A Blind Watermarking Method for Color Digital Images Based on Contourlet Transform and Schur Decomposition

Abstract

Taking advantage of the strong robustness of the frequency-domain digital watermarking algorithm, the present invention discloses a blind watermarking method for color digital images based on Contourlet transform and Schur decomposition. According to the characteristics of multi-scale, multi-directionality, translational invariance of the Contourlet transform and low complexity of Schur decomposition, the present invention first performs hierarchical processing on the host image and conducts Contourlet transform on the hierarchical image. Then, the selected coefficient blocks are subjected to Schur decomposition to obtain an upper triangular matrix, and the embedding and blind extraction of the color digital watermark are completed by quantifying the first main diagonal element of the upper triangular matrix. The present invention belongs to the technical field of cyberspace security, not only has good watermark concealment, but also has the characteristics of strong robustness and high security, and is suitable for occasions where color image copyright protection is carried out quickly and efficiently.

Description

Technical Field

[0001] The present invention belongs to the technical field of cyberspace security, and relates to copyright protection of color image digital watermarks with high invisibility, strong robustness and high security. Background Art

[0002] With the rapid development of 5G networks, the application scope of network technology has been expanded. As a result, various types of infringements have gradually shifted from offline to online, and the ways of infringement have emerged in an endless stream, which has seriously affected the healthy development of cyberspace and brought more severe challenges to the copyright protection of digital multimedia. Therefore, network security needs to be improved day by day, and the copyright protection of digital works is imminent. It is urgent to study more effective digital watermarking methods to deal with digital infringements in the current environment.

[0003] In daily life, color images have become the main carrier of multimedia data transmission due to their advantages of larger information volume and better visual effects. However, the widespread transmission of color digital images on the Internet also greatly increases the possibility of attacks. Therefore, the copyright protection of color digital images has also attracted extensive attention from scholars at home and abroad. The strong robustness of the frequency domain digital watermarking algorithm can improve the ability of color digital images to resist attacks. Therefore, how to make full use of the frequency domain digital watermarking algorithm to design a color image digital watermarking algorithm with high invisibility, strong robustness and high security has become one of the research hotspots at this stage. Summary of the invention

[0004] The purpose of the present invention is to provide a color digital image blind watermarking method based on Contourlet transform and Schur decomposition, which is characterized by being implemented through a specific watermark embedding process and a watermark extraction process. The watermark embedding process is described as follows:

[0005] Step 1: First, a color watermark image W of size N×N is subjected to dimensionality reduction processing to obtain three layered watermark images of red, green and blue; then, each layered watermark image is subjected to a key-based Lorenz chaotic mapping to obtain the three scrambled layered watermark images W i ; The layered watermark image W i Each decimal pixel value in is converted into an 8-bit binary number and concatenated to a length of 8N 2 The layered watermark bit sequence SW i , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0006] Step 2: First, a color host image H of size M×M is subjected to dimensionality reduction processing to obtain three layered host images H of red, green and blue i , for each hierarchical host image H iPerform the Contourlet transform and extract its low-frequency coefficient matrix B i ; Then, divide its low-frequency coefficient matrix B i into non-overlapping coefficient blocks of size m×m, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0007] Step 3: Use the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select a coefficient block csblock of size m×m from each layer of the low-frequency coefficient matrix B i , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0008] Step 4: According to formula (1), perform the Schur decomposition on the coefficient block csblock to obtain the unitary matrix U and the upper triangular matrix V;

[0009] [U, V] = schur(csblock) (1)

[0010] Among them, the non-zero elements λ j on the main diagonal of the upper triangular matrix V are the j-th eigenvalue of the coefficient block csblock, j = 1, 2,..., r, where r represents the rank of the coefficient block csblock, and the elements on its main diagonal satisfy λ1 > λ2 > λ3 >... > λ r ;

[0011] Step 5: Select the watermark bit w to be embedded from the hierarchical watermark bit sequence SW i in sequence; Quantize the first main diagonal element λ1 in the upper triangular matrix V using formula (2) to embed the watermark bit w, and obtain the watermarked first main diagonal element λ1 * ;

