A lossless watermarking method based on uncertainty perception and regular singularity judgment

Abstract

The application provides a lossless watermarking method based on uncertainty perception information and regular singular judgment. At the sending end, first, pre-processing is performed on an original image to obtain a pre-processed image and a bit plane; the pre-processed image is input into a trained model to obtain model output and binarization into a reference bit plane; a regular singular graph is obtained by detecting the bit plane and the reference bit plane and is compressed; uncertainty perception information is obtained through the model output; and the regular singular graph and the uncertainty perception information are combined to perform lossless watermarking embedding. At the receiving end, pre-processing is performed on a watermarking image to obtain a pre-processed image and a bit plane; the pre-processed image is input into a trained model to obtain model output and binarization into a reference bit plane; uncertainty perception information is obtained through the model output, the order of watermarking embedding is determined, and watermarking information is extracted accordingly; and a compressed regular singular graph is extracted to assist in original image recovery. Compared with the prior art, the application has good performance in embedding capacity and efficiency.

Description

A lossless watermarking method based on uncertainty perception and regular singularity judgment Technical Field

[0001] This invention studies the field of digital watermarking in multimedia security, specifically involving a lossless watermarking method based on uncertainty perception and regular singularity discrimination. Background Technology

[0002] With the rapid development of internet technology, the exchange of digital media and personal privacy data via the internet has become increasingly common. Given that this exchange of private information occurs through transparent online channels, it is vulnerable to eavesdropping and other forms of infringement, posing a serious threat to people's physical, mental, and financial security. On the other hand, as people's living standards improve, they are no longer satisfied with just material needs; their demand for spiritual and cultural enrichment is also growing. In particular, people's awareness of their rights is increasing, and they are paying more attention than ever before to the security and protection of their privacy information.

[0003] The leakage of private information can pose serious threats to personal safety and property. Numerous examples exist of injuries, deaths, and property losses caused by privacy breaches. The consequences of unwittingly leaked private data require significant effort to mitigate. While current laws effectively deter perpetrators from violating privacy laws, they do not fundamentally protect privacy at its source. Therefore, there is an urgent need to develop a method for achieving lossless watermarking, providing a solution for the transmission of private data between users. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of privacy data leakage in the network and to provide a lossless watermarking method based on uncertainty perception and regular singularity discrimination.

[0005] The technical solution steps of this invention are as follows:

[0006] A lossless watermarking method based on uncertainty-aware information and regular singularity judgment is used for image transmission between a sender and a receiver, characterized by:

[0007] At the transmitting end, a digital watermark is embedded in the original image I according to steps S11 to S14:

[0008] S11. Perform preprocessing on the original image I to obtain the preprocessed image I2 and bit plane B;

[0009] S12. Input the preprocessed image I2 into the trained model M, obtain the model output O, and binarize the output O into the reference bit plane BR.

[0010] S13. By detecting bit plane B and reference bit plane BR, obtain the regular singular graph RSM, and compress the regular singular graph RSM to obtain the compressed regular singular graph CRSM.

[0011] S14. Obtain uncertainty-aware information UM through model output O; combine the compressed regular singular graph CRSM and uncertainty-aware information UM to determine the watermark embedding order, perform lossless watermark embedding, and obtain the watermark image WI.

[0012] At the receiving end, the received watermarked image WI is extracted and the original image I is restored according to steps S21 to S24:

[0013] S21. Perform preprocessing on the received watermark image WI to obtain the preprocessed image WI2 and the bit plane WB;

[0014] S22. Input the preprocessed image WI2 into the trained model M, obtain the model output WO, and binarize the output WO into the reference bit plane WBR.

[0015] S23. Obtain uncertainty-aware information WUM through the model output WO, determine the order of watermark embedding, and extract watermark information accordingly.

[0016] S24. Extract the compressed regular singular graph CWRSM from the extracted watermark information and decompress it to obtain the regular singular graph WRSM. With the help of the regular singular graph WRSM, restore the original image and obtain the original image I.

