Robust reversible watermark embedding method and extraction method based on pseudo-zernike moments

Abstract

This invention relates to the field of digital watermarking technology, and discloses a robust reversible watermark embedding and extraction method based on pseudo-Zernike moments. The method includes: calculating the pseudo-Zernike moments of the original image, performing adaptive normalization on pseudo-Zernike moments of different orders, performing a pseudo-Zernike inverse transform on the difference between the pseudo-Zernike moments calculated from the robust watermarked image and the pseudo-Zernike moments used to reconstruct the robust watermarked image, and embedding the watermark using a quantized watermarking method; 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 provides different watermark strengths for pseudo-Zernike moments of different orders, making the robust reversible image more robust to geometric attacks and conventional processing. The obtained error image is compensated into the robust watermarked image to further reduce the amount of distortion information, thereby achieving high-capacity watermark embedding.

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 pseudo-Zernike moments. Background Technology

[0002] Digital watermarking technology embeds digital information such as image identifiers, numbers, text, and serial numbers into digital media to serve an identification function. Significant progress has been made in the robustness research of digital image watermarking in recent years, but considerable difficulties remain in dealing with geometric attacks such as rotation, scaling, and translation. Robust reversible watermarking has the characteristic that when the carrier image is unaffected, the embedded watermark information can be correctly extracted and the carrier image can be completely recovered; and even when the carrier image is attacked to a certain extent, the watermark information can still be extracted correctly without loss.

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

[0004] However, the above method does not take into account the different watermark strengths required for Zernike moments of different orders during the watermark embedding process, resulting in excessive distortion information. Furthermore, the method does not compensate for the distortion information generated during the forward and inverse Zernike transforms, which further increases the amount of distortion information used for reversible watermark embedding, resulting in low robustness and inability to meet the requirements of large-capacity watermark embedding. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, such as low robustness and inability to meet the requirements of large-capacity watermark embedding, this invention provides a robust and reversible watermark embedding and extraction method based on pseudo-Zernike moments.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0007] In the first aspect, this invention proposes a robust reversible watermark embedding method based on pseudo-Zernike moments, comprising the following steps:

[0008] S1: Obtain the original image I .

[0009] S2: Calculate the original image Inth order m-fold pseudo-Zernike moments .

[0010] S3: For the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. .

[0011] S4: Normalized pseudo-Zernike moments Quantization watermark embedding is performed to obtain normalized pseudo-Zernike moments with robust watermarks. and quantization distortion .in, This indicates robust watermark information.

[0012] S5: For the normalized pseudo-Zernike moments with robust watermarks Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments with robust watermarks. .

[0013] S6: For the pseudo-Zernike matrix with robust watermark Perform a pseudo-Zernike inverse transform and rounding operation to obtain an image with a robust watermark. .

[0014] S7: Calculate images with robust watermarks Pseudo Zernike Matrix Then calculate the pseudo Zernike moments. With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation to obtain the error image. Error image With images with robust watermarks The image is overlaid by performing the overlay process. .

[0015] S8: For the superimposed image Perform watermark removal to obtain a watermark-free overlay image. .

[0016] S9: Calculate the original image I Image overlay with watermark removal Rounding distortion .

[0017] S10: Reduce the quantization distortion The rounding distortion mentioned and overlay images The former NThe least significant bit of each pixel is embedded into the image with robust watermarking. In the process, an intermediate image containing both robust and reversible watermarks is obtained. .in, This is reversible watermark information.

[0018] S11: Generate intermediate image hash value and the hash value Replace the intermediate image The former N The least significant bit of each pixel is used to obtain a robust reversible watermark image. .

[0019] Secondly, this invention also proposes a robust reversible watermark extraction method based on pseudo-Zernike moments, comprising:

[0020] Obtaining robust reversible watermark images and overlay images The robust reversible watermark image and overlay images The watermark is generated using a robust reversible watermark embedding method based on pseudo-Zernike moments as described in the first aspect.

[0021] Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the middle image. hash value And use a reversible watermarking method to robustly reversibly watermark the image. Restore to intermediate image .

