Image Robust Watermarking Method Based on DWT-SVD Transform and Chaotic Map

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Introduction
With the development of digital image technology, our lives are becoming increasingly dependent on digital images.However, with the growing use of digital images, to transmit and share personal and confdential information, privacy and security concerns have become more pronounced [1][2][3].Digital images are vulnerable to malicious tampering, theft, and misuse, causing signifcant harm to individuals, businesses, and entire societies.Terefore, the development of image watermarking technology is crucial for protecting the privacy and security of digital images.By using image watermarking, digital image copyrights can be verifed and traced without compromising their perceptual quality [4,5].Tis technology is essential for achieving image authentication, ownership protection, and content tracing, and has signifcant applications in various felds, including military, data hiding, and multimedia [6][7][8].
Te motivation for this research stems from the pressing need to address privacy and security concerns surrounding digital images.Existing solutions may either compromise image quality or fail to provide adequate security.Terefore, our study aims to develop an advanced watermarking technology that ensures the perceptual quality of digital images while efectively safeguarding their privacy and security.
Existing watermarking algorithms are mainly based on the spatial domain and the transform domain [9], among which the spatial domain-based algorithm is mainly implemented by modifying the pixels of the image directly.Te least signifcant bit (LSB) algorithm is the most important spatial domain algorithm, whose principle is to quantize the image pixel bit, and then embed the watermark information bit to be hidden in the least signifcant bit.Tis algorithm is fast, easy to implement, and can also achieve a good watermark invisibility, but cannot resist various attacks, exhibiting poor robustness [10,11].
Another algorithm is based on the transform domain, which transforms the image into the frequency domain using various methods, and then embeds the watermark information into the frequencies.Common transformation methods include discrete cosine transform (DCT), discrete Fourier transform (DFT), and discrete wavelet transform (DWT).
Te frequency domain algorithm is more suitable for the human visual system (HVS) [12,13], which embeds the watermark in the visually insensitive region, which not only increases the robustness of the watermark but also does not degrade the quality of the image.Compared with DCT and DFT, DWT describes HVS more accurately and has better robustness to some attacks such as additional noise and resizing [14,15].Terefore, the watermark embedding algorithm based on DWT has attracted extensive attention in the research feld.
Te feld of digital watermarking has realized signifcant achievements in recent years, with many researchers proposing various techniques for protecting digital data.Ernawan et al. proposed an improved image watermarking method by modifying selected discrete wavelet transform and discrete cosine transform coefcients, and the method achieved better imperceptibility and robustness compared to the existing methods [16].Zermi et al. proposed a blind watermarking approach for protecting medical images based on a DWT-SVD combination, maintaining high-quality watermarked images and demonstrating high robustness against several conventional attacks [17].Li et al. presented a DWT digital watermarking algorithm based on 2D-LICM hyperchaotic mapping, and the proposed method can resist attacks, including geometric distortion, fltering, and noise, and maintains high watermark imperceptibility [18].Abdel-Wahab et al. introduced an efcient combination of RSA cryptography, lossy, and lossless compression steganography techniques to conceal data, and the achieved highsecurity level encompasses both data confdentiality and integrity [19].Nawaz et al. introduced a sophisticated medical image processing approach, amalgamating deep feature extraction with encrypted watermarking techniques alongside discrete wavelet transform and discrete cosine transform, and through this method, they not only successfully extracted essential features and encrypted watermarks from medical images but also ensured dependable retrieval of ownership and watermark details, showcasing formidable resilience against both conventional and geometric attacks [20].Kant and Chaudhary proposed a watermarking-based approach for protecting templates in a multimodal biometric system, and the method ensures high security by embedding the watermark within the template and validating it by using a secret key [21].Ming and Fuken presented a robust and secure watermarking algorithm based on DWT and SVD in the fractional order Fourier transform domain, and the proposed method achieved a high robustness against various attacks, including fltering, noise, and geometric distortion [22].Singha and Ullah proposed an audio watermarking method to decentralize the watermarks, and the proposed method achieved a high robustness and security by distributing the watermark information among several audio segments [23].
Besides, the rapid advancement of deep learning has revolutionized numerous felds, including computer vision and pattern recognition.Deep learning models, such as convolutional neural networks (CNNs) and graph convolutional networks (GCNs), have demonstrated remarkable performance in tasks such as image classifcation, object detection, and natural language processing [24].Deep learning models can provide enhanced features for watermark embedding and extraction, enabling more robust and imperceptible watermarking schemes.
In this paper, a robust watermarking algorithm is proposed, utilizing a combination of DWT and SVD.To heighten the security of the watermark information, the logistic-tent map is introduced for encrypting the watermark image in conjunction with the Arnold transform.In addition, the algorithm is implemented in the frequency domain and is suitable for grayscale watermark images.Considering the robust resistance of high-frequency components to geometric attacks such as shearing and rotation, the highfrequency subband is selected as the embedding area.Tis portion is chosen for SVD to amplify the numerical values.Subsequently, SVD is applied to the encrypted watermark image, and the watermark information is fnally embedded into the S-domain of the high-frequency subband.A profcient watermarking algorithm ensures not only the invisibility of the watermark but also its robustness.Te algorithm performs admirably in both aspects.
Te rest of the paper is organized as follows: Section 2 introduces the relevant theoretical background.Section 3 provides a performance analysis of the proposed logistic-tent map.Section 4 describes the watermark embedding and extraction processes of the algorithm.Section 5 presents the simulation tests for invisibility, robustness, sensitivity, complexity, and encryption watermark performance.Finally, Section 6 summarizes the paper.

