Robust zero watermark algorithm and system based on NSCT-UPEMD-PHT

Abstract

The invention discloses a robust zero watermarking algorithm based on NSCT and UPEMD-PHT. The method comprises the following steps: step 1, carrying out Tent chaotic encryption on a watermark image; step 2, embedding a watermark; step 3, extracting a watermark; and 4, decrypting the watermark image. According to the method, before a carrier image is embedded, encryption of a watermark image is carried out based on Tent chaotic mapping so as to ensure the security of the watermark, non-subsampled contourlet transform (NSCT) is carried out on a host image, low-frequency information is extracted, and then uniform phase empirical mode decomposition (UPEMD) and polar harmonic transform (PHT) are carried out on the low-frequency information so as to complete watermark embedding. According to the invention, a chaotic mapping algorithm and a novel watermarking technology are organically combined, and the method for embedding the digital zero watermark in the digital image is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of information security, and relates to a robust zero-watermark algorithm, specifically to a robust zero-watermark algorithm based on polar harmonic transform (PHT), non-subsampled contourlet transform (NSCT), complete ensemble empirical mode decomposition (CEEMD), and Hilbert curve. Background Art

[0002] In the current era of rapid development of informatization and digitalization, a vast amount of information is transmitted and stored through the Internet; people can obtain information from all over the world more quickly and conveniently. However, behind the convenience brought by this rapid technological development, there lurks a more serious crisis. More and more people begin to use various technologies to steal the achievements and information of others. To address this crisis, digital watermarking technology has been proposed.

[0003] As a commonly used decomposition method, empirical mode decomposition is less applied in the watermark algorithm. Hu et al. proposed a robust and efficient image watermarking algorithm based on Hilbert curve and one-dimensional empirical mode decomposition (EMD). The focus is to use the Hilbert curve to reduce the two-dimensional problem to one dimension to improve the efficiency of the algorithm, and then the algorithm also adopts a repeated embedding strategy to improve the robustness of the algorithm. Mohammad et al. proposed a dual-image reversible DHT algorithm based on empirical mode decomposition (EMD). This algorithm uses the data hiding technology (DHT) based on the modified direction (EMD) to provide medium data hiding ability and high-quality stego images. Summary of the Invention

[0004] The purpose of the present invention is to provide a robust zero-watermark algorithm and system based on NSCT-UPEMD-PHT, which uses complete ensemble empirical mode decomposition (CEEMD) to find more stable modes, and while ensuring high robustness against general attacks, it integrates non-subsampled contourlet transform (NSCT) and polar harmonic transform (PHT) to improve the robustness of the algorithm. Among them, the polar harmonic transform is to process the modes using the method in the polar coordinate domain to increase the robustness against geometric attacks. Its robustness is measured by the normalized correlation (NC) and the bit error rate (BER).

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] The robust watermark algorithm and system based on NSCT-UPEMD-PHT includes the following steps:

[0007] (1) Perform Tent chaotic encryption on the watermark image :

[0008] From the initial value Generate a chaotic sequence, which is represented as after binarization, and perform an exclusive OR operation with the watermark image, then save as the decryption key for the encrypted watermark image to obtain the encrypted watermark image ;

[0009] (2) Embedding of the watermark:

[0010] Step 1. Perform NSCT transformation on the entire carrier image to obtain a low-frequency sub-band and four high-frequency sub-bands; denotes the carrier image.

[0011] Step 2. Select the low-frequency sub-band for Hilbert curve dimensionality reduction to obtain a one-dimensional low-frequency sub-band.

[0012] Step 3. Use wavelet packet decomposition on the low-frequency sub-band to decompose the signal into different frequency bands, each with a signal component, and select the most stable mode 5.

[0013] Step 4. After performing inverse Hilbert curve dimensionality increase on mode 5, process it in the polar coordinate domain to take the values inside the unit circle.

[0014] Step 5. After performing polar harmonic transform (PHT) on the processed mode 5 to obtain the PHT moments, perform the following calculations on the PHT moments.

[0015]

[0016] where is the processed PHT value, is the value before processing.

[0017] Step 6. Average the PHT moments and perform an exclusive OR operation with the encrypted watermark image to obtain the key .