[0012]

[0013] Among them, round(.) is the rounding function, xor(.) is the exclusive OR function, mod(.) is the remainder function, and QT is the selected quantization step;

[0014] Step 6: Replace the first main diagonal element λ1 in the original upper triangular matrix V with the watermarked first main diagonal element λ1 * to obtain the watermarked upper triangular matrix V * ; Perform the inverse Schur decomposition using formula (3) to obtain the watermarked low-frequency coefficient block csblock * ;

[0015] csblock * = U × V * ×U T (3)

[0016] Step 7: The watermarked low-frequency coefficient block csblock * is updated to its corresponding position in the hierarchical low-frequency coefficient matrix B i where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0017] Step 8: Repeat steps 3 to 7 of this process until all the watermark information is embedded, and thus obtain the watermarked hierarchical low-frequency coefficient matrix B i * ; Then, perform the inverse Contourlet transform on the watermarked hierarchical low-frequency coefficient matrix B i * to obtain the watermarked hierarchical host image H i * where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0018] Step 9: Combine the three layers of watermarked hierarchical host images H i * to obtain the watermarked image H * where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0019] The watermark extraction process is described as follows:

[0020] Step 1: First, divide the watermarked image H * into three watermarked hierarchical images H of red, green, and blue through dimensionality reduction processing i * ; At the same time, perform the Contourlet transform on each watermarked hierarchical image H i * to extract its low-frequency coefficient matrix B i * ; Then, divide the low-frequency coefficient matrix B i * into non-overlapping coefficient blocks of size m×m, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0021] Step 2: Use the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select the watermarked coefficient block csblock i * from the watermarked low-frequency coefficient matrix B * where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0022] Step 3: Use formula (4) to perform the Schur decomposition on the watermarked coefficient block csblock * to obtain the unitary matrix U and the upper triangular matrix V* ;

[0023] [U, V * = schur(csblock * )(4)

[0024] Among them, the non - zero elements λ * on the main diagonal of the upper triangular matrix V j * are the j - th eigenvalues of the coefficient block csblock * , j = 1, 2, …, r, where r represents the rank of the coefficient block csblock * , and the elements on its main diagonal satisfy λ1 * > λ2 * > λ3 * > … > λ r * ;

[0025] Step 4: Using the first non - zero element λ1 * on the main diagonal in the upper triangular matrix V * , extract the watermark bit w * from the watermarked coefficient block csblock * according to formula (5);

[0026]

[0027] Among them, fix(.) is the rounding - towards - zero function, mod(.) is the remainder function, and QT is the selected quantization step;

[0028] Step 5: Repeat the second and fourth steps of this process to obtain the extracted binary hierarchical watermark bit sequence SW i * ; Then, successively divide every 8 - bit binary information in SW i * into a group and convert it into a decimal pixel value to form a hierarchical scrambled watermark image; Then, perform an inverse Lorenz chaotic mapping based on the key on the hierarchical scrambled watermark image, and finally obtain the extracted hierarchical watermark image W i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0029] Step 6: Combine the extracted hierarchical watermark images W i * to form the final extracted watermark image W * , where i = 1, 2, 3 represent the red, green, and blue layers respectively.

[0030] This method is based on the Contourlet transform and Schur decomposition technology, and uses the quantization index modulation technology for the first main diagonal element obtained from the V matrix to complete the embedding and blind extraction of color digital watermarks. This method not only has good watermark invisibility, but also has strong robustness of the watermark algorithm and high watermark security. Description of the Drawings

[0031] Figure 1 (a) and (b) are two original color host images.

[0032] Figure 2 is the original color watermark image.

[0033] Figure 3 (a), Figure 3 (b) are the watermarked images obtained by sequentially embedding the watermarks shown in Figure 2 into the carrier images Figure 1 (a), Figure 1 (b). Their structural similarity SSIM values are 0.9705 and 0.9827 respectively, and their peak signal-to-noise ratio PSNR values are 40.3535 dB and 40.3973 dB respectively.