[0017] Preferably, in step S11, the third bit plane of the original image I is extracted to form bit plane B, and all bits of the third bit plane of image I are set to 0 to form a preprocessed image I2.

[0018] Preferably, in S12, the model M is composed of a first convolutional layer, multiple RK units, a second convolutional layer, and a third convolutional layer cascaded in sequence. The input image of the model first passes through the first convolutional layer to obtain a first feature map. The first feature map then passes through multiple RK units in sequence to output a second feature map. The residuals of the first feature map and the second feature map are connected and then passed through the second convolutional layer and the third convolutional layer in sequence to obtain the final output image.

[0019] Each RK unit contains three convolutional modules consisting of convolutional layers followed by PreLU activation functions. The original input feature y of the RK unit is... n First, the first intermediate feature y1 is obtained by passing it through the first convolutional module, and then the weighted features are... The second intermediate feature y2 is obtained by inputting into the second convolutional module, and the weighted feature y is then... n+2y2-y1 is input into the third convolutional module to obtain the third intermediate feature y3, which is then weighted as a feature. As the final output feature y n+1 .

[0020] Preferably, the model M contains 20 RK units.

[0021] Preferably, in step S13, a regular singular graph RSM is obtained by detecting bit plane B and reference bit plane BR, and the regular singular graph RSM is compressed to obtain a compressed regular singular graph CRSM. The specific method is as follows:

[0022] S131: Divide the bit plane B into several non-overlapping 2*2 size first blocks A1, and flip each element value of the first block A1 to obtain the second block A2;

[0023] S132: Divide the reference bit plane BR into several non-overlapping 2*2 size third blocks A3;

[0024] S133: Calculate two parameters based on the element values ​​of the first block A1, the second block A2, and the third block A3. and

[0025]

[0026]

[0027] Among them, a1 i a2 i and a3 i These are the values ​​of the i-th element in A1, A2, and A3, respectively; k is the number of elements in a single block of A1, A2, and A3;

[0028] S134: Perform regular singularity checks on each first block A1 to determine its category. The determination method is as follows:

[0029]

[0030] Where R represents the regularity class, S represents the oddity class, and U represents the unusable class;

[0031] S135: After obtaining the category of each first block A1 through regular singularity judgment, the first block A1 in the image belonging to the regular class is marked as 1, and the first block A1 belonging to the singular class is marked as 0, thus forming a regular singular graph RSM; and the regular singular graph RSM is compressed to form a compressed regular singular graph CRSM.

[0032] Preferably, in step S14, uncertainty-aware information UM is obtained through model output O; lossless watermark embedding is performed by combining regular singular graph RSM and uncertainty-aware information UM to obtain watermark image WI, specifically as follows:

[0033] S141: Divide the model output O into several non-overlapping 2*2 size fourth blocks A4;

[0034] S142: Based on the element values ​​of the first block A1, the second block A2, and the fourth block A4, calculate the uncertainty-aware information u(A1) for each first block A1, specifically:

[0035]

[0036]

[0037]

[0038] Among them, a1 i a2 i and a4 i These are the values ​​of the i-th element in A1, A2, and A4, respectively.

[0039] S143: Calculate an uncertainty-aware information for each first block A1 Then, an uncertainty-aware information graph UM is formed, and uncertainty-aware information for all first blocks A1 is processed. Sort the images in ascending order, select the top N first blocks A1, find the image blocks corresponding to these N first blocks A1 on the original image I as watermark embedding blocks, and perform lossless watermark embedding to obtain the watermark image WI, thereby ensuring the quality of the watermark image and improving the embedding efficiency.

[0040] Preferably, in step S143, when performing lossless watermark embedding on the original image I, the specific method is as follows:

[0041] S1431: Concatenate the compressed regular singular graph (CRSM) with the bitstream of the watermark to be embedded as the information to be embedded;

[0042] S1432: The information to be embedded is embedded bit by bit into each watermark embedding block of the original image I, thereby obtaining the watermark image WI; wherein, each watermark embedding block is modified to the corresponding first block A1 or second block A2 according to the different bits of the information to be embedded and the category to which the corresponding first block A1 belongs. The modification rules for the watermark embedding block when performing embedding are as follows:

[0043]

[0044] Where m is a bit of information to be embedded in the current watermark embedding block, and A′ is the corresponding image block in the watermark image WI after embedding.