Preliminary Knowledge
2.1.Logistic-Tent Map.Te logistic map is a classic model for studying chaotic systems, with simple structure and complex chaotic dynamics, so it is often used in the feld of encryption [25].Te logistic map is described as follows: where the control parameter µ ∈ (0, 4] and the variable x ∈ (0, 1).When µ ∈ [3.57, 4.00], the system exhibits chaos, and it generates a set of one-dimensional nonperiodic and nonconvergent chaotic sequences.Te tent map is a piecewise linear map with a simple mathematical structure, uniform distribution function, and good correlation, which is widely used in chaotic encryption systems such as image encryption.Te tent map is described as [26] follows: where the control parameter µ ∈ (0, 2] and the variable x ∈ [0, 1].When µ ∈ [1, 2], the system is chaotic.Regardless of whether it is the logistic map or the tent map, they are not surjective maps and the distribution of chaos in the system is uneven.Te range of the chaotic parameter μ is small and the system parameters are few, which results in a small key space.To address these issues, this paper proposes a new map called the logistic-tent map by combining the structural forms of the logistic and the tent maps.Its mathematical expression is as follows: where "mod" represents the remainder operation, the control parameter µ ∈ (0, ∞], and the variable x ∈ [0, 1].When μ is greater than 0, the system shows chaotic states.
When an image with the size of M × N is encrypted, the logistic-tent map needs to iterate M × N times to obtain a one-dimensional sequence with the length of M × N. Ten, the one-dimensional chaotic sequence is transformed into a two-dimensional matrix of M × N, and XOR operation is performed with the original image, where x 0 and μ are the keys.Due to the high sensitivity of chaotic sequences to keys, the sequences generated by the map will be very diferent even if the key values are extremely close.Terefore, it is difcult for attackers to derive the key value from a fnitelength sequence [27,28].

Arnold Transform.
Arnold transform is to permute the pixel position in an image, which can be defned by the following equation [29]: where a and b are scrambling parameters, (x, y) is the pixel coordinate of the original image, and (x′, y′) is the pixel coordinate of the new image after transformation, N is the size of the image, and mod represents the remainder operation.Te reverse Arnold transformation is used to restore the image, which is described as follows: When a transformed image is attacked, even if the attacker obtains an encrypted image, the original image cannot be restored without knowing the number of the Arnold transforms.So the Arnold transform can further ensure the security of the image.

