtain PCET moments with robust watermarks. ; S4: Calculate PCET moments and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. ; S5: Modify robust watermark difference moments Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. ,in, For watermark information; S6: For the robust watermarked image Perform pixel overflow detection and record overflow information. ; S7: The robust watermark difference moment and overflow information Embedded into robust watermarked images In the process, an image containing a robust reversible watermark is obtained. ;in, This is reversible watermark information; S8: Will include images with robust reversible watermarks The least significant bit of the first few pixels is replaced with 0, and a hash value is generated. Replace images containing robust reversible watermarks with hash values. The least significant bits of the first few pixels are used to obtain the robust reversible watermark image. Robust and reversible watermark embedding is achieved.

[0034] In its implementation, this embodiment addresses the robustness differences of PCET moments at different orders and degrees by using the AFCM clustering algorithm to select moments with better robustness as the watermark embedding carrier, thereby enhancing robustness. When calculating reversible information, this invention uses optimal normalization parameters to reduce the amount of reversible information data, thus reducing distortion of the robust reversible watermark image. This invention enables robust reversible watermark images to achieve stronger robustness against conventional signal attacks and geometric transformation attacks while maintaining lower image distortion.

[0035] Example 2 More specifically, this embodiment provides a robust and reversible watermark embedding method based on moment clustering and normalization optimization, including: In one specific embodiment, in step S1, the original image is acquired. And calculate the original image of Step Secondary PCET moments The specific steps are as follows: S101: Obtain the original image I The original image The size is ; In this embodiment ; S102: Based on size The original image The center is the center of the circle. K Given a positive integer, use it to create the original image. The inscribed circle is used to construct PCET moment basis functions. Using the inscribed circle as the unit circle, according to the PCET moment basis function... Calculate the nth-order m-th PCET moment of the pixels within the unit circle. The specific expression is:

[0036]

[0037]

[0038] Among them, PCET basis functions It is a complete orthogonal basis on the unit circle. Represents the original image I The x Each horizontal axis Represents the original image I The y One vertical axis, Represents the original image I The x-axis step size of the unit circle. Represents the original image I The step size of the ordinate in the unit circle. Represents the pixels within the unit circle.

[0039] In one specific embodiment, in step S2, since the amplitude changes of PCET moments caused by conventional signal processing attacks such as AWGN and JPEG compression vary depending on the order and number of PCET moments, the moment for embedding watermark information is also considered. The simulation attack experiment was conducted, and the PCET moments with the strongest robustness were selected by clustering algorithm. The specific steps are as follows: S201: Randomly select from the BOWS2 database Zhang Image ; In this embodiment, =1000.

[0040] S202: Calculate the image of Step Secondary PCET moments ; S203: Regarding the PCET moment Attack simulation experiments were conducted, using AWGN, JPEG compression, and JPEG2000 compression to analyze images. Perform a simulated attack to obtain the PCET moments of the attacked image. That is,

[0041] in, Let be the order of the PCET moments. Let be the order of the PCET moments. Indicates that the variance is Gaussian noise simulation attack, Indicates the compression rate JPEG compression simulation attack Indicates the compression rate A JPEG2000 compression simulation attack.

[0042] In this embodiment, , , 。

[0043] S204: Calculate the difference values ​​of the moments of order and degree for each image in the dataset. and will Step The corresponding difference values ​​form the difference vector. ; S205: For the difference vector The difference value in the middle is used min-max The normalization process is performed to obtain the normalized difference vector. Then normalize the difference vector The AFCM clustering algorithm was used to determine the number of classifications. Classification, AFCM clustering algorithm The specific expression is as follows:

[0044] ,

[0045] ,

[0046] ,

[0047] in, Represents the number of clusters, Indicates the total number of data. For the corresponding vectors and clusters The probability of belonging, Represents clustering parameters, Represents the vector to be classified. Indicates the cluster center; In this embodiment, .