[0045] Preferably, in step S21, the third bit plane of the watermark image WI is extracted to form bit plane WB, and all bits of the third bit plane of the watermark image WI are set to 0 to form a preprocessed image WI2.

[0046] Preferably, in step S23, uncertainty-aware information WUM is obtained through the model output WO, the watermark embedding order is determined, and watermark information is extracted accordingly. The specific method is as follows:

[0047] S231: Divide the model output WO into several non-overlapping 2*2 size fifth blocks A5;

[0048] S232: Divide the bit plane WB into several non-overlapping 2*2 size sixth blocks A6, and flip each element value of each sixth block A6 to obtain the corresponding seventh block A7.

[0049] S233: Based on the element values ​​of block A6, block A7, and block A5, calculate the uncertainty-aware information for each block A6. Specifically:

[0050]

[0051]

[0052]

[0053] Among them, a6 i a7 i and a5 i These are the values ​​of the i-th element in A6, A7, and A5, respectively.

[0054] S234: Calculate an uncertainty-aware information for each sixth block A6 Then, an uncertainty-aware information graph WUM is formed, and uncertainty-aware information for all sixth blocks A6 is generated. Sort in ascending order, select the top N sixth blocks A6, and find the corresponding image blocks A′ on the watermark image WI as the watermark extraction blocks;

[0055] S235: Sequentially extract watermark information bits from all image blocks A′ within the watermarked image WI that serve as watermark extraction blocks. The bit extraction rule for a single image block A′ is related to the category to which image block A′ belongs, determined by regular singularity determination:

[0056]

[0057] The extracted bits m are concatenated to form the extracted watermark information.

[0058] Preferably, in step S24, a compressed regular singular graph (CWRSM) is extracted from the extracted watermark information and decompressed to obtain a regular singular graph (WRSM). The original image is then recovered with the assistance of the regular singular graph (WRSM) to obtain the original image I. The specific method is as follows:

[0059] S241: Extract the compressed regular singular graph CWRSM from the extracted watermark information and decompress it to obtain the regular singular graph WRSM;

[0060] S242: Based on the regular singular graph WRSM, determine whether each image block A′ used as a watermark extraction block originally belonged to a regular class or a singular class. If its original class is consistent with the class to which A′ belongs, then A′ is the block of the original image; otherwise, the element values ​​of A′ need to be flipped before it is used as a block of the original image I. After all the image blocks A′ of the watermark extraction blocks on the watermark image WI are restored, the lossless restoration of the original image I is finally achieved.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0062] This invention designs a model composed of convolutional layers and multiple RK units. Based on the model's output, uncertainty-aware information can be obtained. Then, by combining the compressed regularized singular graph and the uncertainty-aware information, lossless watermark embedding can be performed on the original image, thereby obtaining a watermarked image. Compared with other existing technologies, the solution provided by this invention exhibits superior performance in terms of embedding capacity and embedding efficiency. Attached Figure Description

[0063] Figure 1 is a schematic diagram of the architecture of model M.

[0064] Figure 2 is a schematic diagram of the RK unit.

[0065] Figure 3 shows the watermark image quality test data.

[0066] Figure 4 shows the test data for uncertainty measurement.

[0067] Figure 5 shows the rate-distortion curves for different methods. Detailed Implementation

[0068] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments.

[0069] In a preferred embodiment of the present invention, a lossless watermarking method based on uncertainty-aware information and regular singularity judgment is provided for transmitting secret information between a sender and a receiver. The following description, using an 8-bit grayscale image as the original image, elaborates on the specific implementation processes of the sender and receiver in this embodiment of the invention, in conjunction with the accompanying drawings.

