A Zero-Watermarking Algorithm Based on Scale-Invariant Feature Reconstruction Transform

Abstract

In order to effectively protect and verify the copyright information of multimedia digital works, this paper proposes a zero-watermarking algorithm based on carrier image feature point descriptors. The constructed feature matrix of this algorithm consists of two parts: the feature descriptor vector calculated from scale-invariant feature reconstruction transform (SIFRT) and the multi-radius local binary pattern (MrLBP) descriptor vector. The algorithm performs a standardization, feature decomposition, and redundancy reduction on the traditional keypoint descriptor matrix, combines it with the texture feature matrix, and achieves the dimensional matching of copyright information. The advantage of this algorithm lies in its non-modification of the original data. Compared to computing global features, the local features computed from a subset of key points reduce the amount of attack interference introduced during copyright verification, thereby reducing the number of erroneous pixel values that are introduced. The algorithm introduces a timestamp mechanism when uploading the generated zero-watermarking image to a third-party copyright center, preventing subsequent tampering. Experimental data analysis demonstrates that the algorithm exhibits good discriminability, security, and robustness.

1. Introduction

In digital works, digital images are a widely used network information carrier. Image processing and the internet have made it easier to duplicate, modify, reproduce, and distribute digital images at low cost and with approximately immediate delivery without any degradation of quality [1]. Digital watermarking is a trend in security techniques that hides data using data embedding and data extraction processes. Therefore, it is very effective in encrypting data for applications running on limited resources and can be used to solve copyright disputes and other issues in digital products [2]. Digital watermarking can be classified into embedded watermarking and zero-watermarking based on whether it modifies the carrier information. Zero-watermarking does not modify the original data of the propagation carrier and is suitable for fields with high image-quality requirements. The key idea is to generate feature information based on the image’s own data and bind it with copyright data through computation. This ensures the accurate expression of the original visual effect of the image. This technology is widely applied in sensitive digital image domains where information tampering is a concern, such as military radar images, patient pathology images [3], and artistic heritage images.

In recent years, research on zero-watermarking has mainly focused on two steps: constructing various feature matrices and encrypting copyright information. In terms of local features, Ghadi et al. [4] proposed a zero-watermarking algorithm based on image block features. The host image is divided into 8 × 8 blocks, and the joint photographic experts group (JPEG) quantization matrix of each block is calculated to generate the actual block matrix. The mean value of this local block and the above block matrix are then input into a Jacobian model to generate meaningful watermarking information. To distinguish watermarking information in similar images, Zou et al. [5] proposed a zero-watermarking algorithm for distinguishing the similarity between fundus images in the medical field. They constructed image features by extracting the grayscale distinctiveness of the sector region in the fundus image and combined this feature with visual cryptography to enhance the security of the information. However, when the grayscale features of the fundus carrier image are partially truncated, the grayscale features in that part exhibit a stepped change. This leads to the extracted watermarking image containing more noise, indicating a lack of robustness in the algorithm. In terms of the geometric moment features of images, continuous orthogonal moments have become the main tool used in zero-watermarking algorithms. However, existing research has found defects in both computational accuracy and numerical stability when using integer-order continuous orthogonal moments, which affects the zero-watermarking performance. Xia et al. [6] proposed a conversion from integer-order radial harmonic Fourier moments (IoRHFMs) to fractional-order radial harmonic Fourier moments (FoRHFMs). This conversion improves computational accuracy and helps alleviate the numerical instability issue associated with such moments. The algorithm exhibits strong robustness against geometric attacks and common attacks, surpassing the performance of the IoRHFM-based zero-watermarking algorithm. To enhance the security of digital images, Hannoun K et al. [7] proposed a robust digital image watermarking system with a fractional-order discrete-time chaotic system and discrete wavelet transform-singular value decomposition (DWT-SVD). The inclusion method inserts an encrypted image into the dynamics of an integer-order discrete-time chaotic system and the resulting cipher serves as a host image watermark.