[0048] S206: Accumulate and calculate the normalized difference vector for each class after classification. difference This yields the set of orders corresponding to the minimum accumulated difference value. and number set .

[0049] In one specific embodiment, in step S3, the PCET moment is... Perform quantized watermark embedding to obtain PCET moments with robust watermarks. The specific steps are as follows: S301: Based on whether the embedded watermark information is '0' or '1', find the nearest '0 interval' or '1 interval' where the carrier is located, and move it a corresponding distance. The specific expression is:

[0050] in, To quantize the step size, The jitter value. For embedding the first The order of the PCET moment of the watermark bits. For embedding the first The number of times the PCET moment of each watermark bit, For the first The bit value corresponding to each watermark bit; In this embodiment, .

[0051] S302: PCET matrix with robust watermark Restored to PCET moments The specific expression is: .

[0052] In one specific embodiment, in step S4, the PCET moment is calculated. and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. The specific steps are as follows: S401: Calculate the robust watermark difference between the embedded robust watermark PCET moment and the original PCET moment. ; S402: Randomly select from the database Zhang images as a dataset Perform the S3 operation on the image; In this embodiment, .

[0053] S403: Calculate the dataset Robust watermark difference between the PCET moments of the image with embedded robust watermark and the original PCET moments. And robust watermark difference for each image. Normalization coefficients The reversible information was embedded in the simulation and normalized experiment to obtain normalized reversible information. ; S404: For the above dataset Normalized reversible information The simulation embedding experiment was performed, and S5-S7 operations were executed on it to obtain a set of simulated images with robust reversible information. ; S405: Calculate the dataset and robust reversible information simulation image set PSNR, and simulation image set of robust reversible information An attack simulation experiment was conducted, and the watermark extraction error rate was calculated. The optimal normalization parameters are obtained. ; In this embodiment, ; S406: Robust watermark difference Use the optimal normalization parameters Normalization is performed to obtain robust watermark difference moments. .

[0054] In one specific embodiment, in step S5, the robust watermark difference moment is... Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. The specific expression is: .

[0055] In one specific embodiment, in step S6, the robust watermark image is... Perform pixel overflow detection and record overflow information. ; In one specific embodiment, in step S7, the robust watermark difference moment is... and overflow information Embedded into robust watermarked images In the process, an image containing a robust reversible watermark is obtained. ;in, This is reversible watermark information; In one specific embodiment, in step S8, the intermediate image is... The least significant bit of the first few pixels is replaced with 0, and a hash value is generated using the SHA-256 algorithm. Replace intermediate images with hash values By analyzing the least significant bits of the first few pixels, a robust reversible watermark image is obtained, thus completing the robust reversible watermark embedding. .

[0056] Example 3 like Figure 2 As shown, the robust and reversible watermark extraction method based on moment clustering and normalization optimization includes the following specific steps: S21: Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the image containing the robust reversible watermark. hash value And use the reversible watermarking method to create a robust reversible watermark image. Restored to an image containing a robust reversible watermark. ; S22: Extract robust watermark image The former S The least significant bit of each pixel is extracted, and the extracted result replaces the image containing the robust reversible watermark. forward S After retrieving the least significant bit of each pixel, an image containing a robust reversible watermark is generated. hash value ; S23: Compare hash values and hash value If the hash value equal to hash value If the robust and reversible watermarked image has not been attacked, proceed to step S24; if the hash value... Not equal to hash value If the robust reversible watermark image is attacked, proceed to step S25. S24: Extract unattacked images containing robust reversible watermarks The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I ; S25: Extract the attacked image containing a robust reversible watermark. The watermark information.