[0070] At the sending end, a digital watermark is embedded in the original image I according to steps S11 to S14. The specific process is as follows:

[0071] S11. Perform preprocessing on the original image I to obtain the preprocessed image I2 and bit plane B.

[0072] In an embodiment of the present invention, in step S11 above, the third bit plane of the original image I is extracted to form bit plane B, and all the third bit planes of image I are set to 0 to form a preprocessed image I2.

[0073] S12. Input the preprocessed image I2 into the trained model M, obtain the model output O, and binarize the output O into the reference bit plane BR.

[0074] In an embodiment of the present invention, in step S12, the model M is composed of a first convolutional layer, multiple RK units, a second convolutional layer, and a third convolutional layer cascaded sequentially, as shown in Figure 1. The input image of the model first passes through the first convolutional layer to obtain a first feature map. The first feature map then passes through multiple RK units sequentially to output a second feature map. The residuals of the first and second feature maps are concatenated and then passed through the second and third convolutional layers sequentially to obtain the final output image. The final output image can be binarized into a reference bit plane BR.

[0075] Figure 2 shows the specific structure of each RK unit, which contains three convolutional modules consisting of convolutional layers followed by PreLU activation functions. The original input feature y of the RK unit is... n First, the first intermediate feature y1 is obtained by passing it through the first convolutional module, and then the weighted features are... The second intermediate feature y2 is obtained by inputting into the second convolutional module, and the weighted feature y is then... n +2y2-y1 is input into the third convolutional module to obtain the third intermediate feature y3, which is then weighted as a feature. As the final output feature y n+1 The output features of the previous RK unit are then used as the input features of the next RK unit.

[0076] In an embodiment of the present invention, the number of RK units in the above model M can be adjusted and optimized according to actual conditions; here, it is optimized to 20 units.

[0077] S13. By detecting bit plane B and reference bit plane BR, obtain regular singular graph RSM, and compress regular singular graph RSM to obtain compressed regular singular graph CRSM.

[0078] In an embodiment of the present invention, the specific method for obtaining the compressed regular singular graph CRSM in step S13 above is as follows:

[0079] S131: Divide the bit plane B into several non-overlapping 2*2 size first blocks A1, and flip each element value of the first block A1 to obtain the second block A2.

[0080] S132: Divide the reference bit plane BR into several non-overlapping 2*2 size third blocks A3.

[0081] S133: Calculate two parameters based on the element values ​​of the first block A1, the second block A2, and the third block A3. and

[0082]

[0083]

[0084] Among them, a1 i a2 i and a3 i These are the i-th element values ​​of A1, A2, and A3, respectively; k is the number of elements in a single block of A1, A2, and A3; each first block A1 corresponds to an image block in the original image I.

[0085] S134: Perform regular singularity checks on each first block A1 to determine its category. The determination method is as follows:

[0086]

[0087] Where R represents the regularity class, S represents the singularity class, and U represents the unusable class.

[0088] S135: After obtaining the category of each first block A1 through regular singularity judgment, the category of each image block can be determined. Specifically, the first block A1 belonging to the regular class can be marked as 1, and the first block A1 belonging to the singular class can be marked as 0, thus forming a regular singular graph RSM. Then, the regular singular graph RSM is compressed to form a compressed regular singular graph CRSM.

[0089] S14. Obtain uncertainty-aware information UM through model output O; combine the compressed regular singular graph CRSM and uncertainty-aware information UM to determine the watermark embedding order, perform lossless watermark embedding, and obtain the watermark image WI.

[0090] In an embodiment of the present invention, in step S14 above, uncertainty-aware information UM is obtained through model output O; lossless watermark embedding is performed by combining regular singular graph RSM and uncertainty-aware information UM to obtain watermark image WI. The specific method is as follows:

[0091] S141: Divide the model output O into several non-overlapping 2*2 size fourth blocks A4;

[0092] S142: Based on the element values ​​of the first block A1, the second block A2, and the fourth block A4, calculate the uncertainty-aware information of each first block A1. Specifically:

[0093]

[0094]

[0095]

[0096] Among them, a1 i a2 i and a4 i These are the values ​​of the i-th element in A1, A2, and A4, respectively.