2. Related Work

2.1. Feature Matrix Based on SIFRT

Scale-invariant feature transform (SIFT) is a local feature descriptor algorithm that is widely used in the field of image processing. Taking human visual perception as an example, our eyes have the ability to perceive differences in the size and clarity of objects. The scale space construction step of SIFT is inspired by this observation. It uses the process of upsampling and downsampling to simulate the perception of distance in an image and employs Gaussian convolution kernels to model different levels of smoothness or blurriness. The SIFT algorithm was proposed by Canadian professor David G. Lowe in 1999. It detects and describes local features in multi-scale space, rendering the generated descriptors scale-invariant. It exhibits strong robustness in handling image transformations such as rotation, illumination changes, and image-capture position shifts. Consequently, SIFT finds wide application in image stitching and specialized image-matching fields. Zhao et al. [8] utilized the SIFT algorithm to generate a series of images with different stylistic patterns, resolving the issue of resolution differences between style and content images. They performed feature extraction on these images and generated the matching patches required for image synthesis. This algorithm assists in finding the correct style of image, facilitating image-correction and -matching processes. Dong et al. [9] applied SIFT to feature point extraction and image-matching in synthetic aperture radar (SAR) satellite images, thereby improving the efficiency of SAR image-matching. Apart from image-matching techniques, SIFT is also used in various information processing tasks such as biometrics feature recognition [10] and the sets of feature descriptors [11]. By simplifying the computational complexity through local feature calculations, SIFT significantly enhances the efficiency of the corresponding algorithm.

In the application field of zero-watermarking technology, the process of extracting copyright information from digital images does not involve the image-matching step in the traditional SIFT algorithm. In order to reduce unnecessary computational complexity, this paper proposes an improved feature matrix construction algorithm, the scale-invariant feature reconstruction transformation (SIFRT) descriptor algorithm. After using the SIFT algorithm to extract image keypoints and compute feature descriptors, this algorithm standardizes the keypoints’ descriptors and decomposes the resulting matrix into eigenvectors. The purpose of this step is to retain vectors with abundant feature information while eliminating redundant data from vectors with less feature information. The theoretical basis is that SIFT descriptors are composed of feature vectors from various local regions of the image, with each region further decomposed into multiple subregions. When calculating the gradient histograms of regions with low contrast or unclear textures, their contribution may be small and ignored by the thresholding step of gradient magnitude, leading to an excess of zero-value elements in the keypoints’ descriptors. Although these zero-value elements can enhance the redundancy and discriminability of the algorithm during feature-point-matching, the zero-watermarking algorithm only involves a single image as the computational target and does not require matching or stitching between two images. Users are more concerned about the stability and discriminability of the feature matrix. Therefore, it is necessary for the new algorithm to compress the traditional SIFT feature descriptors to ensure that the constructed feature matrix contains as much rich feature information as possible, reducing redundant information used for image-matching.

The SIFRT algorithm proposed in this article reduces the redundant data in the traditional 128-dimensional SIFT descriptors. The collected feature descriptors are used to generate the dataset for algorithm training. This algorithm normalizes the matrix formed by combining feature vectors, ensuring a mean of 0 and a variance of 1 for each dimension, thus ensuring equal theoretical contributions from each dimension. To eliminate redundant information in the feature matrix and preserve vectors with a high information content, the algorithm performs eigenvalue decomposition on the standardized feature matrix to obtain eigenvalues and corresponding eigenvectors. Then, the original 128-dimensional SIFT descriptors are matrix-projected, with the basis vectors being a subspace composed of vectors with large eigenvalues. For users to better perceive the algorithm’s performance vividly and clearly, copyright information is set in image form, with the image size set to 128*128. Combined with the 32-dimensional texture feature descriptors constructed by the proposed Multi-Radius Local Binary Pattern (MrLPB) algorithm, it can be computed that the keypoint descriptors need to be compressed to 92 dimensionality, and then concatenated to obtain the SIFRT feature matrix. The specific process is illustrated in Figure 1.