[0034] Figure 4 (a), Figure 4 (b) are the watermarks extracted from Figure 3 (a), Figure 3 (b) respectively. Their normalized cross-correlation coefficient NC values are 1.0000 and 1.0000 respectively.

[0035] Figure 5 (a), Figure 5 (b), Figure 5 (c), Figure 5 (d), Figure 5 (e), Figure 5 (f), Figure 5 (g) are the watermarks extracted after sequentially attacking the watermarked image shown in Figure 3 (a) with JPEG compression (70), JPEG 2000 compression (4:1), salt-and-pepper noise (0.2%), median filtering (3×3), low-pass filtering (100, 6), scaling (4:1), cropping (12.5%), etc. Their normalized cross-correlation coefficient NC values are 0.9999, 0.9999, 0.9847, 0.9902, 0.9886, 0.9997, 0.9392 respectively.

[0036] Figure 6 (a), Figure 6 (b), Figure 6 (c), Figure 6 (d), Figure 6 (e),Figure 6 (f), Figure 6 (g) are the watermarks extracted after subjecting the watermarked image shown in Figure 3 (b) to attacks such as JPEG compression (70), JPEG 2000 compression (4:1), salt-and-pepper noise (0.2%), median filtering (3×3), low-pass filtering (100, 6), scaling (4:1), and cropping (12.5%). Their normalized cross-correlation coefficient NC values are 0.9999, 0.9995, 0.9759, 0.9890, 0.9886, 1.0000, and 0.9384 respectively. Detailed implementation manners

[0037] The object of the present invention is to provide a blind watermarking method for color digital images based on Contourlet transform and Schur decomposition, which is characterized in that it is realized through a specific watermark embedding process and a watermark extraction process. The watermark embedding process is described as follows:

[0038] Second step: First, perform dimensionality reduction on a color watermark image W with a size of 32×32 to obtain three layered watermark images for red, green, and blue; then, perform Lorenz chaotic mapping based on a key on each layered watermark image to obtain three scrambled layered watermark images W i ; Convert each decimal pixel value in the layered watermark image W i into an 8-bit binary number (for example: the decimal number 181 can be converted into the binary sequence '10110101'), and connect them in sequence to form a layered watermark bit sequence SW with a length of 8×32×32 = 8192 i , where i = 1, 2, 3 respectively represent the red, green, and blue layers;

[0039] Second step: First, perform dimensionality reduction on a color host image H with a size of 512×512 to obtain three layered host images H for red, green, and blue i , perform Contourlet transform on each layered host image H i to extract its low-frequency coefficient matrix B i ; Then, divide its low-frequency coefficient matrix B i into non-overlapping coefficient blocks with a size of 4×4, where i = 1, 2, 3 respectively represent the red, green, and blue layers;

[0040] Third step: Use the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select coefficient blocks csblock with a size of 4×4 from each layer of low-frequency coefficient matrix B i , where i = 1, 2, 3 respectively represent the red, green, and blue layers. Here, assume i = 1, and the coefficient block csblock selected from the first-layer low-frequency coefficient matrix B1 is

[0041]

[0042] Step 4: According to formula (1), perform Schur decomposition on the coefficient block csblock to obtain the unitary matrix U and the upper triangular matrix V;

[0043] [U, V]=schur(csblock) (1)

[0044] Among them, the non-zero elements λ on the main diagonal of the upper triangular matrix V j are the j-th eigenvalue of the coefficient block csblock, j = 1, 2,..., r, where r represents the rank of the coefficient block csblock, and the elements on its main diagonal satisfy λ1>λ2>λ3>…>λ r ; here, the obtained unitary matrix upper triangular matrix The rank r of the pixel block csblock is 4, i = 1, and the first main diagonal element λ1 of the upper triangular matrix V is 554.7984;

[0045] Step 5: Select the watermark bit w to be embedded from the hierarchical watermark bit sequence SW i in sequence; use formula (2) to quantize the first main diagonal element λ1 in the upper triangular matrix V to embed the watermark bit w, and obtain the watermark-containing first main diagonal element λ1 * ;