[0097] S143: Calculate an uncertainty-aware information for each first block A1 Then, an uncertainty-aware information graph UM is formed, and uncertainty-aware information for all first blocks A1 is processed. Sort the data in ascending order, select the first N blocks A1 with the smallest uncertainty values, find the image blocks corresponding to these N first blocks A1 on the original image I as watermark embedding blocks, and perform lossless watermark embedding to obtain the watermark image WI, thereby ensuring the quality of the watermark image and improving the embedding efficiency.

[0098] It should be noted that the specific value N needs to be adjusted according to the length of the watermark information, but no limit is specified here.

[0099] Furthermore, in step S143 above, when performing lossless watermark embedding on the original image I, the specific method is as follows:

[0100] S1431: Concatenate the compressed regular singular graph (CRSM) with the bitstream of the watermark to be embedded as the information to be embedded;

[0101] S1432: The information to be embedded is embedded bit by bit into each watermark embedding block of the original image I, thereby obtaining the watermark image WI; wherein, each watermark embedding block is modified to either the corresponding first block A1 or the second block A2 according to the different bits of the information to be embedded and the category to which the corresponding first block A1 belongs. The modification rules for the watermark embedding block during embedding are as follows:

[0102]

[0103] Where m is a bit of information to be embedded in the current watermark embedding block, and A′ is the corresponding image block in the watermark image WI after embedding.

[0104] At the receiving end, the watermarked image WI is extracted and the original image I is restored according to steps S21 to S24. The specific process is as follows:

[0105] S21. Perform preprocessing on the received watermark image WI to obtain the preprocessed image WI2 and the bit plane WB.

[0106] In an embodiment of the present invention, in step S21 above, the third bit plane of the watermark image WI is extracted to form bit plane B, and all the third bit planes of the watermark image WI are set to 0 to form a preprocessed image WI2.

[0107] S22. Input the preprocessed image WI2 into the trained model M, obtain the model output WO, and binarize the output WO into the reference bit plane WBR.

[0108] S23. Obtain uncertainty-aware information WUM through the model output WO, determine the order of watermark embedding, and extract watermark information accordingly.

[0109] In an embodiment of the present invention, the specific method for extracting watermark information in step S23 is as follows:

[0110] S231: Divide the model output WO into several non-overlapping 2*2 size fifth blocks A5;

[0111] S232: Divide the bit plane WB into several non-overlapping 2*2 size sixth blocks A6, and flip each element value of each sixth block A6 to obtain the corresponding seventh block A7.

[0112] S233: Based on the element values ​​of block A6, block A7, and block A5, calculate the uncertainty-aware information for each block A6. Specifically:

[0113]

[0114]

[0115]

[0116] Among them, a6 i a7 i and a5 i These are the values ​​of the i-th element in A6, A7, and A5, respectively.

[0117] S234: Calculate an uncertainty-aware information for each sixth block A6 Then, an uncertainty-aware information graph WUM is formed, and uncertainty-aware information for all sixth blocks A6 is generated. Sort in ascending order, select the top N sixth blocks A6, and find the corresponding image blocks A′ on the watermark image WI as the watermark extraction blocks;

[0118] S235: Sequentially extract watermark information bits from all image blocks A′ within the watermarked image WI that serve as watermark extraction blocks. The bit extraction rule for a single image block A′ is related to the category to which image block A′ belongs, determined by regular singularity determination:

[0119]

[0120] The extracted bits m are concatenated to form the extracted watermark information.

[0121] It should be noted that the regular singularity determination rule for image block A′ is consistent with the determination rule for the first block A1 mentioned above.

[0122] S24. Extract the compressed regular singular graph CWRSM from the extracted watermark information and decompress it to obtain the regular singular graph WRSM. With the help of the regular singular graph WRSM, restore the original image and obtain the original image I.