2.2. Multi-Radius Local Binary Pattern Descriptors

Generally, constructing a zero-watermark feature matrix requires multiple sources of feature data and diverse computational approaches. If only the reduced redundancy keypoint descriptor matrix is used to construct the target matrix, both the computational form and the source of the feature data would appear to be overly singular, resulting in poor discriminability of the generated zero-watermark images. To enhance the discriminability and robustness of the feature matrix, this paper introduces texture feature descriptors beyond those used for the aforementioned feature data. These descriptors set the keypoint coordinates as the origin and compute appropriate distance neighborhood texture features. It is worth noting that both types of feature descriptor need to satisfy similar properties. When generating texture features, the algorithm needs to ensure that the computed texture feature descriptors possess rotational invariance and compatibility. We improve the traditional LBP algorithm and propose a novel MrLBP algorithm for extracting texture feature information from multiple circular neighborhoods around feature keypoints. Initially, we compute three keypoints (x_na, y_na), (x_nb, y_nb), and (x_nc, y_nc), which are geometrically close to the feature keypoint (x_n, y_n), with distance R_i, where i ∈ {a, b, c}. The initial angle θ_i, where i ∈ {a, b, c}, is determined by the point with the maximum pixel value within a single circular neighborhood. Twelve directional angles are set clockwise, with Ri as the radius, and the pixel values of the sampling points on these 12 angles are compared with the pixel value of the central keypoint to generate 36-dimensional MrLBP descriptors. For a given keypoint (x_n, y_n), its neighborhood pixel positions are calculated using Formulas (1) and (2):

$$x_{nri}=x_n+Ri\cos \left(\frac{2\pi p}{P}+\theta i\right)$$

(1)

$$y_{nri}=y_n-Ri\sin \left(\frac{2\pi p}{P}+\theta i\right)$$

(2)

where P represents the total number of sampling points in a single-radius neighborhood; thus, P = 12. The number of sampling points can be flexibly adjusted according to the actual dimensional requirements, where p denotes the (p + 1)-th sampling point in the single-radius neighborhood, with p ∈ [0, 11] and p being an integer. Due to the discrete nature of digital images, the sampling point coordinates in circular neighborhoods are typically non-integer, and their coordinates do not correspond to pixel values in the discrete image. To address this issue, this paper introduces bilinear interpolation to approximate the pixel values of these virtual points. Bilinear interpolation reduces the loss of feature information during information transmission compared to the nearest neighbor interpolation method, preserving the grayscale continuity of the image and better matching the analog gradient relationships in the real world. This facilitates the generation of more accurate texture feature descriptors, as illustrated in Figure 2.

The pixel values of the four points in Figure 2 are represented by different colors. According to the principle diagram, it can be observed that the pixel value of the virtual point (x, y) is derived from the pixel values of its four neighboring points, weighted based on their geometric distances. The closer the distance, the larger the weighting coefficient, and the larger the corresponding colored area in the image. Suppose the coordinates of the sampling point (x, y) do not correspond to actual points on the 2D image. In this case, we consider the four discrete pixel points Q₁₁, Q₁₂, Q₂₁, and Q₂₂, with coordinates (x1, y1), (x₁, y₂), (x₂, y₁), and (x₂, y₂), respectively. The pixel value corresponding to this sampling point on the image can be approximated as f(x, y). Note that, here, f( , ) represents only the expression for calculating the pixel value at this virtual coordinate point. For point Qij that can be determined on the discrete image, f(Qij) equals the pixel value of that point without needing to use the function expression calculation, as shown in Formula (3).

$$\begin{array}{cc}f(x,y)\approx & \frac{f\left(Q_{11}\right)}{\left(x_2-x_1\right)\left(y_2-y_1\right)}\left(x_2-x\right)\left(y_2-y\right)+\\ & \frac{f\left(Q_{21}\right)}{\left(x_2-x_1\right)\left(y_2-y_1\right)}\left(x-x_1\right)\left(y_2-y\right)+\\ & \frac{f\left(Q_{12}\right)}{\left(x_2-x_1\right)\left(y_2-y_1\right)}\left(x_2-x\right)\left(y-y_1\right)+\\ & \frac{f\left(Q_{22}\right)}{\left(x_2-x_1\right)\left(y_2-y_1\right)}\left(x-x_1\right)\left(y-y_1\right)\end{array}$$

(3)

Unlike traditional zero-watermarking algorithms, the construction of the feature matrix based on SIFRT does not aim to compute the overall feature information of the image, but instead focuses on computing various local feature descriptors centered around keypoints. As the feature matrix generated by the MrLBP algorithm consists of binary elements (0 s and 1 s), while the keypoint feature matrix after feature compression has not undergone binarization, it requires the introduction of a threshold for binarization to ultimately generate a binary matrix. To enhance the security of the algorithm, the zero-watermark feature matrix needs to adhere to statistical principles in cryptography, specifically maintaining a balance between the quantities of 0 s and 1 s in the matrix. To achieve this, when invoking the MrLBP algorithm to generate texture features, the algorithm in this paper also counts the occurrences of 0 s and 1 s in the statistical MrLBP descriptors. This step statistically constrains the binary matrix of keypoint descriptors in terms of quantity relationships. Multiple vectors correspond to multiple thresholds, and the use of different thresholds with overall constraints strengthens the coordination of various local regions in the image, thus improving the overall security and robustness of the algorithm.