[0057] In one specific embodiment, in step S24, the unattacked image containing the robust reversible watermark is extracted. The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I， The specific steps are as follows: S2401: Extract unattacked images containing robust reversible watermarks The former S The least significant bit of each pixel is used to extract the robust reversible watermark from the unaffected image. Restore to robust watermark image And extract the watermark information Robust watermark difference moments ; S2402: Calculating Robust Watermarked Images PCET moments ; S2403: PCET moment Watermark information is extracted using a quantized watermarking method. Its expression is as follows:

[0058]

[0059]

[0060] in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, For quantization step size, This is the jitter value; S2404: For the robust watermark difference Use normalization parameters Perform the inverse operation of normalization Robust watermark difference moment ; For the robust watermark difference Performing PCET inverse moment transform and rounding operations yields the original image with the watermark removed. Its expression is as follows:

[0061] in, L Indicates the length of the robust watermark information.

[0062] In one specific embodiment, step S25 involves extracting the attacked image containing a robust reversible watermark. The watermark information, the specific steps are as follows: Calculate the attacked image containing a robust reversible watermark. PCET moments , and for PCET moments Watermark information is extracted using a quantized watermarking method. w 1. Its expression is as follows:

[0063]

[0064]

[0065] in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, This is for quantization step size.

[0066] In this embodiment, the reversible watermark is obtained through prediction error expansion and histogram translation techniques, and the specific steps include: The diamond pattern prediction scheme divides all pixels in the image into two intersecting sets, called the cross set and the point set, respectively. The cross set is used to embed information, and the point set is used to calculate the predicted value. Among them, the center pixel The predicted value is obtained by using the pixels around it ( The mean of the values ​​is calculated by using the center pixel. The prediction error of a pixel is obtained by subtracting the actual value from the predicted value; similarly, the prediction error of all cross-set pixels is obtained. Calculate the local variance of all fork set pixels and sort them in ascending order to obtain the robust watermark difference moments. Overflow information The prediction error sequence of the least significant bits of the first S pixels of the image; The robust watermark difference moment is obtained by using the histogram translation method. Overflow information With the image front S The least significant bit of each pixel is embedded into the sorted prediction error sequence to obtain a reversible watermark.

[0067] Finally, the histogram shifting method is used to transform the robust watermark difference moments. Overflow information With the image front S The least significant bit of each pixel is embedded in the sorted prediction error sequence.

[0068] In the actual implementation process, when verifying copyright information, it is only necessary to use the robust reversible watermark image. Center front N The value of the least significant bit of each pixel, i.e., the image containing the robust reversible watermark. hash value Extract it, and you will get an image containing a robust reversible watermark. The former N The least significant bit of each pixel is "0" (because the content has been extracted).

[0069] Then add the robust watermark image Replace the least significant bit of the image containing the robust reversible watermark. The least significant bit (because of the robust watermark image) The least significant bit and the image containing a robust reversible watermark (The least significant bits are exactly the same), at which point a robust reversible watermark image is included. It was able to be recovered, and its hash value was generated. ; This represents an image containing a robust, reversible watermark when embedding a watermark. hash value, This represents an image containing a robust, reversible watermark during watermark extraction. hash, The fact that the two are identical proves that the image has not been attacked.

[0070] Example 4 In this embodiment, for the robust reversible watermark embedding and extraction method based on moment clustering and normalization optimization, an image with watermark information is considered to have good robustness if the bit error rate is below 20% after being attacked. The specific experimental results are as follows: Table 1: Bit error rate results when the image Lena is attacked (with a robust watermark embedded at 128 bits).

[0071] As shown in Table 1, the robust watermark embedded in the table is 128 bits. Experimental results based on the image Lena show that the method of this embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attacks with a compression ratio of 100:1, rotation attacks from 0 degrees to 360 degrees, scaling attacks with a stretching factor of 0.5 to 2.0, and Gaussian noise attacks with a mean of 0 and a variance of 0.009 to 0.029. The PSNR of the image Lena after embedding the robust reversible watermark is 39.98 dB compared to the original image.