[0022] Extracting overlay images The former S The least significant bit of each pixel is extracted, and the result is used to replace the intermediate image. forward S After retrieving the least significant bit of each pixel, the intermediate image is generated. hash value .

[0023] When hash value equal to hash value At that time, determine the robust reversible watermark image. Unattacked and intermediate image If no attack has occurred, proceed with the following steps:

[0024] Extracting unattacked intermediate images The watermark information.

[0025] For unattacked intermediate images Perform a recovery operation to retrieve the unattacked intermediate image. Restore to the original image I .

[0026] When hash value Not equal to hash value At that time, determine the robust reversible watermark image. Attacked and intermediate image If attacked, perform the following steps:

[0027] Extracting intermediate images from the attacked site The watermark information.

[0028] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0029] (1) This invention performs adaptive normalization on pseudo-Zernike moments of different orders, giving different watermark intensities to pseudo-Zernike moments of different orders, making robust reversible images more robust against geometric attacks and conventional processing.

[0030] (2) The present invention calculates pseudo Zernike moments from images with robust watermarks. and the pseudo-Zernike moments used to reconstruct the image with the robust watermark. The difference between the two images is subjected to a pseudo-Zernike inverse transform, and the resulting error image is used to compensate the image with the robust watermark, further reducing the amount of distorted information and achieving high-capacity watermark embedding. Attached Figure Description

[0031] Figure 1 This is a flowchart of the robust reversible watermarking embedding method based on pseudo-Zernike moments of the present invention.

[0032] Figure 2 This is a flowchart of the robust reversible watermark extraction method based on pseudo-Zernike moments of the present invention. Detailed Implementation

[0033] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0034] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0035] Example 1

[0036] Please see Figure 1 This embodiment proposes a robust reversible watermark embedding method based on pseudo-Zernike moments, including the following steps:

[0037] S1: Obtain the original image I .

[0038] S2: Calculate the original image I nth order m-fold pseudo-Zernike moments .

[0039] S3: For the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. .

[0040] S4: Normalized pseudo-Zernike moments Quantization watermark embedding is performed to obtain normalized pseudo-Zernike moments with robust watermarks. and quantization distortion .in, This indicates robust watermark information.

[0041] S5: For the normalized pseudo-Zernike moments with robust watermarks Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments with robust watermarks. .

[0042] S6: For the pseudo-Zernike matrix with robust watermark Perform a pseudo-Zernike inverse transform and rounding operation to obtain an image with a robust watermark. .

[0043] S7: Calculate images with robust watermarks Pseudo Zernike Matrix Then calculate the pseudo Zernike moments. With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation to obtain the error image. Error image With images with robust watermarks The image is overlaid by performing the overlay process. .

[0044] S8: For the superimposed image Perform watermark removal to obtain a watermark-free overlay image. .

[0045] S9: Calculate the original image I Image overlay with watermark removal Rounding distortion .

[0046] S10: Reduce the quantization distortion The rounding distortion mentioned and overlay images The former N The least significant bit of each pixel is embedded into the image with robust watermarking. In the process, an intermediate image containing both robust and reversible watermarks is obtained. .in, This is reversible watermark information.

[0047] S11: Generate intermediate image hash value and the hash value Replace the intermediate image The former N The least significant bit of each pixel is used to obtain a robust reversible watermark image. .

[0048] In the specific implementation, by adaptively normalizing the pseudo-Zernike moments of different orders, different watermark strengths are assigned to the pseudo-Zernike moments of different orders, making the robust reversible image more robust against geometric attacks and conventional processing. The pseudo-Zernike moments calculated from the image with the robust watermark are shown below. and the pseudo-Zernike moments used to reconstruct the image with the robust watermark. The difference between the two images is subjected to a pseudo-Zernike inverse transform, and the resulting error image is used to compensate the image with the robust watermark, further reducing the amount of distorted information and achieving high-capacity watermark embedding.

[0049] Example 2

[0050] This embodiment is an adjustment based on the robust reversible watermarking embedding method based on pseudo-Zernike moments proposed in Embodiment 1.