In conclusion, the algorithm combines the feature matrix of compressed keypoint descriptors with the local texture feature matrix to generate the SIFRT feature matrix, which exhibits excellent performance. The matrix dimension of the SIFRT feature matrix can be flexibly adjusted according to the size of the target copyright image, aiming to retain the stable feature information of digital images as much as possible. Moreover, it innovatively integrates texture feature information, demonstrating good distinguishability and robustness in subsequent experiments.

2.3. Logistic Chaotic Encryption

Zero-watermarking algorithms typically need to consider security issues. Therefore, this paper adds encryption steps to the proposed algorithm to encrypt both the binary feature matrix and the watermarking information. In the process of constructing the binary feature matrix, this paper ensures that the statistical properties of the binary feature matrix comply with cryptographic statistical principles by introducing texture feature constraints and multiple threshold determinations. Building upon this foundation, this section further incorporates the logistic chaos encryption algorithm to encrypt the watermarking information and feature matrix of the image multiple times. In subsequent security experiments, this paper simulates exhaustive attacks under extreme conditions, and the experimental data confirm the security of the algorithm. During the process of layer-by-layer encryption, even if the specific steps of this algorithm are publicly disclosed, attackers would find it difficult to decrypt these copyrighted digital carrier images and tamper with the bound watermarking information without the key.

The logistic mapping formula originates from mathematical models describing the growth trends of biological populations in natural environments. Subsequent scholars utilized the Euler method to discretize the continuous logistic growth model and introduced a dimensionless population density parameter μ. This yields the logistic mapping expression that is widely used in the field of digital image encryption, as depicted in Formula (4).

$$x_{k+1}=\mu x_k\left(1-x_k\right)$$

(4)

where the control parameter µ ∈ (0, 4), x_k ∈ (0, 1) represents the current value, and x_k+1 is the value after iteration calculation. The mathematical definition of the logistic chaos model is based on equations of nonlinear dynamical systems. Its behavior exhibits irregular trajectories in phase space, demonstrating high sensitivity to initial conditions and unpredictability. When the control parameter of the chaos model reaches a certain value range, specifically 3.5699456 < µ ≤ 4, the system transitions from a stable state to an unpredictable chaotic state. From a geometric perspective, this property is specifically manifested by the distribution of output values mapped using input values, which creates fractal structures within the coordinate system, as illustrated in Figure 3.

Therefore, in image information protection, the logistic mapping can be used to achieve the bitwise encryption of pixel values [12]. This involves performing XOR operations between the image matrix and the sequence generated by the logistic mapping. Consequently, each pixel value in the image undergoes random changes. This pixel-level encryption makes both local and global features of the image difficult to discern and predict, thereby enhancing the security of watermarking embedding algorithms.

This paper utilizes multiple chaotic sequences generated by the logistic chaos mapping for the following encryption operations: pixel value encryption of the feature matrix, position mapping of the watermarking information, and iterative calculation of the control parameter µ. To disrupt the correlation of the watermarking information image in two-dimensional space, pixel positions undergo Arnold mapping for position scrambling [13], followed by the introduction of chaotic keys for pixel value transformation. For each pixel, the algorithm applies different keys for encryption processing at both the spatial position distribution and pixel amplitude levels, ensuring the security and imperceptibility of the original copyright information and significantly reducing the probability of decryption by attackers.

3. Algorithm Process

3.1. Zero-Watermarking Generation Algorithm

Both the zero-watermarking generation process and the subsequent copyright information extraction process inevitably involve a core step, which is the construction of a binary feature image based on SIFRT. The pseudocode of the core algorithm in this article is shown in Algorithm 1.

Algorithm 1: Binary feature generation algorithm based on SIFRT

In this algorithm, F represents the carrier image, T represents the unencrypted binary feature image, N represents the number of feature points, L represents the sequence matrix used to store the sorted SIFT feature descriptor vector group, S represents the SIFT descriptor matrix, M represents the MrLBP descriptor matrix, Vi represents the difference in the number of 0 s and 1 s in M(:, i), and Di represents the threshold for binarizing S(:, i).