[0072] Table 2: Bit Error Rate Results for Goldhill Images Under Attack (128 bits embedded with robust watermark)

[0073] As shown in Table 2, experimental results based on the Goldhill image demonstrate that the method described in this embodiment is resistant to JPEG compression with a quality factor of 10, JPEG2000 attacks with a compression ratio of 100:1, rotation attacks ranging from 0 to 360 degrees, scaling attacks with stretching factors from 0.5 to 2.0, and Gaussian noise attacks with a mean of 0 and a variance of 0.009 to 0.029. The PSNR of the Goldhill image after embedding the robust reversible watermark is 40.69 dB compared to the original image.

[0074] Table 3: Bit error rate results when image Peppers are attacked (128 bits embedded with robust watermark)

[0075] As shown in Table 3, experimental results based on image Peppers demonstrate that the method of this embodiment is resistant to JPEG compression with a quality factor of 10, JPEG2000 attacks with a compression ratio of 100:1, rotation attacks from 0 to 360 degrees, scaling attacks with a stretching factor of 0.5 to 2.0, and Gaussian noise attacks with a mean of 0 and a variance of 0.009 to 0.029. The PSNR of the Peppers image after embedding the robust reversible watermark is 40.08 dB compared to the original image.

[0076] Table 4: Bit error rate results when the image Barbara is attacked (with a robust watermark embedded at 128 bits).

[0077] As shown in Table 4, experimental results based on the Barbara image demonstrate that the method of this embodiment is resistant to JPEG compression with a quality factor of 10, JPEG2000 attacks with a compression ratio of 100:1, rotation attacks from 0 to 360 degrees, scaling attacks with stretching factors from 0.5 to 2.0, and Gaussian noise attacks with a mean of 0 and a variance of 0.009 to 0.029. The PSNR of the Barbara image after embedding the robust reversible watermark is 40.04 dB compared to the original image.

[0078] In this embodiment, grayscale images of Lena, Goldhill, Peppers, and Barbara are used as experimental subjects. These four sets of images have different characteristics. For example, Lena image includes flat blocks, clear and detailed textures, gradually changing light and shadow, and varying shades of color; Barbara image has more high-frequency details; Peppers image has more bright and dark areas, similar colors within blocks, and large color differences between blocks; Barbara image has a large number of regular textures. Various images in daily life possess these characteristics, therefore using these four sets of images as experimental subjects makes the experimental results generalizable. The image size selected in this embodiment is 512×512, and the differences between different images are not significant, thus it can be generalized to various types of images.

[0079] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

[0080] The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A robust and reversible watermark embedding method based on moment clustering and normalization optimization, characterized in that, Includes the following steps: S1: Obtain the original image And calculate the original image of Step Secondary PCET moments ; S2: Choose the order and degree to satisfy the optimal set of orders. and the set of optimal times PCET moments As a watermark embedding carrier; Also, the treatment of embedded watermark information The simulation attack experiment was conducted, and the PCET moments with the strongest robustness were selected by clustering algorithm. The specific steps are as follows: S201: Randomly select from the BOWS2 database Zhang Image ; S202: Calculate the image of Step Secondary PCET moments ; S203: Regarding the PCET moment Attack simulation experiments were conducted, using AWGN, JPEG compression, and JPEG2000 compression to analyze images. Perform a simulated attack to obtain the PCET moments of the attacked image. That is, in, Let be the order of the PCET moments. Let be the order of the PCET moments. Indicates that the variance is Gaussian noise simulation attack, Indicates the compression rate JPEG compression simulation attack Indicates the compression rate A JPEG2000 compression simulation attack; S204: Calculate the difference values ​​of the moments of order and degree for each image in the dataset. and will Step The corresponding difference values ​​form the difference vector. ; S205: For the difference vector The difference value in the middle is used min-max The normalization process is performed to obtain the normalized difference vector. Then normalize the difference vector The AFCM clustering algorithm was used to classify the following numbers: Classification, AFCM clustering algorithm The specific expression is as follows: in, Represents the number of clusters, Indicates the total number of data. For the corresponding vectors and clusters The probability of belonging, Represents clustering parameters, Represents the vector to be classified. Indicates the cluster center; S206: Accumulate and calculate the normalized difference vector for each class after classification. difference This yields the set of orders corresponding to the minimum accumulated difference value. and number set ; S3: PCET moment Perform quantized watermark embedding to obtain PCET moments with robust watermarks. ; S4: Calculate PCET moments and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. ; S5: Modify robust watermark difference moments Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. ,in, For watermark information; S6: For the robust watermarked image Perform pixel overflow detection and record overflow information. ; S7: Calculate the robust watermark difference moment and overflow information Embedded into robust watermarked images In the process, an image containing a robust reversible watermark is obtained. ;in, This is reversible watermark information; S8: Will include images with robust reversible watermarks The least significant bit of the first few pixels is replaced with 0, and a hash value is generated. Replace images containing robust reversible watermarks with hash values. The least significant bits of the first few pixels are used to obtain the robust reversible watermark image. Robust and reversible watermark embedding is achieved.