[0046]

[0047] Among them, round(.) is the rounding function, xor(.) is the exclusive OR function, mod(.) is the remainder function, and QT is the selected quantization step; at this time, select the watermark bit w = 1 to be embedded from the hierarchical watermark bit sequence SW i , QT = 26, then according to formula (2), λ1 * = 559;

[0048] Step 6: Replace the first main diagonal element λ1 in the original V matrix with the watermark-containing main diagonal element λ1 * to obtain the watermark-containing upper triangular matrix V * ; use formula (3) to perform inverse Schur decomposition to obtain the watermark-containing low-frequency coefficient block csblock * ;

[0049] csblock * = U×V * ×U T (3)

[0050] Here

[0051] Step 7: Repeat Steps 3 to 6 of this process until all the watermark information is embedded, thereby obtaining the watermarked hierarchical low-frequency coefficient matrix B i * ; then, for the watermarked hierarchical low-frequency coefficient matrix B i * Perform the inverse Contourlet transform to obtain the watermarked hierarchical host image H i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0052] Step 8: Combine the three watermarked hierarchical host images H i * to obtain the watermarked image H * , where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0053] The watermark extraction process is described as follows:

[0054] Step 1: First, divide the watermarked image H * into three watermarked hierarchical images H i * for red, green, and blue through dimensionality reduction processing; meanwhile, perform the Contourlet transform on each watermarked hierarchical image H i * to extract its low-frequency coefficient matrix B i * ; then, divide the low-frequency coefficient matrix B i * into non-overlapping coefficient blocks of size 4×4, where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0055] Step 2: Use the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select the watermarked coefficient block csblock i * from the watermarked low-frequency coefficient matrix B * , where i = 1, 2, 3 represent the red, green, and blue layers respectively; here

[0056] Step 3: Use formula (4) to perform Schur decomposition on the watermarked coefficient block csblock * to obtain the unitary matrix U and the upper triangular matrix V * ;

[0057] [U * ,V * =schur(csblock *)(4)

[0058] Among them, the upper triangular matrix V * The non-zero elements λ on the main diagonal j * are the j-th eigenvalue of the coefficient block csblock * where j = 1, 2, …, r, and r represents the rank of the coefficient block csblock * The elements on its main diagonal satisfy λ1 * > λ2 * > λ3 * > … > λ r * ; Here, the unitary matrix The upper triangular matrix The watermarked pixel csblock * has a rank r = 4, i = 1, and the first main diagonal element λ1 of the upper triangular matrix V* * = 557.8743;

[0059] Step 4: Use the first main diagonal element λ1 in the upper triangular matrix V * to extract the watermark bit w * from the watermarked coefficient block csblock * according to formula (5); * ;

[0060]

[0061] Among them, fix(.) is the rounding function towards zero, mod(.) is the remainder function, and QT is the quantization step size; At this time, the quantization step size QT = 26, and the extracted watermark bit w * = 1;

[0062] Step 5: Repeat the second and fourth steps of this process to obtain the extracted binary hierarchical watermark bit sequence SW i * ; Then, successively divide every 8-bit binary information in SW i * into a group and convert it into a decimal pixel value to form a hierarchical scrambled watermark image; Then, perform an inverse Lorenz chaotic mapping based on the key on the hierarchical scrambled watermark image to finally obtain the extracted hierarchical watermark image W i * where i = 1, 2, 3 represent the red, green, and blue layers respectively;

[0063] Step 6: Combine the extracted hierarchical watermark images W i * to form the final extracted watermark image W * where i = 1, 2, 3 represent the red, green, and blue layers respectively.

[0064] Based on the Contourlet transform and Schur decomposition, this method uses the quantization index modulation technique for the first principal diagonal element obtained from the V matrix to complete the embedding and blind extraction of color digital watermarks. This method not only has good watermark invisibility, but also has strong robustness and security of the watermark algorithm.