Combining the pseudocode above, an explanation of the specific steps of the zero-watermark generation algorithm can be provided as follows:

• Select the original image requiring copyright protection. Utilize the SIFRT algorithm to statistically extract N stable keypoints from the carrier image under various attacks and calculate the descriptor arrays storing these keypoints. Reduce the dimensionality of their 128-dimensional SIFT descriptor vectors and remove redundant information to generate feature-rich vector matrices;
• Use the MrLBP algorithm to generate 36-dimensional MrLBP descriptor vectors and count the number of 0 s and 1 s in the vectors. Based on the number of 0 s and 1 s in the MrLBP descriptor vectors, determine the threshold size for the corresponding 92-dimensional keypoint feature vectors and binarize them to ensure roughly equal numbers of 0 s and 1 s in the concatenated 128-dimensional vectors. Combine and arrange the obtained keypoint feature vector matrix and local texture feature matrix to generate a binary feature matrix based on the SIFRT algorithm;
• Perform Arnold position scrambling and logistic chaos encryption on the watermarking information that is to be embedded. Conduct an XOR operation using the encrypted image and the final encrypted SIFRT binary feature matrix obtained in Algorithm 1 to obtain the zero-watermarking image. Apply for a timestamp from a reputable timestamp authority, bind the final zero-watermarking signal with this, and register the bound signal in the intellectual property right database (IPRD). The construction and registration process of the zero-watermarking signal is now complete.

The above algorithm steps demonstrate the feature extraction of digital copyright images and the generation of their zero-watermarking images using the SIFRT algorithm proposed in this paper, as shown in Figure 4.

3.2. Copyright Information Extraction Algorithm

Because the feature matrix construction algorithm required for copyright information extraction is the same as that shown Algorithm 1, we will not re-introduce the algorithm framework here. We will only provide a textual description and a flowchart.

• Preprocess the attacked copyright image that is to be verified and obtain the unencrypted SIFRT binary feature matrix using steps 1–2 in Section 3.1. Combine the encryption algorithm and key to perform chaotic encryption on the SIFRT binary feature matrix, facilitating subsequent XOR operations;
• Retrieve the corresponding zero-watermarking image information from a third-party intellectual property database. XOR this information with the SIFRT binary feature image encrypted with the cipher to generate the watermarking image that requires secondary decryption and a restoration of scrambling order;
• Decipher the watermarking image in ciphertext format obtained in the previous step to obtain an image containing copyright information symbols. Ensure that both subjective perception and objective indicators allow for the identification and differentiation of copyright information.
• In the case of multiple copyright disputes, apply for a timestamp from a timestamp authority to bind the date. This provides legal copyright protection.

The timestamp mechanism in this algorithm prevents copyright disputes caused by the illegal binding of watermarking information to copyright images for a second time. Since zero-watermarking does not have embedding capacity limitations, a single image can be embedded with multiple public keys using one private key. The original author and various copyright holders can generate their corresponding chaotic watermarking using their own keys to confirm exclusive copyright ownership, as shown in Figure 5.

4. Experimental Results and Analysis

4.1. Experimental Materials

To assess the performance of the algorithm proposed in this paper, a set of standard test images with a pixel size of 400 × 400 was selected to provide carrier images. These images include a squirrel, butterfly, human figure, and flower. Additionally, visual information images with a pixel size of 128 × 128, displaying the Chinese characters “水印信息” (watermarking information), were chosen to simulate copyright information, as shown in Figure 6.

4.2. Effectiveness and Security Test

The application scenarios of digital watermarking algorithms largely depend on the effectiveness and security of the algorithms. If the key of a zero-watermarking algorithm is easily cracked, it poses a significant threat to both the carrier image and the copyright watermarking image. The encryption algorithm of zero-watermarking should ensure that even if the algorithm for constructing zero-watermarking is fully disclosed, the feature images generated by outlaws without the correct key have no meaning and cannot be jointly verified with third-party intellectual property databases to confirm the copyright information. The effectiveness can be verified by analyzing the correlation between the binary features of different images generated by the same zero-watermarking algorithm. The NC value ranges from 0 to 1, where a higher value indicates a higher similarity to the original image. Specific metrics can be derived from the NC value, which can be calculated using Formula (5).

$$NC=\frac{{{\displaystyle \sum }}_{i=1}^m{{\displaystyle \sum }}_{j=1}^{n}W(i,j)W^{\prime }(i,j)}{\sqrt{{{\displaystyle \sum }}_{i=1}^m{{\displaystyle \sum }}_{j=1}^{n}W{(i,j)}^2}\sqrt{{{\displaystyle \sum }}_{i=1}^m{{\displaystyle \sum }}_{j=1}^n{W}^{\prime }{(i,j)}^2}}$$

(5)

From Figure 7, it is evident that each image is highly consistent with its own feature image, while the similarity values with feature images of other experimental materials remain around 0.5. This demonstrates the effectiveness of the algorithm.

