Color stereo image zero-watermark processing method based on eight-element matrix decomposition

Abstract

The invention discloses a color three-dimensional image zero-watermark processing method based on eight-element matrix factorization, which comprises the following steps of: firstly, cutting square invariant feature region images at the centers of left and right viewpoints of a three-dimensional image, and carrying out non-subsampled dual-tree complex wavelet transform on the invariant feature region images in different channels; averaging the four low-frequency sub-bands obtained by each channel image to obtain a low-frequency mean sub-band, then performing block scrambling on the low-frequency mean sub-band from each channel, selecting a part of sub-blocks to construct an octuple matrix, and performing real number field octuple singular value decomposition on the octuple matrix; obtaining a maximum singular value matrix and then binarizing the maximum singular value matrix to obtain a robust binary feature matrix; and finally, carrying out XOR on the binary watermark which is scrambled and encrypted by the four-wing chaotic system and the cyclic code and the robust binary feature matrix to obtain a zero-watermark image. Before watermark authentication, a KAZE matching algorithm is used to correct left and right viewpoints of a to-be-authenticated stereo image. The method has relatively high robustness on common non-geometric attacks and geometric attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to a color stereo image zero-watermark processing method based on octonion matrix decomposition. Background Art

[0002] With the continuous advancement of science and technology and the continuous improvement of people's living standards, traditional single-viewpoint images can no longer meet people's needs. Instead, they are being replaced by stereoscopic images that provide a stronger sense of presence and a more vivid experience. As the scope of application of stereoscopic images continues to expand, the risks of theft, tampering, and duplication are increasing. How to avoid these risks has become an urgent problem that needs to be solved. The widespread use of digital watermarking technology provides an effective means for protecting digital media copyrights. Traditional digital watermarking technology generally embeds watermark information in the carrier image. When copyright authentication is required, the watermark is extracted and ownership authentication is completed. Although this method can effectively protect image copyrights, the embedding process damages the carrier image, resulting in distortion of the carrier image. To address this problem, zero watermark technology has been proposed.

[0003] At present, the research on zero watermark algorithm for single-viewpoint images has been relatively mature. However, it is not completely applicable to stereoscopic images, because stereoscopic images are generally composed of left and right viewpoint images. If the traditional single-viewpoint image zero watermark algorithm is applied to the left and right viewpoint images of stereoscopic images respectively, it will not only increase the computational complexity of the algorithm, but also may lead to insufficient robustness of the algorithm due to not considering the correlation between the left and right viewpoint images. How to better utilize the correlation between the left and right viewpoints of stereoscopic images and design a more robust stereoscopic image zero watermark method has become a very critical issue. Summary of the Invention

[0004] The embodiment of the present invention provides a color stereo image zero watermark processing method based on octonion matrix decomposition, which can effectively resist various common image attacks and solve the technical problems of low robustness and poor anti-geometric attack performance of existing stereo image zero watermark methods.

[0005] The embodiment of the present invention provides a method for processing zero watermarks for color stereo images based on octonion matrix decomposition, comprising:

[0006] Embed zero watermark in the original color stereo image and extract zero watermark from the color stereo image to be authenticated;

[0007] The embedding of a zero watermark in the original color stereo image comprises:

[0008] The four-wing chaotic system and cyclic code are used to perform scrambling and encryption on the original binary watermark image W of size M×M, and the processed binary watermark image W of size P×M is obtained.g ;

[0009] In the original color binocular stereo image, the left and right viewpoints I L and I R Extract the invariant feature region image C L and C R , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri , where i = R, G, B;

[0010] The low frequency mean subband D Li and D Ri The non-overlapping blocks of size T×T are respectively performed, and then three scrambled sequences S1~S3 are generated using the 3D Duffing chaotic system, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li and D Ri Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li and E Ri ;

[0011] The low-frequency mean subband E after scrambling Li and E Ri Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) and F Ri (k), where i = R, G, B; k = 1, 2, ..., P × M, using F Li (k) and F Ri (k) Construct octonion matrix OC k ;

[0012] For the octonion matrix OC k Perform singular value decomposition of the real domain octonion to obtain the maximum singular value matrix SS of size P×M. Binarize SS by calculating the mean of SS to obtain the robust binary feature matrix J.