[0018] (3) Extraction of the watermark

[0019] Step 1. Perform NSCT transformation on the entire carrier image to obtain a low-frequency sub-band and four high-frequency sub-bands; denotes the carrier image.

[0020] Step 2. Select the low-frequency sub-band for Hilbert curve dimensionality reduction to obtain a one-dimensional low-frequency sub-band.

[0021] Step 3. Use wavelet packet decomposition on the low-frequency sub-band to decompose the signal into different frequency bands, each with a signal component, and select the most stable mode 5.

[0022] Step 4: After performing inverse Hilbert curve dimensionality elevation on Modal 5, process it using the polar coordinate domain and take the values within the unit circle.

[0023] Step 5: After performing polar harmonic transform (PHT) on the processed Modal 5 to obtain the PHT moments, perform the following calculations on the PHT moments.

[0024]

[0025] where is the processed PHT value, is the value before processing.

[0026] Step 6: Average the PHT moments and perform exclusive OR with the secret key to obtain the encrypted watermark.

[0027] (4) Decryption of the watermark:

[0028] Use the decryption key obtained during the encryption process to perform exclusive OR with the encrypted watermark obtained in Step 6 of 3 to obtain the original watermark information.

[0029] (5) Watermark system:

[0030] Step 1: Generate a watermark image according to user requirements or read the watermark image uploaded by the user.

[0031] Step 2: Read the carrier image uploaded by the user, execute the above 1 to 4, and save the watermark key.

[0032] Step 3: Save the zero watermark key to a trusted third-party library and return the key number to the user for copyright protection.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] Experimental results show that the robust watermark algorithm of the present invention can handle more complex situations than existing watermark algorithms, especially showing better performance under noise attacks and filtering attacks, and has good robustness. Description of the Drawings

[0035] Figure 1 is the watermark flow chart;

[0036] Figure 2 is the original host image: Figure 1 (a) is a chest CT image, Figure 1 (b) is a brain CT image;

[0037] Figure 3 is the original watermark image;

[0038] Figure 4 is the image encrypted by Tent chaotic mapping;

[0039] Figure 5 is the carrier image after being attacked: Figure 5 (a) is Gaussian noise, Figure 5 (b) is salt-and-pepper noise, Figure 5 (c) is JPEG compression, Figure 5 (d) is median filtering, Figure 5 (e) is mean filtering, Figure 5 (f) is Gaussian low-pass filtering, Figure 5 (g) is rotation attack, Figure 5 (h) is cropping attack;

[0040] Figure 6 is the watermark image extracted after being attacked: Figure 6 (a) is Gaussian noise, Figure 6 (b) is salt-and-pepper noise, Figure 6 (c) is JPEG compression, Figure 6 (d) is median filtering, Figure 6 (e) is mean filtering, Figure 6 (f) is Gaussian low-pass filtering, Figure 6 (g) is rotation attack, Figure 6 (h) is cropping attack; Detailed implementation manners

[0041] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0042] The present invention provides a robust watermarking algorithm and system based on NSCT-UPEMD-PHT. The system includes a memory, a processor, and a computer program stored on the memory. The computer program is executed by the processor to achieve copyright protection. The binary watermark image is encrypted by Tent chaotic mapping, and then the host image is decomposed by NSCT. The decomposed low-frequency subbands are decomposed by UPEMD, and mode five is selected for polar harmonic transform to obtain PHT moments. The processed PHT moments are averaged and XORed with the encrypted watermark image to obtain a key, completing watermark embedding. The algorithm mainly includes four parts: watermark encryption, watermark embedding, watermark extraction, and watermark decryption. The processes of watermark embedding and extraction are generally similar, as Figure 1 shown, and specifically include the following steps:

[0043] (1) For the watermark image Perform Tent chaos encryption:

[0044] Generate a chaotic sequence from the initial value After binarization processing, it is represented as , perform an exclusive OR operation with the watermark image, and save As the decryption key for the encrypted watermark image, obtain the encrypted watermark image ;

[0045] (2)Embedding of the watermark:

[0046] Step 1: After reading the host image, select a suitable channel among the three channels according to the image characteristics. Most images, even if they appear black and white, are actually color images in terms of actual data, and still need to be processed channel by channel during processing.