To verify the security of the algorithm proposed in this paper, let us consider an extreme scenario where all key sequences, except for the chaotic initial value key, K1, used for watermarking information encryption, have been stolen. To crack the K1 sequence, attackers would need to determine the length of the key. Here, we assume the key length is 7, and the correct key is set as K1 = 0.2124650. In the security test, the experimenter uses 0.2124601 as the first test value and 0.2124700 as the last test value. These 100 keys are numbered, and the NC values for the 100 deciphered images and the correctly decrypted image are calculated within each interval. From Figure 8, we can observe that, excluding the NC value for the correct key, the NC values for the other 99 incorrect keys are in the range [0.4898, 0.5106]. The similarity of the images remains stable at around 0.5, as shown in Figure 8.

4.3. Distinguishability Test

To test the distinguishability of the zero-watermarking algorithm for similar images, this paper presents an SIFRT feature extraction for five similar images. A comparative analysis is then performed to assess the image similarity level of the binary feature images generated under the proposed algorithm. This is intended to test whether the SIFRT feature matrices of similar images exhibit strong distinguishability.

The content shown in Figure 9 consists of five similar images, with detailed displays of the binary feature images generated by the SIFRT zero-watermarking algorithm proposed in this paper. Based on this, we conducted a similarity analysis on the generated binary feature matrix, as shown in Figure 10. From a comparative analysis of the data in Figure 10, the following conclusions can be drawn. The NC values of the feature images generated from similar images are slightly higher compared to the similarity of the watermarking generated from incorrect keys, as shown in Figure 7, with NC values fluctuating at around 0.57 overall. This indicates that, even for images judged to be highly similar based on human physiological perception, the feature matrices generated by the SIRFT algorithm can effectively distinguish their differences, further enhancing the persuasiveness of the algorithm in professional applications.

4.4. Distinguishability Test

The performance of a digital watermarking can be measured from various perspectives. For embedding watermarkings, effectiveness and invisibility are important considerations. For zero-watermarking algorithms, invisibility may not be a concern because, theoretically, these algorithms do not modify the original image, thus eliminating visibility issues. Apart from security and distinguishability, zero-watermarking algorithms should also prioritize robustness, meaning whether the algorithm can still effectively extract copyright information after the copyright image has been subjected to a certain degree of attack, as shown in

Table 1. The integrity of watermarking information under various attacks.

	Median Filtering	Gaussian Noise	Salt and Pepper Noise	Partial Cropping	Clockwise Rotation 3°	Clockwise Rotation−3°	JPEG Compression
Butterfly	0.9714	0.9523	0.9797	0.9631	0.9795	0.9801	0.9944
Squirrel	0.9868	0.9541	0.9812	0.9679	0.9857	0.9859	0.9997
Flower	0.9957	0.9543	0.9837	0.9682	0.9832	0.9834	0.9998
Woman	0.9943	0.9540	0.9807	0.9682	0.9854	0.9853	1

.

From the analysis of Table 1, it can be observed that the copyright information of the experimental materials listed in Figure 6 is effectively preserved at the subjective visual level after various attacks. At the objective level, regarding JPEG compression attacks, the algorithm exhibits good robustness, with an NC mean value of 0.9985, close to 1, indicating that the feature data are well preserved under low JPEG compression. However, for image cropping attacks, where 1/16 of the content from the top left corner is removed, there is a certain degree of impact, with an NC mean value of 0.9668. Additionally, for attacks involving the addition of Gaussian noise, the NC mean value decreases to 0.9536, indicating the poorest robustness among the aforementioned attacks, suggesting room for improvement in subsequent iterations.