[0051] S1: Obtain the original image I .

[0052] S2: Calculate the original image I nth order m-fold pseudo-Zernike moments .

[0053] In this embodiment, the size is B × B The original image I The center is the center of the circle. B Given a positive integer, use it to create the original image. I The inscribed circle, and a pseudo-Zernike basis is constructed based on the inscribed circle. Using the inscribed circle as the unit circle, based on the pseudo-Zernike basis... Calculate the nth order m-fold pseudo-Zernike moments of pixels within the unit circle. The specific expression is as follows:

[0054]

[0055]

[0056]

[0057] , ,

[0058]

[0059] Among them, pseudo-Zernike base It is a complete orthogonal basis on the unit circle. It is a pseudo-Zernike polynomial. Represents the original image I The s Each horizontal axis Represents the original image I The t 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, where k ranges from 0 to... Integers.

[0060] In this embodiment, B The value is 512.

[0061] S3: For the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. The specific expression is as follows:

[0062]

[0063]

[0064] in, For embedding the first i The order of the pseudo-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit i For the first i One watermark bit,j For the first i The bit value corresponding to each watermark bit. For the 0th order, 0-weight pseudo-Zernike moments, N order n The upper limit, For adaptive normalized weights, The initial values ​​for the adaptive normalized weights, This is a global parameter used to adjust the watermark strength.

[0065] In this embodiment, N=26. =2400, =10.

[0066] An adaptive normalization scheme is adopted, which uses different adaptive normalization weights for different orders of pseudo-Zernike moments. This enables the embedding of watermark information of different strengths into pseudo-Zernike moments of different orders, improving the robustness against geometric attacks and conventional processing. It also enables watermark extraction and image restoration when not under attack, and effective watermark extraction when under attack.

[0067] S4: Normalized pseudo-Zernike moments Quantization watermark embedding is performed to obtain normalized pseudo-Zernike moments with robust watermarks. and quantization distortion ;in, Indicates robust watermark information The specific expression is as follows:

[0068]

[0069]

[0070]

[0071] in, Indicates constraints as jitter value, This is the quantization step size; express The decimal between the nearest integer and the nearest whole number, for example, if ,So =3, at this time =0.3.

[0072] In this embodiment, the quantization step size =32.

[0073] The quantization watermark embedding method used in this embodiment employs rounding operations, ensuring that the robust quantization watermark is only embedded into the pseudo-Zernike moments. The integer part, while the original image I Pseudo Zernike Matrix The fractional part is preserved, ensuring that the distortion caused by different watermark information is the same, significantly reducing the amount of distortion information used for reversible watermark embedding and achieving high-capacity watermark embedding. Based on the rotation and scaling invariance property of the absolute value of pseudo-Zernike moments, it can effectively resist rotation and scaling attacks, and can effectively extract watermark information and restore images when not attacked.

[0074] S5: For the normalized pseudo-Zernike moments with robust watermarks Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments with robust watermarks. The specific expression is as follows:

[0075] .

[0076] S6: For the pseudo-Zernike matrix with robust watermark Perform a pseudo-Zernike inverse transform and rounding operation to obtain an image with a robust watermark. The specific expression is as follows:

[0077]

[0078] in, L Indicates the length of the robust watermark information.

[0079] S7: Calculate images with robust watermarks Pseudo Zernike Matrix Then calculate the pseudo Zernike moments. With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation to obtain the error image. Then the error image With images with robust watermarks The image is overlaid by performing the overlay process. The specific expression is as follows:

[0080]

[0081] .

[0082] In this embodiment, although the pseudo Zernike moments are orthogonal transformations on the unit circle, information loss occurs during the forward and inverse transformations. Therefore, by constructing an error image, the distorted information is compensated for in the image with a robust watermark. This can reduce the degree of information loss. Therefore, robust watermarking is needed for images. The calculated pseudo Zernike moments and the pseudo-Zernike moments used to reconstruct the image The difference between them is subjected to a pseudo-Zernike inverse transform.