Discrete Wavelet Transform (DWT).
Image information includes low-frequency information that refects the main information of the image and high-frequency information that refects the details of the image.After discrete wavelet transformation, an image is decomposed into four subbands with diferent resolutions, namely, one low-frequency band LL with the main information of the image and three highfrequency bands LH, HL, and HH with detailed information, as shown in Figure 1.
It can be seen from Figure 1 that the image in the LL subband is closest to the original image, indicating that the LL subband concentrates the main energy of the image, so selecting this area to embed the watermark can greatly ensure the invisibility of the watermark.Still, it has poor robustness when facing attacks such as rotation and noise.
Te HH subband exhibits a preponderance of dark pixels, whose value is close to zero.Tis characteristic provides a favorable foundation for watermark protection since the HH subband has minimal susceptibility to image attacks.Embedding the watermark information within this region efectively shields the attacks and augments its robustness [30].However, embedding watermarks directly within the HH subband results in great changes to the pixel values, leading to visible watermarks that compromise their intended invisibility.

Singular Value Decomposition (SVD).
A non-negative matrix can represent any image.If the image is represented by A, SVD can be expressed as follows [31]: where U and V are orthogonal matrices, and S is a matrix whose nondiagonal terms are all 0, as follows: where Σ r � diag(λ 1 , λ 2 , . . ., λ r ) is the diagonal matrix, λ i satisfes λ 1 ≥ λ 2 ≥ . . .≥ λ r , and r is the rank of S.
When the image is attacked by geometric attacks, such as rotation, scaling, and compression, the S value of the image matrix changes little.Terefore, the S area is often chosen to embed the watermark, to improve the ability of the watermark to resist geometric attacks.In the watermark embedding algorithm, SVD is usually used together with the frequency domain algorithm to achieve a better embedding efect [32].
To ensure the invisibility of the watermark, an SVD processing step is introduced for the HH subband before embedding the watermark information.Tis technique allows for the preservation of imperceptibility, and the integrity of the original image structure by modifying the singular values.By selecting appropriate singular values to embed the watermark, both the visual quality of the image and the invisibility of the watermark can be maintained.In Complexity addition, the robustness of the watermark is enhanced via the inherent characteristics of the HH subband, such as their resistance to image processing [33].
Figure 2 shows the values of the HH subband in Figure 1, as well as the values of the S feld after SVD.
In Figure 2, the S feld post SVD transformation exhibits a diagonal matrix pattern, where the diagonal sections possess non-zero values while the remaining areas are zero.Moreover, the values on the diagonal are amplifed, prompting the embedding of the watermark into the diagonal matrix.

Bifurcation Diagram. Te bifurcation diagram refects
the law that the iterative value of a system changes with its parameters, so it vividly describes the chaotic behaviors of the system [34].Te bifurcation diagrams of the logistic map, tent map, and logistic-tent map are shown in Figures 3(a)-3(c), respectively.
Compared with the logistic map and tent map, the logistic-tent map is a map with uniform distribution and a large chaotic parameter area, which indicates that the logistic-tent map has better chaotic properties.

Lyapunov Exponent.
Te Lyapunov exponent can be used to describe the sensitivity of chaotic systems to initial conditions.If a Lyapunov exponent of a chaotic system is positive, it indicates it is chaotic.Te larger the range of Lyapunov exponent values, greater than 0, the better the chaotic characteristics of the system, besides, the larger the value, the greater the sensitivity to initial conditions [35].Te Lyapunov exponents of the logistic map, tent map, and logistic-tent map are shown in Figures 4(a)-4(c), respectively, where the yellow shaded regions represent the parameter domain with the chaotic property.
We observe from Figure 4 that the logistic-tent map has a greater positive Lyapunov exponent over the range of μ ∈ (0, 2], that is, the logistic-tent map has stronger chaotic characteristics and higher sensitivity to the initial value.Tis suggests that it may be a more appropriate choice for secure image encryption applications.