[0065] Verification of the effectiveness of the present invention

[0066] To prove the effectiveness of the present invention, two 24-bit standard color images with a size of 512×512 as shown in Figure 1 (a), Figure 1 (b) are selected as carrier images, and 24-bit color images with a size of 32×32 as shown in Figure 2 are used as digital watermarks for verification.

[0067] Figure 3 (a), Figure 3 (b) are the watermarked images obtained by sequentially embedding the watermarks shown in Figure 2 into the carrier images Figure 1 (a), Figure 1 (b). Their structural similarity SSIM values are 0.9705 and 0.9827 in sequence, and their peak signal-to-noise ratio PSNR values are 40.3535 dB and 40.3973 dB in sequence. Figure 4 (a), Figure 4 (b) are the watermarks extracted from Figure 3 (a), Figure 3 (b) in sequence. Their normalized cross-correlation coefficient NC values are 1.0000 and 1.0000 respectively.

[0068] Figure 5 (a), Figure 5 (b), Figure 5 (c), Figure 5 (d), Figure 5 (e), Figure 5 (f), Figure 5 (g) are the watermarks extracted after sequentially attacking the watermarked image shown in Figure 3 (a) with JPEG compression (70), JPEG 2000 compression (4:1), salt-and-pepper noise (0.2%), median filtering (3×3), low-pass filtering (100, 6), scaling (4:1), shearing (12.5%), etc. Their normalized cross-correlation coefficient NC values are 0.9999, 0.9999, 0.9847, 0.9902, 0.9886, 0.9997, 0.9392 respectively.

[0069] Figure 6 (a), Figure 6(b), Figure 6 (c), Figure 6 (d), Figure 6 (e), Figure 6 (f), Figure 6 (g) is the watermark extracted after subjecting the watermarked image shown in Figure 3 (b) to attacks such as JPEG compression (70), JPEG 2000 compression (4:1), salt-and-pepper noise (0.2%), median filtering (3×3), low-pass filtering (100, 6), scaling (4:1), and cropping (12.5%) in sequence. The normalized cross-correlation coefficient NC values are 0.9999, 0.9995, 0.9759, 0.9890, 0.9886, 1.0000, and 0.9384 respectively.

[0070] This algorithm has been run nearly ten thousand times on a platform with 1.00GHz, 1.19GHz CPU, 16.00GB RAM, Win10, and MATLAB (R2017a). The average embedding time of the digital watermark is 1.0409518 seconds, the average extraction time is 0.5527982 seconds, and the total time is 1.59375 seconds.

[0071] In summary, the watermarked image has a high PSNR value, indicating that this method has high watermark invisibility; the color image digital watermark extracted from various attacked images has good recognizability and high NC values, indicating that this method has strong robustness; at the same time, the Lorenz chaotic mapping scrambling method used in this algorithm is extremely sensitive to the initial value, and its key space is 10 48 above, far greater than 2 100 , having high security; therefore, this method meets the requirements of color image digital watermark copyright protection for high invisibility, strong robustness, and high security.