[0083] S8: For the superimposed image Perform watermark removal to obtain a watermark-free overlay image. The specific steps include:

[0084] Calculate overlay images Pseudo Zernike Matrix ;

[0085] For the pseudo Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ;

[0086] By extracting the normalized pseudo-Zernike moments Quantization distortion The normalized pseudo-Zernike moments for robust watermark removal are obtained.

[0087] For the normalized pseudo-Zernike moments Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments. The calculation formula is as follows:

[0088]

[0089] Calculate pseudo Zernike moments With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation, and the rounding result is compared with the superimposed image. The image is then overlaid to obtain a watermark-free overlaid image. The calculation formula is as follows:

[0090]

[0091] S9: Calculate the original image I Image overlay with watermark removal Rounding distortion Its expression is as follows:

[0092]

[0093] S10: Use a reversible watermarking method to remove the quantization distortion. The rounding distortion mentioned and overlay images The former N The least significant bit of each pixel is embedded into the image with robust watermarking. In the process, an intermediate image containing both robust and reversible watermarks is obtained. ;in, This is reversible watermark information.

[0094] S11: Generate intermediate image hash value and the hash value Replace the intermediate image The former N The least significant bit of each pixel is used to obtain a robust reversible watermark image. .

[0095] In this embodiment, the SHA-256 algorithm is used to generate the intermediate image. hash value .

[0096] Example 3

[0097] Please see Figure 2 This embodiment proposes a robust reversible watermark extraction method based on pseudo-Zernike moments, including:

[0098] Obtaining robust reversible watermark images and overlay images The robust reversible watermark image and overlay images The watermark is generated using the robust reversible watermark embedding method based on pseudo-Zernike moments as described in Example 1 or 2.

[0099] Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the middle image. hash value And use a reversible watermarking method to robustly reversibly watermark the image. Restore to intermediate image ;

[0100] Extracting overlay images The former S The least significant bit of each pixel is extracted, and the result is used to replace the intermediate image. forward S After retrieving the least significant bit of each pixel, the intermediate image is generated. hash value ;

[0101] When hash value equal to hash value At that time, determine the robust reversible watermark image. Unattacked and intermediate image If no attack has occurred, proceed with the following steps:

[0102] Extracting unattacked intermediate images The watermark information, and the specific steps include:

[0103] Extracting unattacked intermediate images The former S Least significant bit of each pixel, quantization distortion and rounding distortion And use a reversible watermarking method to separate the unattacked intermediate image. Restore to an image with a robust watermark ;

[0104] Calculate images with robust watermarks Pseudo Zernike Matrix and the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ;

[0105] According to the normalized pseudo-Zernike moments Robust watermark information is extracted using a quantized watermarking method. w 1. Its expression is as follows:

[0106]

[0107]

[0108] in, For embedding the first i The order of the pseudo-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit i For the first i One watermark bit, j For the first i The bit value corresponding to each watermark bit. Indicates constraints as jitter value, This is the quantization step size;

[0109] For unattacked intermediate images Perform a recovery operation to retrieve the intermediate image. Restore to the original image I Specifically, this includes:

[0110] According to the quantization distortion The normalized pseudo-Zernike moments Convert to pseudo-Zernike moments Its expression is as follows:

[0111]

[0112] For the pseudo Zernike moments Perform the inverse operation of adaptive normalization Pseudo Zernike Matrix ;

[0113] For the pseudo Zernike moments Perform a pseudo-Zernike inverse transform and rounding operation to obtain the watermark-free overlay image. Its expression is as follows:

[0114]

[0115] in, L Indicates the length of the robust watermark information;

[0116] According to rounding distortion Remove watermark and overlay image Convert to original image I Its expression is as follows:

[0117] .