NIST SP800-22 Test.
To assess the randomness of the chaotic sequence generated by the logistic-tent map, this paper utilized the National Institute of Standards and Technology SP800-22 Standard (NIST SP800-22) for testing.Te NIST SP800-22 standard comprises 15 methods for detecting randomness, with each test generating a corresponding P value.P value greater than 0.01 indicates that the sequence passes the test [36].In this study, 1000 sets of random sequences were generated using the logistic-tent map, each sequence comprising a length exceeding 10 6 .Te test results are presented in Table 1.
It follows from Table 1 that all P values of all test items are greater than 0.01, indicating that the sequence generated by the logistic-tent map has passed the NIST randomness test.Tus, the sequence has good randomness and is suitable for application in encryption algorithms.

Watermark Embedding. Let the size of the carrier image
A and the watermark image W be M × N and M/2 × N/2, respectively.Te watermark embedding process is mainly divided into chaotic encryption (steps 1 to 3) and encrypted watermark embedding (steps 4 to 8), as shown in Figure 5.
Step 1: the logistic chaotic sequence E with length M/2 × N/2 is generated by using the keys x and μ, and the sequence is converted to the interval [0, 255], obtaining the sequence C: where "foor" represents a downward integer operation.
Step 2: we divided the chaotic sequence C into M/2 parts and arranged them into N/2 rows, forming a chaotic image C′ with a length of M/2 and a width of N/2.
Step 3: the XOR operation is then performed between the chaotic image C′ and the watermark image W, and then a and b are inputted as scrambling parameters for Arnold transform to obtain the encrypted watermark image W m .

Complexity
Step 4: the DWT operation is performed on the carrier image A, and the HH subband is chosen for SVD to acquire the singular value diagonal matrix S, which is then stored in the key area.
Step 5: the SVD transform is applied to the watermark image W m resulting in the singular value matrix S w , as well as the ordinary matrices U w and V w .Both U w and V w are subsequently stored in the key area.
Step 6: S w is then embedded into S to obtain S′ with watermark information.Te specifc operations are as follows: where λ is the embedded strength coefcient.Since the energy of the HH domain is low, the corresponding singular value is also low.If the singular value is modifed too much, it will lead to great changes in the HH domain of the carrier image and afect the image quality.Terefore, the maximum element in the singular value matrix of the carrier image and the watermark image is taken to calculate the calculation formula as follows:  6 Complexity where S 1 is the frst element in the singular value matrix of the carrier image in the HH domain and S W1 is the frst element in the singular value matrix of the watermark image.
Step 7: the high-frequency subband HH ′ with watermark information is obtained through inverse SVD transformation, and the calculation formula is as follows: Step 8: the fnal watermarked image A w is obtained by IDWT transform.

Watermark Extraction.
Te watermark extraction process is the reverse process of the encryption process, as shown in Figure 6.
Step 1: a DWT is performed on image A w , which embeds the watermark, to generate subbands LL, LH, HL, and the subband HH′ with watermark information.
Step 2: the subband HH′ is selected for SVD to generate U and V without watermark information and S′ with watermark information.Since the watermark information exists in the S′ domain, we only operate on the S′ domain.
Step 3: the watermark image S w ' value is then calculated by extracting S from the key area and performing calculations with S ′ .Te specifc operations are as follows: Step 4: By extracting U w and V w in the key area and combining S w , the encrypted watermark image W m is restored.Te specifc operations are as follows: Step 5: a length M/2 × N/2 chaotic sequence E is then generated using x and μ extracted from the key area.
Step 6: the chaotic sequence E is then converted into a chaotic sequence C following the calculation formula (8).
Step 7: the sequence C is arranged in rows of M/2 to create a chaotic image C′ of size M/2 × N/2.
Step 8: Using the scrambling parameters a and b, the re-Arnold transform is performed on W m , and then the XOR operation on C′ is performed to obtain the watermark image W.