[0047] Step 2: Perform NSCT on the selected channel. Select the low-frequency domain for one-dimensionalization by Hilbert curve for convenient processing. After dimensionality reduction, the data calculation amount can be reduced, and the Hilbert curve can also ensure the correlation between pixel points.

[0048] Step 3: After performing uniform phase empirical mode decomposition (UPEMD) on the one-dimensional data, through experimental result comparison, we obtained that the 5th eigenmode vector is the most stable data and also the best mode for experimental results. Therefore, we choose to use the 5th eigenmode as the input data for the following polar harmonic transform. Perform the inverse Hilbert curve on this eigenmode and use polar coordinate domain processing to take the values within the unit circle.

[0049] Step 4: Next, perform block division. Divide according to Perform block division, perform polar harmonic transform on each divided block, calculate the PHT moment, and perform the following calculation on the PHT moment:

[0050]

[0051] Note: Both J and N above are user-defined. The initial value of J is 3, and the initial value of N is 45, where N belongs to the key part; .

[0052] After performing mean binarization on the calculated values, store them as the information for exclusive OR with the encrypted watermark image next.

[0053] Step 5: Decryption of the watermark image: The watermark image with size and the Tent map obtain the binary encryption matrix , perform an exclusive OR on the binary to obtain the encrypted watermark image . The initial value of the Tent map here is set to . The watermark image is also encrypted using Tent chaotic mapping.

[0054] Step 6: XOR the medical image feature vectors obtained in Step 4 and Step 5 and the encrypted watermark image to obtain a binary logical sequence , and then save it on a third-party server for subsequent watermark decryption.

[0055] (3) Watermark extraction:

[0056] Step 1: After reading the host image, select the corresponding channel for watermark extraction according to the key. At this time, the key already includes which channel selected from the RGB channels is used as the part for feature extraction.

[0057] Step 2: Perform NSCT on the channel selected by the key. Select the low-frequency domain for one-dimensionalization by Hilbert curve for easy processing. After dimensionality reduction, the data calculation amount can be reduced, and the Hilbert curve can also ensure the correlation between pixel points.

[0058] Step 3: After performing uniform phase empirical mode decomposition (UPEMD) on the one-dimensional data, perform the inverse Hilbert curve on this intrinsic mode 5, and use polar coordinate domain processing to take the values within the unit circle.

[0059] Step 4: Next, perform block division. Divide it according to , perform polar harmonic transform on each divided block, calculate the PHT moments, and perform the following calculations on the PHT moments:

[0060]

[0061] After mean binarization of the obtained values, use them as the next step to XOR with the key to obtain the encrypted watermark sequence and perform the inverse Hilbert curve.

[0062] Step 5: Decryption of the watermark image: XOR the processed PHT moments and the key to obtain the watermark sequence , and perform the inverse Hilbert transform to obtain the watermark image

[0063] (4) Decryption of the watermark:

[0064] Step 1: Use the decryption key obtained during the encryption process to XOR with the encrypted watermark obtained in Step 5 of (3) to obtain the original watermark information.

[0065] Step 2. Since the present invention is a digital watermarking algorithm and system based on Tent chaotic mapping, NSCT, and UPEMD-PHT, the NSCT transform, UPEMD decomposition, and PHT have strong anti-geometric attack capabilities, anti-conventional attack capabilities, and strong anti-hybrid attack capabilities. In addition, zero watermark technology is used to ensure the integrity of the image, thus resolving the conflict between the robustness and invisibility of watermark embedding. Therefore, it has high practical value in the field of information security, and this algorithm can be applied to other fields using the concept of a third party, adapting to the practicality and standardization of current network promotion.

[0066] The following is illustrated from the theoretical basis and experimental data:

[0067] 1. Nonsubsampled Contourlet Transform (NSCT)

[0068] The main method is to first use the nonsubsampled pyramid filter (NSP) to decompose the source image into a low-frequency subband and high-frequency subbands. The low-frequency subband is further processed and decomposed using NSP, while the high-frequency subbands use the nonsubsampled directional filter bank (NSDFB) to obtain subband coefficients in different directions and scales. NSCT replaces the downsampling of the directional filter in Contourlet with a nonsubsampled pyramid structure (NSP) and converts the downsampling in the directional filter to nonsubsampled directional filtering (NSDFB), thereby making the algorithm translation invariant and fixing the problem of pseudo-Gibbs effects in the fused image.