[0118] When hash value Not equal to hash value At that time, determine the robust reversible watermark image. Attacked and intermediate image If attacked, perform the following steps:

[0119] Extracting intermediate images from the attacked site The watermark information, and the specific steps include:

[0120] When hash value Not equal to hash value At that time, extract the intermediate image that was attacked. The steps involved in watermarking information include:

[0121] Calculate the intermediate image under attack Pseudo Zernike Matrix For the pseudo Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ;

[0122] For normalized pseudo Zernike moments Perform a quantized watermark extraction operation to obtain the attacked intermediate image. watermark information Its expression is as follows:

[0123]

[0124]

[0125] in, For embedding the first i The order of the pseudo-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit i For the first i One watermark bit, j For the first i The bit value corresponding to each watermark bit. Indicates constraints as jitter value, This is for quantization step size.

[0126] In this embodiment, the reversible watermarking method is based on prediction error expansion and histogram shifting techniques. The specific steps include:

[0127] The diamond pattern prediction scheme divides all pixels in the image into two intersecting sets, called the fork set and the point set, respectively. The fork set is used to embed information, and the point set is used to calculate the predicted value.

[0128] 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 for a pixel is obtained by subtracting the actual value from the predicted value. Similarly, the prediction errors for all "fork set" pixels can be obtained.

[0129] Further calculation of the local variance of all cross-set pixels and their ascending order yields a result suitable for embedding quantization distortion. Rounding distortion With the image front S The prediction error sequence of the least significant bits of each pixel.

[0130] Finally, the histogram shifting method is used to reduce quantization distortion. Rounding distortion With the image frontS The least significant bit of each pixel is embedded in the sorted prediction error sequence.

[0131] 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 middle image. hash value Extract it, and you will get the intermediate image at this point. The former N The least significant bit of each pixel is "0" (because the content has been extracted).

[0132] Then overlay the images Replace the least significant bit of the middle image The least significant bit (because of the superimposed image) Least significant bit and intermediate image (The least significant bits are exactly the same), at this time the intermediate image It was able to be recovered, and its hash value was generated. ; This represents the intermediate image when embedding the watermark. hash value, This represents the intermediate image during watermark extraction. hash, The fact that the two are identical proves that the image has not been attacked.

[0133] In this embodiment, for the robust reversible watermark embedding and extraction method based on pseudo-Zernike moments, an image with watermark information is considered to have good robustness if the bit error rate is below 20% after being attacked. Specific experimental results are as follows:

[0134] Table 1: Bit error rate results when the image Lena is attacked (with a robust watermark embedded at 256 bits).

[0135]

[0136] As shown in Table 1, the embedded robust watermark is 256 bits. A bit error rate exceeding 20% ​​is indicated by "—". 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 0.01 to 0.03.

[0137] Table 2: Bit error rate results when image Peppers are attacked (256 bits for embedded robust watermark)

[0138]

[0139] As shown in Table 2, the experimental results based on image Peppers show that the method of this embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100:1, rotation attack from 0 degrees to 360 degrees, scaling attack with a stretching factor of 0.5 to 2.0, and Gaussian noise attack with a mean of 0 and a variance of 0.01 to 0.03.

[0140] Table 3: Bit error rate results when the image Barbara is attacked (with a robust watermark embedded at 256 bits).

[0141]

[0142] As shown in Table 3, the experimental results based on the image Barbara show that the method of this embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100:1, rotation attack from 0 degrees to 360 degrees, scaling attack with a stretching factor of 0.5 to 2.0, and Gaussian noise attack with a mean of 0 and a variance of 0.01 to 0.03.

[0143] Table 4: Bit error rate results when images are attacked using Baboon (with robust watermark embedded at 256 bits).

[0144]

[0145] As shown in Table 4, the experimental results based on image Baboon show that the method of this embodiment can resist JPEG compression with a quality factor of 10, JPEG2000 attack with a compression ratio of 100:1, rotation attack from 0 degrees to 360 degrees, scaling attack with a stretching factor of 0.5 to 2.0, and Gaussian noise attack with a mean of 0 and a variance of 0.01 to 0.03.