Experimental Results and Discussion
In this section, we test the invisibility, robustness, sensitivity, and complexity of the algorithm and the performance of the encrypted watermark image.All of the experiments were carried out on a Workstation with an Intel i7 CPU and 16 GB RAM, using the MATLAB 2020b version.Te images used in the experiment include (a-g) from the USC-SIPI Image Database and landscape photos (h-j).Te grayscale size of each image is 512 × 512.In addition, a binary watermark image of size 256 × 256 was used in Figure 7(k).
Te peak signal noise ratio (PSNR) and structural similarity (SSIM) are used to evaluate the invisibility of the watermark.Te normalized cross-correlation (NC) and bit error rate (BER) are used to evaluate the robustness of the watermark.Te number of pixels change rate (NPCR), unifed average changing intensity (UACI), pixel correlation, and information entropy are used to evaluate the performance of the encrypted watermark image.
PSNR is the ratio between the maximum value of the measured signal and the amount of noise afecting the signal, which is used to compare the quality of the carrier image before and after embedding the watermark image in decibels (dB).PSNR value lower than 30 dB indicates a low image quality and higher than 40 dB indicates a high image quality [37].Te calculation formula of PSNR is as follows: where M × N represents the size of the image, A represents the carrier image, and A w represents the watermarked image.
SSIM is an index used to measure the similarity between the carrier image and the watermarked image.Te closer the SSIM value is to 1, the smaller the diference between the two images, and vice versa, and the greater the diference [38].Te calculation formula of SSIM is as follows: where μ A and μ Aw represent the average value of A and A w , σ A and σ Aw represent the variance of A and A w , σ AAw represents the covariance of A and A w , and c 1 and c 2 are constants.
NC is used to evaluate the similarity between the extracted watermark and the original watermark, which can be calculated by [39] NC BER is used to calculate the error bit ratio between the extracted watermark and the original watermark.Te lower the BER, the stronger the robustness of the watermark [40].Te calculation formula of BER is as follows: where sum represents the sum operation and ⊕ represents the XOR operation.8 Complexity change.Te calculation formulas of NPCR and UACI are as follows [41]: where W 1 (i, j) and W 2 (i, j) are the pixel values of the pixels in row i and column j of the W 1 image and W 2 image, respectively.When W 1 (i, j) � W 2 (i, j), G (i, j) � 0, otherwise G (i, j) � 1. Te expected values of NPCR and UACI for grayscale images are 99.6094% and 33.4635%, respectively [28].
Te correlation between adjacent pixels refers to the degree of correlation or correlation between adjacent pixels in the image.Te range of correlation coefcient r is [−1, 1].Te closer the absolute value of correlation is to 0, the smaller the correlation between pixels is.Te correlation calculation formula is as follows [42]: where x and y are the gray values of adjacent pixels, cov(x, y) is the covariance, D is the variance, and E is the expectation.Image information entropy is an index to measure the complexity of image information content.Te maximum entropy of a gray image is 8. Te better the encryption efect is, the closer the information entropy is to 8. Te calculation is as follows [43]: where P i is the probability of gray value i.

Invisibility Test.
In the watermark invisibility analysis experiment, the watermark embedding algorithm proposed in this paper is used to embed Figure 7(k) into Figures 7(a)-7(j), respectively, to obtain the watermarked images.
To visually demonstrate the invisibility of the watermark, the analysis focuses on the grayscale distribution of the images through the use of image histograms.An image histogram, acting as a statistical table, illustrates the distribution of grayscale values across the image, ofering insights into the overall grayscale distribution.In Figure 8, a comparison is made between the histograms of the original images and the watermarked images from Figures 7(a)-7(g).Tis comparison facilitates an assessment of how the watermark infuences the overall distribution of grayscale values in the images.
To further assess the quality of the watermarked images, a comparative analysis is performed by comparing them with the original carrier images.Te results of this evaluation are presented in Table 2, which includes important metrics such as PSNR and SSIM.
Besides, the watermark invisibility of our watermark embedding algorithm is compared with that of other watermark embedding algorithms mentioned in prior literature.Te results of the comparison are presented in Table 3.
Te attack types and descriptions are shown in Table 4, the extracted watermark images are presented in Table 5, the corresponding NC values are shown in Table 6, and the BER values are reported in Table 7.
Another experiment was conducted using lena, pepper, and boat as the carrier images to evaluate the NC values of the extracted watermark under diferent attacks, including Gaussian noise (variance 0.001), salt and pepper noise (density 0.001), cropping (25% center, 25% rows, and 50% rows), and JPEG compression (compression factor 70 and 60).Te results were compared with those of references [46,47], as shown in Table 8.