[0123] In an embodiment of the present invention, the specific method for obtaining the original image I in step S24 above is as follows:

[0124] S241: Extract the compressed regular singular graph CWRSM from the extracted watermark information and decompress it to obtain the regular singular graph WRSM;

[0125] S242: Based on the regular singular graph WRSM, determine whether each image block A′ used as a watermark extraction block originally belonged to a regular class or a singular class. If its original class is consistent with the class to which A′ belongs, then A′ is the block of the original image; otherwise, the element values ​​of A′ need to be flipped before it is used as a block of the original image I. After all the image blocks A′ of the watermark extraction blocks on the watermark image WI are restored, the lossless restoration of the original image I is finally achieved.

[0126] To demonstrate the effects achievable by the present invention, the above method is applied to a specific embodiment below. The specific steps will not be repeated here, but the specific parameters and technical effects are mainly shown below.

[0127] Example

[0128] (1) Concealment test

[0129] The visual effects of the four watermarked images obtained in this embodiment are shown in Figure 3. It can be observed that the human eye can hardly distinguish the difference between the original image and the watermarked image, thus making it difficult to detect traces of privacy information. Meanwhile, data measurements show that the PSNR of both the original image and the watermarked image is above 52.00 dB, further demonstrating that the present invention has excellent privacy protection.

[0130] (2) Uncertainty Measurement Test

[0131] This embodiment evaluates the performance of a watermark embedding method (referred to as the NDCS method) based on a deep learning model (i.e., the aforementioned model M) combined with uncertainty-aware discriminant analysis. More specifically, this embodiment statistically analyzes the performance of the NDCS+Rand, NDCS+Seq, and NDCS+Sort methods in providing embedding capacity under different block counts. Here, NDCS+Seq indicates that the selection order of embedding blocks during watermark embedding is determined by raster scanning; NDCS+Rand indicates that the selection order of embedding blocks during watermark embedding is random; and NDCS+Sort indicates that the selection order of embedding blocks during watermark embedding is determined based on the uncertainty of each block, from low to high. NDCS+Sort refers to the lossless watermarking method based on uncertainty-aware information and regular singularity judgment in S11-S14 and S21-S24 of the aforementioned preferred embodiment of the present invention. In all the methods compared above, model M is trained using only text loss.

[0132] As shown in Figure 4, the embedding capacity (ER) provided by the NDCS+Sort method of this invention is significantly higher than that of the NDCS+Seq and NDCS+Rand methods, especially in the early stages of the curve. Although this trend weakens as more embedding capacity is added, it always maintains a slight lead. This is mainly due to the fact that the NDCS+Sort method can effectively select blocks with low uncertainty-aware information to participate in information embedding, that is, it selects a large number of R-type blocks with high probability to participate in the steganography process first.

[0133] (3) Embedded capacity test

[0134] To further demonstrate the advantages of the NDCS+sort method of this invention, this embodiment compares rate-distortion performance under different configurations using UNet and UNet* as controls, as shown in Figure 5. UNet refers to a conventional steganography method employing sequential selection of embedding blocks, where the network structure is UNet and the model is trained using only text loss. UNet* refers to a conventional steganography method employing sequential selection of embedding blocks, where the network structure is UNet and the model is trained using a combination of text loss and adversarial loss. Clearly, the method of this invention achieves better rate-distortion performance.

[0135] (4) Performance comparison

[0136] Table 1 shows a comparison of the ER and pure ER of four images between NDCS+Sort and other RS ​​methods [1, 2]. ER refers to the average effective payload carried by each pixel in the watermarked image, and pure ER refers to the average number of watermark bits that each pixel in the watermarked image can carry. From the perspective of ER, the method of the present invention provides a higher ER value than the schemes [1, 2]. For pure ER, the NDCS+Sort method of the present invention also achieves a significant improvement over the schemes [1, 2]. As a result, the NDCS+Sort method of the present invention is able to carry more watermark bits.

[0137] Table 1. Comparison of ER and pure ER between NDCS+Sort and other RS ​​methods.

[0138]

[0139] For details on the comparison methods [1] and [2], please refer to the following references:

[0140] [1] Fridrich J., Goljan M., and Du R., "Lossless Data Embedding New Paradigm in Digital Watermarking," EURASIP Journal on Applied SignalProcessing, 2002, 2: 185-196.