[0069] 2. Uniform Phase Empirical Mode Decomposition (UPEMD)

[0070] UPEMD selects a noise interference signal with uniform phase to reduce the mode splitting and residual noise effects in empirical mode decomposition (EMD). The algorithm in this paper is applied to image signals, and compared with audio information, the details are observed more carefully, so the requirements for relevant parameters are very different from those of audio. The amplitude and phase number of the perturbation signal are two important parameters in UPEMD.

[0071] Step 1. Generate signal copies with uniform phase perturbations:

[0072] Design an auxiliary sine signal , where is uniformly distributed in .

[0073] Generate perturbation signals:

[0074]

[0075] Step 2. Multilevel decomposition:

[0076] According to the signal length Setting decomposition technology:

[0077]

[0078] Gradually adjust the perturbation frequency and amplitude , and decompose according to the dyadic filter bank structure .

[0079] The finally extracted satisfies the strict reconstruction condition:

[0080]

[0081] 3. Polar harmonic transform (PHT)

[0082] If we use to represent an image of size size, then the order kernel function defined on the unit circle and can be expressed as PHT is a linear combination with the repetition number of , that is:

[0083]

[0084] where represents the PHT moment.

[0085] The PHT moment is calculated as and the product of

[0086]

[0087] where is a constant, is the conjugate of

[0088] The kernel function of PHT consists of a radial component and a circular component and is composed of

[0089]

[0090] The kernel function should satisfy the following orthogonality condition

[0091]

[0092] where is defined as the Kronecker function as

[0093]

[0094] In fact, PHT is the general term for the Polar Complex Exponential Transform (PCET), the Polar Cosine Transform (PCT), and the Polar Sine Transform (PST). Different orthogonal moments have different radial components. The radial components of PCET, PCT, and PST are respectively , , .

[0095] The above are all defined in the continuous domain, while digital images in practical applications are discretely represented. In this case, PCET can be calculated as

[0096]

[0097] where , , , Using the PCET moment and its kernel function to reconstruct the image function, that is

[0098]

[0099] The calculations of the PCT and PST moments in the discrete domain and their corresponding image reconstruction formulas are similar to those of the PCET moment and are omitted here for simplicity.

[0100] 4. Tent Chaotic Map

[0101] A chaotic system refers to a deterministic system in which there exists seemingly random irregular motion, and its behavior is characterized by uncertainty, non-repeatability, and unpredictability, which is the chaotic phenomenon.

[0102] The tent map, in mathematics, refers to a piecewise linear map, so named because its function graph resembles a tent. In addition, it is also a two-dimensional chaotic map, which is widely used in chaotic encryption systems (such as image encryption), and is also often used in the generation of chaotic spread-spectrum codes, the construction of chaotic encryption systems, and the implementation of chaotic optimization algorithms.

[0103] The definition of the tent map is as follows:[[]]

[0104]

[0105] where , the tent map is a chaotic map within its parameter range and has a uniform distribution function and good correlation. It should also be noted that the tent map and the logistic map are topologically conjugate maps, and within the range of acceptable values, the system is in a chaotic state. Especially when , the system presents a short-period state, so generally is not taken.. When using this mapping, it should be noted that the initial value of the system cannot be the same as the system parameter . Otherwise, it will evolve into a periodic system, and at this time it is no longer a chaotic system.

[0106] Example:

[0107] In the experiment, carrier images of size were tested. The size of the watermark image is . First, the watermark image was encrypted using the Tent chaotic mapping. The encrypted image is shown in Figure 4. It can be seen that the image has changed greatly, improving the security significantly. We tested the performance of the watermarking scheme proposed in the present invention from the aspect of robustness. The robustness was measured by applying various attack means such as filtering attack, additive noise, and geometric attack.