Sensitivity Test.
Using the logistic-tent map for chaotic encryption of the watermark can further ensure the security of watermark information.In the process of chaotic mapping encryption of the watermark, x 0 and μ are used to encrypt and decrypt the watermark.Only users who possess  the correct keys can successfully extract the watermark information, thereby protecting the watermark.By using Figure 7(k) as the watermark image, the watermark was initially encrypted through a chaotic encryption process with the parameters x 0 and μ.Following this, the watermark embedding algorithm proposed in this study was utilized for the embedding process.An extraction algorithm was then applied to recover the encrypted watermark.Troughout the watermark decryption process, one parameter was held constant while making minor adjustments to the other.Subsequently, the decrypted images were extracted, and the results are depicted in Figure 9.

Complexity
Test.An efective watermark algorithm should guarantee minimal computational cost for both embedding and extracting watermark information.Table 10 presents a time comparison between the presented approach and various methods.Te time required for the maximum embedding and extraction watermark capacity reported in each reference is selected for comparison.Te authors in reference [30] achieved a maximum watermark embedding capacity of 64 × 64 bits, the authors in reference [49] achieved 128 × 128 bits, the authors in reference [50] achieved 256 × 256 bits, and our algorithm achieved a maximum watermark embedding capacity of 256 × 256 bits.

Encryption Watermark Performance Test.
To evaluate the encrypted watermark image, we conducted NPCR, UACI, entropy, and pixel correlation tests on it.
Figure 7(k) is selected as the plaintext image, and a new plaintext image is obtained by randomly changing the pixels of the plaintext image.Ten, the same algorithm is used to encrypt the two plaintext images to obtain the corresponding ciphertext images.Finally, the NPCR and UACI of the two ciphertext images are calculated, respectively.To test the correlation, the plaintext image is frst encrypted using the proposed logistic-tent mapping.Ten, 5000 pairs of pixels are randomly selected from the original image and its related encrypted images in the horizontal, vertical, and diagonal directions.For the information entropy test, the information entropy of plaintext and ciphertext is calculated, respectively.Te results are shown in Table 11.

Discussion.
In this discussion, we will analyze and interpret the fndings presented in Figures 8, 9, and Tables 2 to 11 of the paper.
In Figure 8, it is evident that the histogram of the watermarked images closely resembles that of the original carrier images.Tis observation indicates that the image undergoes minimal alterations upon embedding the watermark.However, when the carrier images exhibit a relatively discrete distribution of pixel values, the pixel value distribution of the watermarked images tends to exhibit an averaging efect.
From Table 2, it is observed that the PSNR values of the carrier images with watermarks are all greater than 43, and the SSIM values are close to 1. Tis suggests that the images with watermarks have higher quality and show minimal diferences from the original carrier images.Hence, the proposed watermarking algorithm demonstrates good invisibility, indicating that the watermark is imperceptible to the human eye.
Table 3 shows that references [40,44], and [45] achieve remarkable performance in terms of watermark invisibility.However, when compared to these references, the proposed algorithm achieves slightly higher PSNR and SSIM values.Tese results highlight the superior performance of the proposed algorithm in terms of watermark invisibility compared to the other references.