[0146] In this embodiment, grayscale images of Lena, Peppers, Barbara, and Baboon are used as experimental subjects. These four sets of images have different characteristics. For example, Lena includes flat blocks, clear and detailed textures, gradually changing light and shadow, and varying shades of color; Peppers has more areas of light and dark, similar colors within blocks, and large color differences between blocks; Barbara has a large number of regular textures; and Baboon has a large number of irregular 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.

[0147] 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.

[0148] 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 reversible watermark embedding method based on pseudo-Zernike moments, characterized in that, Includes the following steps: S1: Obtain the original image I ; S2: Calculate the original image I nth order m-fold pseudo-Zernike moments ; S3: For the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ; S4: Normalized pseudo-Zernike moments Quantization watermark embedding is performed to obtain normalized pseudo-Zernike moments with robust watermarks. and quantization distortion ;in, Indicates robust watermark information; S5: For the normalized pseudo-Zernike moments with robust watermarks Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments with robust watermarks. ; S6: For the pseudo-Zernike matrix with robust watermark Perform a pseudo-Zernike inverse transform and rounding operation to obtain an image with a robust watermark. ; S7: Calculate images with robust watermarks Pseudo Zernike Matrix Then calculate the pseudo Zernike moments. With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation to obtain the error image. ; to the error image With images with robust watermarks The image is overlaid by performing the overlay process. ; S8: For the superimposed image Perform watermark removal to obtain a watermark-free overlay image. ,include: Calculate overlay images Pseudo Zernike Matrix ; For the pseudo Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ; By extracting the normalized pseudo-Zernike moments Quantization distortion The normalized pseudo-Zernike moments for robust watermark removal are obtained. For the normalized pseudo-Zernike moments Perform the inverse operation of adaptive normalization to obtain pseudo-Zernike moments. The calculation formula is as follows: Calculate pseudo Zernike moments With pseudo-Zernike matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation, and the rounding result is compared with the superimposed image. The image is then overlaid to obtain a watermark-free overlaid image. The calculation formula is as follows: ； S9: Calculate the original image I Image overlay with watermark removal Rounding distortion ; S10: Reduce the quantization distortion The rounding distortion mentioned and overlay images The former N The least significant bit of each pixel is embedded into the image with robust watermarking. In the process, an intermediate image containing both robust and reversible watermarks is obtained. ;in, This is reversible watermark information; S11: Generate intermediate image hash value and the hash value Replace the intermediate image The former N The least significant bit of each pixel is used to obtain a robust reversible watermark image. .

2. The robust reversible watermark embedding method based on pseudo-Zernike moments according to claim 1, characterized in that, In S2, the calculation of the original image I nth order m-fold pseudo-Zernike moments The specific steps include: Based on size B × B The original image I The center is the center of the circle. B Given a positive integer, use it to create the original image. I The inscribed circle, and a pseudo-Zernike basis is constructed based on the inscribed circle. Using the inscribed circle as the unit circle, based on the pseudo-Zernike basis... Calculate the nth order m-fold pseudo-Zernike moments of pixels within the unit circle. The specific expression is as follows: Among them, pseudo-Zernike base It is a complete orthogonal basis on the unit circle. Represents the original image I The s Each horizontal axis Represents the original image I The t 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.

3. The robust reversible watermark embedding method based on pseudo-Zernike moments according to claim 1, characterized in that, In S3, the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. The specific expression is as follows: in, For embedding the first i The order of the pseudo-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit j For the first i The bit value corresponding to each watermark bit. For the 0th order, 0-weight pseudo-Zernike moments, N order n The upper limit, For adaptive normalized weights, The initial values ​​for the adaptive normalized weights, This is a global parameter used to adjust the watermark strength.

4. The robust reversible watermark embedding method based on pseudo-Zernike moments according to claim 1, characterized in that, In S4, the normalized pseudo-Zernike moments Quantization watermark embedding is performed to obtain normalized pseudo-Zernike moments with robust watermarks. and quantization distortion The specific expression is as follows: in, Indicates constraints as jitter value, To quantize the step size, express The decimal between the nearest integer and the nearest whole number.