2. The robust reversible watermark embedding method based on moment clustering and normalization optimization according to claim 1, characterized in that, In step S1, the original image is acquired. And calculate the original image of Step Secondary PCET moments The specific steps are as follows: Based on size The original image The center is the center of the circle. K Given a positive integer, use it to create the original image. The inscribed circle is used to construct PCET moment basis functions. Using the inscribed circle as the unit circle, according to the PCET moment basis function... Calculate the nth-order m-th PCET moment of the pixels within the unit circle. The specific expression is: Among them, PCET basis functions It is a complete orthogonal basis on the unit circle. Represents the original image I The x Each horizontal axis Represents the original image The y One vertical axis, Represents the original image I The step size of the x-coordinate in the unit circle. Represents the original image The step size of the ordinate in the unit circle. Represents the pixels within the unit circle.

3. The robust reversible watermark embedding method based on moment clustering and normalization optimization according to claim 1, characterized in that, In step S3, the PCET moment is... Perform quantized watermark embedding to obtain PCET moments with robust watermarks. The specific steps are as follows: S301: Based on whether the embedded watermark information is '0' or '1', find the nearest '0 interval' or '1 interval' where the carrier is located, and move it a corresponding distance. The specific expression is: in, To quantize the step size, The jitter value. For embedding the first The order of the PCET moment of the watermark bits. For embedding the first The number of times the PCET moment of each watermark bit, For the first The bit value corresponding to each watermark bit; S302: PCET matrix with robust watermark Restored to PCET moments The specific expression is: 。 4. The robust reversible watermark embedding method based on moment clustering and normalization optimization according to claim 1, characterized in that, In step S4, the PCET moment is calculated. and PCET matrix with robust watermark The difference is normalized using optimal parameters to obtain the robust watermark difference moment. The specific steps are as follows: S401: Calculate the robust watermark difference between the PCET moment with embedded robust watermark and the original PCET moment. ; S402: Randomly select from the database Zhang images as dataset Perform the S3 operation on the image; S403: Calculate the dataset Robust watermark difference between the PCET moments of the image with embedded robust watermark and the original PCET moments. And robust watermark difference for each image. Normalization coefficients The reversible information was embedded in the simulation and normalized experiment to obtain normalized reversible information. ; S404: For the above dataset Normalized reversible information The simulation embedding experiment was performed, and S5-S7 operations were executed on it to obtain a set of simulated images with robust reversible information. ; S405: Calculate the dataset Robust reversible information simulation image set PSNR, and simulation image set of robust reversible information An attack simulation experiment was conducted, and the watermark extraction error rate was calculated. The optimal normalization parameters are obtained. ; S406: Robust watermark difference Use the optimal normalization parameters Normalization is performed to obtain robust watermark difference moments. .

5. The robust reversible watermark embedding method based on moment clustering and normalization optimization according to claim 1, characterized in that, In step S5, the robust watermark difference moment is... Reconstructed into an error image and the error image With the original image The robust watermark image is obtained by overlay processing. The specific expression is: ； in, L Indicates the length of the robust watermark information.