[0141] [2] Chang CC, "Adversarial Learning for Invertible Steganography," IEEE Access, 2020, 8: 198425-198435.

[0142] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A lossless watermarking method based on uncertainty perception and regular singularity judgment, used for image transmission between a sending end and a receiving end, characterized in that: At the transmitting end, a digital watermark is embedded in the original image I according to steps S11-S14: S11, preprocessing the original image I to obtain a preprocessed image I2 and a bit plane B; S12, inputting the preprocessed image I2 into the trained model M, obtaining the model output O, and binarizing the output O into a reference bit plane BR; the model M is composed of a first convolutional layer, multiple RK units, a second convolutional layer, and a third convolutional layer cascaded sequentially. The input image of the model first passes through the first convolutional layer to obtain a first feature map, the first feature map then passes through multiple RK units to output a second feature map, the residuals of the first feature map and the second feature map are concatenated and then passed through the second and third convolutional layers to obtain the final output image; each RK unit contains three convolutional modules composed of convolutional layers followed by PreLU activation functions, and the original input features of the RK unit... The first intermediate feature is obtained by passing it through the first convolutional module. Weighted features The second intermediate feature is obtained by inputting it into the second convolutional module. Weighted features The third intermediate feature is obtained by inputting it into the third convolutional module. Weighted features As the final output feature S13. By detecting bit plane B and reference bit plane BR, obtain the regular singular graph RSM, and compress the regular singular graph RSM to obtain the compressed regular singular graph CRSM; S14. Obtain uncertainty-aware information UM through model output O; Combine the compressed regular singular graph CRSM and uncertainty-aware information UM to determine the watermark embedding order, perform lossless watermark embedding, and obtain the watermark image WI; At the receiving end, perform watermark extraction on the received watermark image WI according to S21~S24 and restore the original image I: S21. Extract the watermark from the received watermark image WI and restore the original image I. Perform preprocessing to obtain the preprocessed image WI2 and the bit plane WB; S22, input the preprocessed image WI2 into the trained model M, obtain the model output WO, and binarize the output WO into the reference bit plane WBR; S23, obtain the uncertainty-aware information WUM through the model output WO, determine the order of watermark embedding, and extract the watermark information accordingly; S24, extract the compressed regular singular graph CWRSM from the extracted watermark information and decompress it to obtain the regular singular graph WRSM. With the help of the regular singular graph WRSM, restore the original image and obtain the original image I.

2. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 1, characterized in that, In step S11, the third bit plane of the original image I is extracted to form bit plane B, and all bits of the third bit plane of image I are set to 0 to form a preprocessed image I2.

3. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 1, characterized in that, In the model M, there are a total of 20 RK units.

4. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 1, characterized in that, In step S13, a regular singular graph (RSM) is obtained by detecting bit plane B and reference bit plane BR, and the RSM is compressed to obtain a compressed regular singular graph (CRSM). Specifically, the steps are as follows: S131: Divide bit plane B into several non-overlapping 2x2 blocks A1, and flip each element value of the first block A1 to obtain the second block A2; S132: Divide reference bit plane BR into several non-overlapping 2x2 blocks A3; S133: Based on the element values ​​of the first block A1, second block A2, and third block A3, calculate two parameters respectively. and ： in, , and These are the i-th element values ​​of A1, A2, and A3, respectively; k is the number of elements in a single block of A1, A2, and A3; S134: Perform regular singularity determination on each first block A1 to determine its category. The determination method is as follows: Where R represents the regular class, S represents the singular class, and U represents the unusable class; S135: After obtaining the category of each first block A1 through the regular singularity judgment, the first block A1 in the image belonging to the regular class is marked as 1, and the first block A1 belonging to the singular class is marked as 0, thus forming a regular singular graph RSM; and the regular singular graph RSM is compressed to form a compressed regular singular graph CRSM.

5. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 4, characterized in that, In step S14, uncertainty-aware information UM is obtained through the model output O; lossless watermark embedding is performed by combining the regular singular graph RSM and the uncertainty-aware information UM to obtain the watermark image WI. The specific method is as follows: S141: Divide the model output O into several non-overlapping 2*2 size fourth blocks A4; S142: Calculate the uncertainty-aware information of each first block A1 based on the element values ​​of the first block A1, the second block A2, and the fourth block A4. Specifically: in, , and These are the i-th element values ​​of A1, A2, and A4, respectively; S143: Calculate an uncertainty-aware information for each first block A1. Then, an uncertainty-aware information graph UM is formed, and uncertainty-aware information for all first blocks A1 is processed. Sort the images in ascending order, select the top N first blocks A1, find the image blocks corresponding to these N first blocks A1 on the original image I as watermark embedding blocks, and perform lossless watermark embedding to obtain the watermark image WI, thereby ensuring the quality of the watermark image and improving the embedding efficiency.

6. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 5, characterized in that, In step S143, when performing lossless watermark embedding on the original image I, the specific method is as follows: S1431: The compressed regular singular graph CRSM is concatenated with the watermark bitstream to be embedded as the information to be embedded; S1432: The information to be embedded is embedded bit by bit into each watermark embedding block of the original image I, thereby obtaining the watermark image WI; wherein, each watermark embedding block is modified to the corresponding first block A1 or second block A2 according to the different bits of the information to be embedded and the category to which the corresponding first block A1 belongs, and the modification rules for the watermark embedding block when performing embedding are as follows: Where m is a bit of information to be embedded in the current watermark embedding block. This is to complete the image block corresponding to the embedded watermark image WI.

7. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 1, characterized in that, In step S21, the third bit plane of the watermark image WI is extracted to form bit plane WB, and all bits of the third bit plane of the watermark image WI are set to 0 to form a preprocessed image WI2.

8. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 1, characterized in that, In step S23, uncertainty-aware information WUM is obtained through the model output WO to determine the watermark embedding order and extract the watermark information accordingly. Specifically, the method is as follows: S231: Divide the model output WO into several non-overlapping 2*2 size fifth blocks A5; S232: Divide the bit plane WB into several non-overlapping 2*2 size sixth blocks A6, and flip each element value of each sixth block A6 to obtain the corresponding seventh block A7; S233: Based on the element values ​​of the sixth block A6, the seventh block A7, and the fifth block A5, calculate the uncertainty-aware information of each sixth block A6. Specifically: in, , and These are the i-th element values ​​of A6, A7, and A5, respectively; S234: Calculate an uncertainty-aware information for each sixth block A6. Then, an uncertainty-aware information graph WUM is formed, and uncertainty-aware information for all sixth blocks A6 is generated. Sort the data in ascending order, select the top N sixth blocks A6, and find the corresponding image blocks for these N sixth blocks A6 on the watermark image WI. S235: Sequentially extract all image blocks within the watermarked image WI that serve as watermark extraction blocks. Extract watermark information bits from a single image block. bits in Extraction rules and image blocks The category determined by regular singularity check is related to: The extracted bits m are concatenated to form the extracted watermark information.

9. The lossless watermarking method based on uncertainty perception and regular singularity judgment according to claim 8, characterized in that, In step S24, a compressed regular singular graph (CWRSM) is extracted from the extracted watermark information and decompressed to obtain a regular singular graph (WRSM). The original image is then recovered with the assistance of the WRSM to obtain the original image I. Specifically, the method is as follows: S241: Separate the compressed regular singular graph (CWRSM) from the extracted watermark information and decompress it to obtain the WRSM; S242: Based on the WRSM, determine each image block that serves as a watermark extraction block. Whether it originally belonged to the regular class or the singular class, if its original class is the same as... If they belong to the same category, then These are blocks of the original image; Otherwise, it needs to be flipped first. The element values ​​are then used as blocks in the original image I; the image blocks of all watermark extraction blocks on the watermarked image WI. After all images are restored, the original image I is finally restored without loss.

Images