Complexity
From Table 5, it can be observed that the watermark remains identifable for the majority of attacks.
Te results from Tables 6 and 7 indicate that the proposed watermark algorithm withstands all the attacks, maintaining NC values close to 1 and BER values close to 0. Tese results demonstrate that the proposed algorithm exhibits excellent robustness when facing various image attacks.
From Tables 8 and 9, it can be seen that the proposed algorithm performs better than the references in terms of Gaussian noise, salt and pepper noise, and cropping attacks.Complexity However, it is less efective than the reference [46] in countering compression attacks and fltering attacks.Figure 9 demonstrates that even a slight change in the key leads to a completely incorrect decrypted image.Tis fnding emphasizes the strong sensitivity of the watermark, ensuring efective protection of the watermark's security.
From Table 10, it can be observed that our algorithm exhibits superior computational efciency compared to references [49,50].Although our algorithm slightly lags behind reference [30] in terms of computational efciency, the main reason is the inclusion of encryption and decryption of the watermark image during the embedding and extraction processes, respectively.Overall, our algorithm demonstrates satisfactory performance concerning computational efciency.
It can be seen from Table 11 that the NPCR value, UACI value, and entropy value are close to the theoretical value, and the correlation of the encrypted watermark image in the horizontal, vertical, and diagonal directions is close to 0, indicating that the logistic-tent has a good encryption efect.
In conclusion, the results presented in the tables and fgures strongly support the claims made in the paper regarding the efectiveness of the proposed watermarking algorithm.Te algorithm achieves a high level of invisibility, demonstrating robustness against various attacks and ensuring the security of the watermark.Tese fndings underscore the signifcant potential of the proposed algorithm for practical applications in the feld of digital watermarking.

Conclusions
Tis paper introduces a robust image watermarking method based on DWT-SVD and a chaotic map.Te logistic-tent map is frst proposed, and its bifurcation diagram, Lyapunov exponent, and NIST SP800-22 test are tested to demonstrate its robust chaotic properties.By utilizing this map, along with the Arnold transform, the watermark is encrypted.Regarding invisibility, DWT is employed to embed the watermark in the frequency domain, with the highfrequency subband chosen as the embedding region after frequency decomposition.Te algorithm undergoes watermark invisibility and robustness testing, revealing that the PSNR values of watermarked images using this algorithm are consistently above 43, and SSIM values are close to 1. Te algorithm also exhibits strong resistance to various noise and fltering attacks, as well as diferent attack parameters for shear, rotation, and JPEG compression attacks.It demonstrates NC values above 0.9 and BER values below 0.1.Te algorithm showcases robustness, ensuring watermark invisibility and security, making it suitable for applications in copyright protection and security verifcation.
However, the algorithm proposed in this paper has limitations.First, this algorithm is a semiblind watermarking algorithm, requiring the original carrier image and watermark image to participate in the watermark extraction process.Second, the image watermarking algorithm is only applicable to embedding grayscale images.Ten, due to the length and width of the subband images obtained after DWT being half of the original image, the watermark image is limited by the carrier image, with a maximum size of 1/4 of the carrier image.In future work, we will explore blind watermarking technology, and color watermarking embedding, and adjust the embedding position, capacity, and strength of the color watermark based on the diferent characteristics of the embedding region, aiming to achieve a good balance between invisibility and robustness.Furthermore, we will explore new methods to enable watermark image embedding without being constrained by the size of the carrier image.Lastly, traditional watermarking algorithms often rely on manually designed features and rules, while deep learning can automatically extract and embed watermarks by learning features and patterns from data.In subsequent research, we will delve into this area.

Table 3 :
Invisibility test comparison with related work.

Table 4 :
Attack types and descriptions.

Table 5 :
Extracted watermarks for multiple attacks on watermarked images.

Table 6 :
NC values for attacks on watermarked images.

Table 7 :
BER values for attacks on watermarked images.

Table 10 :
Te time of embedding and extraction (second).

Table 11 :
Encryption performance indicators of watermarked image