5. The robust reversible watermark embedding method based on pseudo-Zernike moments according to claim 1, characterized in that, In S6, the pseudo-Zernike matrix with robust watermark is... Perform a pseudo-Zernike inverse transform and rounding operation to obtain an image with a robust watermark. The specific expression is as follows: in, L Indicates the length of the robust watermark information.

6. The robust reversible watermark embedding method based on pseudo-Zernike moments according to claim 1, characterized in that, In S7, the calculation of pseudo-Zernike moments With images with robust watermarks Pseudo Zernike Matrix The difference is then subjected to a pseudo-Zernike inverse transform and rounding operation to obtain the error image. The specific expression is as follows: The error image With images with robust watermarks The image is overlaid by performing the overlay process. The specific expression is as follows: 。 7. A robust and reversible watermark extraction method based on pseudo-Zernike moments, characterized in that, include: Obtaining robust reversible watermark images and overlay images The robust reversible watermark image and overlay images The watermark is generated using the robust reversible watermark embedding method based on pseudo-Zernike moments as described in any one of claims 1 to 6. Extract the robust reversible watermark image The former S The least significant bit of each pixel, i.e., the middle image. hash value And use a reversible watermarking method to robustly reversibly watermark the image. Restore to intermediate image ; Extracting overlay images The former S The least significant bit of each pixel is extracted, and the result is used to replace the intermediate image. forward S After retrieving the least significant bit of each pixel, the intermediate image is generated. hash value ; When hash value equal to hash value At that time, determine the robust reversible watermark image. Unattacked and intermediate image If no attack has occurred, proceed with the following steps: Extracting unattacked intermediate images Watermark information; For unattacked intermediate images Perform a recovery operation to retrieve the unattacked intermediate image. Restore to the original image I ; When hash value Not equal to hash value At that time, determine the robust reversible watermark image. Attacked and intermediate image If attacked, perform the following steps: Extracting intermediate images from the attacked site The watermark information.

8. The robust reversible watermark extraction method based on pseudo-Zernike moments according to claim 7, characterized in that, When hash value equal to hash value At that time, extract the intermediate image that has not been attacked. The steps involved in watermarking information include: Extracting unattacked intermediate images The former S Least significant bit of each pixel, quantization distortion and rounding distortion And use a reversible watermarking method to separate the unattacked intermediate image. Restore to an image with a robust watermark ; Calculate images with robust watermarks Pseudo Zernike Matrix and the pseudo-Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ; According to the normalized pseudo-Zernike moments Robust 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-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit i For the first i One watermark bit, j For the first i The bit value corresponding to each watermark bit. Indicates constraints as jitter value, This is the quantization step size; The intermediate image that has not been attacked Perform a recovery operation to retrieve the unattacked intermediate image. Restore to the original image I The steps include: According to the quantization distortion The normalized pseudo-Zernike moments Convert to pseudo-Zernike moments Its expression is as follows: For the pseudo Zernike moments Perform the inverse operation of adaptive normalization Pseudo Zernike Matrix ; For the pseudo Zernike moments Perform a pseudo-Zernike inverse transform and rounding operation to obtain the watermark-free overlay image. Its expression is as follows: in, L Indicates the length of the robust watermark information; According to rounding distortion Remove watermark and overlay image Convert to original image I Its expression is as follows: 。 9. The robust reversible watermark extraction method based on pseudo-Zernike moments according to claim 7, characterized in that, When hash value Not equal to hash value At that time, extract the intermediate image that was attacked. The steps involved in watermarking information include: Calculate the intermediate image under attack Pseudo Zernike Matrix For the pseudo Zernike moments Perform adaptive normalization to obtain normalized pseudo-Zernike moments. ; For normalized pseudo Zernike moments Perform a quantized watermark extraction operation to obtain the attacked intermediate image. watermark information Its expression is as follows: in, For embedding the first i The order of the pseudo-Zernike moment of the watermark bits. For embedding the first i The multiplicity of the pseudo-Zernike moments of 1 watermark bit i For the first i One watermark bit, j For the first i The bit value corresponding to each watermark bit. Indicates constraints as jitter value, This is for quantization step size.

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