[0013] Combine the robust binary feature matrix J with the processed binary watermark image W g Perform an XOR operation to obtain a zero watermark image ZW, save ZW to the watermark database of a third-party registration agency, and save the control parameters and process parameters used in the binary zero watermark embedding process as keys;

[0014] The zero-watermark extraction of the color stereo image to be authenticated comprises:

[0015] The KAZE feature matching algorithm is used to treat the left and right viewpoints of the color binocular stereo image for authentication legitimacy. L * and I R * Perform geometric attack correction to obtain the corrected left and right viewpoint ICs L * and IC R * , after correction of left and right viewpoint IC L * and IC R * Extract the invariant feature region image C L * and C R * , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L * and C R * The low-frequency mean subband D corresponding to each color channel Li * and D Ri * , where i = R, G, B;

[0016] The low frequency mean subband D Li * and D Ri * The non-overlapping blocks of size T×T are respectively performed, and then three scrambled sequences S1~S3 are generated using the 3D Duffing chaotic system, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li * and D Ri * Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li * and E Ri * ;

[0017] The low-frequency mean subband E after scrambling Li * and E Ri * Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) * and F Ri (k) * , where i = R, G, B; k = 1, 2, ..., P × M, using F Li (k) * and FRi (k) * Construct octonion matrix OC k * ;

[0018] For the octonion matrix OC k * Perform singular value decomposition of real field octonion to obtain the maximum singular value matrix SS of size P×M * , by calculating the maximum singular value matrix SS * The mean of SS * After binarization, the robust binary feature matrix J is obtained * ;

[0019] Take out the zero watermark image ZW stored in the watermark database of the third-party registration agency and compare it with the robust binary feature matrix J * Perform XOR operation to obtain the binary watermark image W to be restored g * ;

[0020] The four-wing chaotic system and cyclic code are used to restore the binary watermark image W g * Perform decryption and descrambling operations to obtain the extracted binary watermark image W * , and finally according to W * The displayed content information is used to identify the color binocular stereo image I to be authenticated L * and I R * Copyright belongs to .

[0021] The present invention provides a zero-watermark processing method for color stereo images based on octonion matrix decomposition. This method uses a four-wing chaotic system and a 3D Duffing chaotic system to encrypt and scramble the original watermark and low-frequency mean subband, respectively, ensuring the security of the zero-watermark algorithm. Cyclic codes are also used to encode the scrambled watermark, improving the robustness of the zero-watermark algorithm. A non-subsampled dual-tree complex wavelet transform is used to obtain the low-frequency mean subband images of each channel of the left and right viewpoints of the color stereo image. A robust binary feature matrix is ​​constructed through real-domain octonion singular value decomposition for zero-watermark generation. This effectively utilizes the correlation between the left and right viewpoint channels of the color stereo image and ensures the robustness of the algorithm. Furthermore, before zero-watermark extraction, the KAZE feature matching algorithm is used to perform geometric attack correction on the color binocular stereo image to be authenticated. This ensures that the algorithm is robust against common non-geometric attacks such as noise, filtering, and compression, while also being highly resistant to geometric attacks such as translation and rotation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0023] Figure 1 This is a flow chart of an embedding method in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0024] Figure 2 This is a flow chart of an extraction method in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0025] Figure 3 (a) is a left viewpoint image of a color stereo image Art in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0026] Figure 3 (b) is a right viewpoint image of the color stereo image Art in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0027] Figure 4 (a) is a left viewpoint image of a color stereo image Teddy in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0028] Figure 4 (b) is a right viewpoint image of a color stereo image Teddy in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0029] Figure 5 Schematic diagram of an original binary watermark image in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0030] Figure 6 This is a table of BER values ​​of the color stereo images Art and Teddy under several non-geometrically symmetric attacks in a color stereo image zero-watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention;

[0031] Figure 7 This is a table of test BER values ​​of color stereo images Art and Teddy under several geometric symmetry attacks in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0033] Figure 1 1 is a flow chart of an embedding method in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention. Figure 2 The present invention provides a flow chart of an extraction method in a zero watermark processing method for color stereoscopic images based on octonion matrix decomposition. This embodiment is applicable to the case where zero watermark is used to protect the copyright of color stereoscopic images.