To facilitate a more intuitive analysis of the performance of our algorithm and other zero-watermarking algorithms, we simulated how digital images were protected by selected mainstream zero-watermarking algorithms after undergoing various attack methods and intensities. Since the application scenarios of zero-watermarking technology mostly involve sensitive data, attackers typically refrain from employing irreversible attack methods to blur or steal copyrights. Undoubtedly, excessive attacks on digital images may lead to certain limitations and disturbances in the subsequent distribution and use of the images. Therefore, this section focuses on observing the integrity of the damaged copyright information extracted by some zero-watermarking algorithms under the conditions of cropping attacks, data compression attacks, and slight rotation attacks. The specific data are shown in

Table 2. Robustness comparison between SIFRT algorithm and other algorithms.

Attack Mode	Attack Intensity	Normalized Cross-Correlation
		SIFRT	[14]	[15]	[16]	[17]	[18]	[19]
Median filtering	3 × 3	0.9957	0.9922	0.6939	0.9974	0.9954	0.9940	0.9872
Gaussian noise	0.1	0.9543	0.9756	0.5961	0.9520	0.9374	0.9283	0.9455
Salt and pepper noise	0.1	0.9837	0.9510	0.6191	0.9748	0.9687	0.9583	0.9637
Partial cropping	1/16	0.9688	0.9360	0.7454	0.9721	0.9501	0.9792	0.8967
Clockwise rotation	3°	0.9832	0.8223	0.9387	0.9052	0.8691	0.9794	0.9437
Clockwise rotation	−3°	0.9834	0.8209	0.7020	0.9126	0.8691	0.9786	0.9623
JPEG	10	0.9164	0.9866	0.6403	0.9922	0.9749	0.9863	0.9872
JPEG	50	0.9998	0.9952	0.7151	0.9957	0.9899	0.9976	0.9949

.

To facilitate the quantitative observation of experimental data by readers, we have bolded the maximum and submaximum values in Table 2. Based on the experiments described above, the following phenomena can be observed: The algorithm proposed in this paper exhibits NC values above 98% for resisting rotation attacks, mild compression attacks, and salt-and-pepper noise attacks, all achieving the maximum values within the group. When resisting median filtering and Gaussian noise attacks, the NC values attain the submaximum values within the group, with a difference of less than 2% compared to the maximum values, all exceeding 95%. These data indicate that the integrity of the copyright information has been well protected. However, when resisting high-intensity image compression attacks, the NC value of the algorithm decreases to 91.64%, showing a significant gap compared to other algorithms. This decrease can be attributed to a certain deviation in determining image keypoints during high-intensity image compression processing, leading to the introduction of some erroneous feature descriptor vectors in the subsequent feature matrix construction, thereby affecting the integrity of copyright information. Based on the above analysis, the algorithm proposed in this paper demonstrates a strong ability to resist most attack methods, indicating its robustness and effectively preserving the integrity of copyright information. These results align with the expectations set forth in the experimental design.

5. Conclusions

Zero-watermarking technology is a form of digital copyright protection that preserves the original data of the carrier, with a superior performance in terms of invisibility and embedding capacity compared to traditional embedding watermark algorithms. Innovative research in this technology can expand the application scope of digital intellectual property protection laws and provide some degree of technical support for the digital transformation of traditional industries. The zero-watermarking algorithm based on SIFRT constrains the extraction range of image feature data to sub-block regions and annular neighborhoods surrounding key points. This not only reduces the computational scale of the algorithm but also avoids introducing excessive interference. The innovative aspect of this algorithm lies in its core feature matrix, which originates from key point descriptors and neighborhoods, inheriting the spatial stability of traditional SIFT. By utilizing the element quantity from the MrLBP texture feature matrix, it imposes constraints on the overall feature matrix. Under the premise of stability in scale and rotation transformations, the concatenation of these two feature matrices yields a high-performance binary feature matrix.

One limitation of the algorithm is that when a significant number of key points and their neighboring areas are erased by attack methods, errors at the vector level arise during the construction of the feature matrix. In the face of high-intensity attacks, the computed watermark information may be incomplete. To address this deficiency, we plan to introduce error-correcting code data-encoding techniques in future algorithmic research [20]. This approach aims to recover lost data using known key point information and encoding constraints. The traditional zero-watermark methods heavily rely on manual design and computation. Future research directions could also focus on applying deep learning and neural network frameworks [21] to the feature construction steps to ensure the creation of higher-performing zero-watermark information.