Claims

1. A blind watermarking method for color digital images based on Contourlet transform and Schur decomposition, characterized in that It is implemented through a specific watermark embedding process and watermark extraction process. The watermark embedding process is described as follows: Step 1: First, perform dimensionality reduction on a color watermark image W of size N×N to obtain three layered watermark images of red, green, and blue; then, perform Lorenz chaotic mapping based on the key on each layered watermark image to obtain three scrambled layered watermark images W i ; Convert each decimal pixel value in the layered watermark image W i into an 8-bit binary number, and sequentially concatenate them into a layered watermark bit sequence SW 2 with a length of 8N i , where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 2: First, perform dimensionality reduction on a color host image H of size M×M to obtain three layered host images H for red, green, and blue i , and for each layered host image H i perform a Contourlet transform to extract its low-frequency coefficient matrix B i ; then, divide its low-frequency coefficient matrix B i into non-overlapping coefficient blocks of size m×m, where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 3: Using the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select coefficient blocks csblock of size m×m from each layer of low-frequency coefficient matrix B i where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 4: According to formula (1), perform Schur decomposition on the coefficient block csblock to obtain the unitary matrix U and the upper triangular matrix V; [U, V]=schur(csblock) (1) Among them, the non-zero elements λ on the main diagonal of the upper triangular matrix V j are the j-th eigenvalue of the coefficient block csblock, where j = 1, 2, …, r, and r represents the rank of the coefficient block csblock. The elements on its main diagonal satisfy λ1 > λ2 > λ3 > … > λ r ; Step 5: Select the watermark bit w to be embedded from the hierarchical watermark bit sequence SW in sequence according to the order; use formula (2) to quantize the first main diagonal element λ1 in the upper triangular matrix V to embed the watermark bit w, and obtain the watermarked first main diagonal element λ1 i ; * ; Among them, round(.) is the rounding function, xor(.) is the exclusive or function, mod(.) is the remainder function, and QT is the selected quantization step size; Step 6: Use the first main diagonal element λ1 with the watermark * to replace the first main diagonal element λ1 in the original upper triangular matrix V, obtaining the upper triangular matrix V with the watermark * ; perform inverse Schur decomposition using formula (3) to obtain the low-frequency coefficient block csblock with the watermark * ; csblock * = U × V * × U T (3) Step 7: The watermark-containing low-frequency coefficient block csblock * is updated to its corresponding position in the hierarchical low-frequency coefficient matrix B i where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 8: Repeat Steps 3 to 7 of this process until all the watermark information is embedded, and thus obtain the watermarked hierarchical low-frequency coefficient matrix B i * ; then, perform the inverse Contourlet transform on the watermarked hierarchical low-frequency coefficient matrix B i * to obtain the watermarked hierarchical host image H i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 9: Combine the three-layer watermarked hierarchical host images H i * to obtain the watermarked image H * , where i = 1, 2, 3 represent the red, green, and blue layers respectively; The watermark extraction process is described as follows: Step 1: First, the watermarked image H is subjected to dimensionality reduction processing * to be divided into three watermarked layer images H for red, green, and blue i * ; meanwhile, for each watermarked layer image H i * Contourlet transform is performed to extract its low-frequency coefficient matrix B i * ; then, the low-frequency coefficient matrix B i * is divided into non-overlapping coefficient blocks of size m×m, where i = 1, 2, 3 represent the red, green, and blue layers respectively; Step 2: Use the MD5 hash pseudo-random block selection algorithm based on the key Kd i to select the watermark-containing coefficient block csblock from the watermark-containing low-frequency coefficient matrix B i * , where i = 1, 2, 3 represent the red, green, and blue layers respectively; * ​ Step 3: Using formula (4), perform Schur decomposition on the watermark-containing coefficient block csblock * to obtain a unitary matrix U and an upper triangular matrix V * ; [U,V * = schur(csblock * )(4) Among them, the upper triangular matrix V * The non-zero elements λ on the main diagonal j * Are the coefficient block csblock * The j-th eigenvalue, j = 1, 2, …, r, where r represents the coefficient block csblock * The rank of, and the elements on its main diagonal satisfy λ1 * > λ2 * > λ3 * > … > λ r * ; Step 4: Use the upper triangular matrix V * The first main diagonal element λ1 * , according to formula (5), extract the watermark bit w * from the watermarked coefficient block csblock * ; Among them, fix(.) is the rounding function towards zero, mod(.) is the remainder function, and QT is the selected quantization step size; Step 5: Repeat the second and fourth steps of this process to obtain the extracted binary hierarchical watermark bit sequence SW i * ; then, successively divide every 8-bit binary information in SW i * into a group and convert it into a decimal pixel value to form a hierarchical scrambled watermark image; then, perform an inverse Lorenz chaotic mapping based on the key on the hierarchical scrambled watermark image to finally obtain the extracted hierarchical watermark image W i * , where i = 1, 2, 3 respectively represent the red, green, and blue layers; Step 6: Combine the extracted hierarchical watermark images W i * to form the final extracted watermark image W * , where i = 1, 2, 3 represent the red, green, and blue layers respectively.

Images