6. A robust and reversible watermark extraction method based on moment clustering and normalization optimization, characterized in that, include: Obtaining a robust reversible watermark image and robust watermarked images The robust reversible watermark image and robust watermarked images The watermark is generated using the robust reversible watermark embedding method based on moment clustering and normalization optimization as described in any one of claims 1 to 5. S21: Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the image containing the robust reversible watermark. hash value And use the reversible watermarking method to create a robust reversible watermark image. Restored to an image containing a robust reversible watermark ; S22: Extract robust watermark image The former S The least significant bit of each pixel is extracted, and the extracted result replaces the image containing the robust reversible watermark. forward S After retrieving the least significant bit of each pixel, an image containing a robust reversible watermark is generated. hash value ; S23: Compare hash values and hash value ; If hash value equal to hash value If the robust and reversible watermarked image has not been attacked, proceed to step S24; if the hash value... Not equal to hash value If the robust reversible watermark image is attacked, proceed to step S25. S24: Extract unattacked images containing robust reversible watermarks The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I ; S25: Extract the attacked image containing a robust reversible watermark. The watermark information.

7. The robust reversible watermark extraction method based on moment clustering and normalization optimization according to claim 6, characterized in that, In step S24, the unattacked image containing the robust reversible watermark is extracted. The watermark information is used to protect unattacked images containing robust and reversible watermarks. Perform a recovery operation to restore the unattacked image containing the robust reversible watermark. Restore to the original image I， The specific steps are as follows: S2401: Extract unattacked images containing robust reversible watermarks The former S The least significant bit of each pixel is used to extract the robust reversible watermark from the unaffected image. Restore to robust watermark image And extract the watermark information Robust watermark difference moments ; S2402: Calculating Robust Watermarked Images PCET moments ; S2403: PCET moment Watermark information is extracted using a quantized watermarking method. Its expression is as follows: in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, For quantization step size, This is the jitter value; S2404: For the robust watermark difference Use normalization parameters Perform the inverse operation of normalization Robust watermark difference moment ; For the robust watermark difference Performing PCET inverse moment transform and rounding operations yields the original image with the watermark removed. Its expression is as follows: in, L Indicates the length of the robust watermark information.

8. The robust reversible watermark extraction method based on moment clustering and normalization optimization according to claim 6, characterized in that, In step S25, the attacked image containing the robust reversible watermark is extracted. The watermark information, the specific steps are as follows: Calculate the attacked image containing a robust reversible watermark. PCET moments , and for PCET moments Watermark information is extracted using a quantized watermarking method. w 1. Its expression is as follows: in, For embedding the first i The order of the pseudo-PCET moment of the watermark bits. For embedding the first i The number of times the PCET moment of each watermark bit, i For the first i One watermark bit, To quantize the step size, This is the jitter value.

9. The robust reversible watermark extraction method based on moment clustering and normalization optimization according to claim 6, characterized in that: The reversible watermark is obtained through prediction error expansion and histogram shifting techniques, and the specific steps include: The diamond pattern prediction scheme divides all pixels in the image into two intersecting sets, called the cross set and the point set, respectively. The cross set is used to embed information, and the point set is used to calculate the predicted value. Among them, the center pixel The predicted value is obtained by using the pixels around it ( The mean of the values ​​is calculated by using the center pixel. The prediction error of a pixel is obtained by subtracting the actual value from the predicted value; similarly, the prediction error of all cross-set pixels is obtained. Calculate the local variance of all fork set pixels and sort them in ascending order to obtain the robust watermark difference moments. Overflow information The prediction error sequence of the least significant bits of the first S pixels of the image; The robust watermark difference moment is obtained by using the histogram translation method. Overflow information With the image front S The least significant bit of each pixel is embedded into the sorted prediction error sequence to obtain a reversible watermark.

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