[0108] The robustness of the algorithm was verified by performing different attacks on the watermark image and detecting the similarity between the extracted watermark and the original watermark. The Normalized Cross-Correlation (NC) and Bit Error Rate (BER) were used to measure the robustness. These attacks were classified as Gaussian noise, Salt & Pepper noise, JPEG Compression, Median Filter, Mean Filtering, Gaussian Low-pass Filter, Rotation, Cropping. The results in Table 1 are the magnitudes of the Normalized Cross-Correlation (NC) after suffering attacks.

[0109] Table 1. Robustness Test

[0110]

[0111] From Table 1 and Figure 6 the experimental data shown in (a ~ h), it can be seen that this watermarking method has the ability to resist conventional attacks and can resist Gaussian noise, Salt & Pepper noise, JPEG compression, median filter, mean filtering, Gaussian low-pass filter. It may perform poorly in resisting geometric attacks, but it also shows good resistance.

Claims

1. A robust watermarking algorithm and system based on NSCT-UPEMD-PHT, characterized in that The method includes the following steps: (1) For the watermark image perform Tent chaotic encryption: From the initial value generate a chaotic sequence, which after binarization is represented as , perform an exclusive OR operation with the watermark image, and save as the decryption key for the encrypted watermark image, and obtain the encrypted watermark image ; (2) Embedding of watermark: Step 1. Perform NSCT transformation on the whole carrier image to obtain one low-frequency offspring and four high-frequency offsprings; denote the carrier image; Step 2: Select the low-frequency subband for Hilbert curve dimensionality reduction to obtain a one-dimensional low-frequency subband; Step 3. Use wavelet packet decomposition for the low-frequency sub-band to decompose the signal into different frequency bands, each frequency band having a signal component, and select the most stable mode 5; Step 4: After the inverse Hilbert curve dimensionality increase of Mode 5, perform processing in the polar coordinate domain to take the values within the unit circle; Step 5: After the processed Mode 5 undergoes polar harmonic transform (PHT) to obtain PHT moments, perform the following calculations: ； wherein is the processed PHT value, is the value before processing; Step 6: Average the PHT moments and perform an exclusive OR operation with the encrypted watermark image to obtain the key ; (3) Extraction of watermark: Step 1. Perform NSCT transform on the entire carrier image to obtain one low-frequency parent and four high-frequency children; denote the carrier image; Step 2: Select the low-frequency subband for Hilbert curve dimensionality reduction to obtain a one-dimensional low-frequency subband; Step 3. Use wavelet packet decomposition for the low-frequency subband to decompose the signal into different frequency bands, each band having a signal component, and select the most stable mode five; Step 4: After the inverse Hilbert curve dimensionality increase of Mode 5, perform processing in the polar coordinate domain to take the values within the unit circle; Step 5: After the processed Mode 5 undergoes polar harmonic transform (PHT) to obtain PHT moments, perform the following calculations: ； wherein is the processed PHT value, is the value before processing; Step 6: Average the PHT moments and perform exclusive OR with the key to obtain the encrypted watermark; (4) Decryption of watermark: Use the decryption key obtained during the encryption process Perform an exclusive OR operation with the encrypted watermark obtained in Step 3.6 to obtain the original watermark information; (5) Generate a watermark image according to the user's requirements or read the watermark image uploaded by the user. Read the carrier image uploaded by the user, execute the above, and save the watermark key. Save the zero-watermark key to a trusted third-party library and return the key number to the user for copyright protection; (6) Watermark system: Step 1: Generate a watermark image according to the user's requirements or read the watermark image uploaded by the user; Step 2: Read the carrier image uploaded by the user, execute the above 1 to 4, and save the watermark key; Step 3: Save the zero-watermark key to a trusted third-party library and return the key number to the user for copyright protection.

2. The robust zero-watermarking algorithm based on NSCT and UPEMD-PHT according to claim 1, wherein In the above (3), during the extraction process of watermark features, after the inverse Hilbert curve dimensionality increase of Mode 5, perform processing in the polar coordinate domain to take the values within the unit circle.

3. The robust zero-watermarking algorithm based on NSCT and UPEMD-PHT according to claim 1, characterized in that In the above (3), the process of extracting watermark features and the method for processing the extreme harmonic transform moments , the initial value of N is 45.

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