[0034] like Figure 1 As shown, the embedding method in the zero watermark processing method of a color stereo image based on octonion matrix decomposition provided in this embodiment specifically includes the following steps:

[0035] S110, using the four-wing chaotic system and cyclic code to perform scrambling and encryption processing on the original binary watermark image W of size M×M, to obtain a processed binary watermark image W of size P×M g .

[0036] Figure 5 Schematic diagram of an original binary watermark image in a method for zero-watermarking a color stereo image based on octonion matrix decomposition provided by an embodiment of the present invention, with a size of M × M. In this embodiment, the above-provided original binary watermark image can be used to implement binary watermark scrambling and encryption processing.

[0037] Exemplarily, the scrambling operation and encryption processing may be performed in the following manner:

[0038] The four-wing chaotic system is used to generate four chaotic sequences K1~K4 with a length of M×M, and then the sequence K is obtained by taking the modules of K1~K4 in pairs. e and K r , using sequence K e The original binary watermark image W of size M×M is scrambled to obtain the scrambled binary watermark sequence W2, and then the scrambled binary watermark sequence W2 is encoded using a cyclic code to obtain a coding matrix W of size P×M. e , and finally use sequence K r The encoding matrix W ePerform chaotic interleaving to obtain the processed watermark image W with a size of P×M g ,include:

[0039] The four-wing chaotic system is expressed by the following formula:

[0040]

[0041] Where x, y, z, and u are all system variables, sinh(z) is the hyperbolic sine function, a0 and b0 are control parameters, and x0, y0, z0, and u0 are the initial values ​​of the four-wing chaotic system. The above control parameters and system initial values, a total of 6 variables, are used together as the key Key1.

[0042] The four-wing chaotic system is used to generate four chaotic sequences K1 to K4 with a length of M×M, and then K1 to K4 are modulo two by two to obtain the sequence K e and K r , expressed using the following formula:

[0043]

[0044] Where K1~K4 are four chaotic sequences of length M×M generated by the four-wing chaotic system, K e (n) and K r (n) are the sequences K e and K r The nth position of

[0045] The use sequence K e Perform a scrambling operation on the original binary watermark image W of size M×M to obtain a scrambled binary watermark sequence W2, including:

[0046] The binary watermark image W is scanned into a one-dimensional vector W1 using Zigzag, and then the sequence K is used to e Perform a scrambling operation on the one-dimensional vector W1 to obtain a scrambled binary watermark sequence W2. This process is expressed by the following formula:

[0047]

[0048] In the formula, sort() is the ascending sort function, BK e K e The sequence obtained after ascending order, Index1 is the position index vector, W2(n) is the nth bit of the scrambled binary watermark sequence W2, and Index1(n) is the nth bit of Index1;

[0049] The scrambled binary watermark sequence W2 is encoded using a cyclic code to obtain a coding matrix W of size P×M e ,include:

[0050] The scrambled binary watermark sequence W2 is grouped into 4-bit groups, and each group of sequences is encoded according to the (7,4) cyclic code encoding rule. After encoding, the groups of sequences are connected in order to obtain a sequence W3 of length M×P, where P=M / 4×7. Finally, the sequence W3 is subjected to Zigzag inverse scanning to obtain a coding matrix W of size M×P. e ;

[0051] The use sequence K r The encoding matrix W e Perform chaotic interleaving to obtain the processed watermark image W with a size of P×M g ,include:

[0052] The encoding matrix W e After transposition, we get a binary matrix W of size P×M f , and K r Arrange in ascending order to obtain the position indication vector Index2. When 0≤n≤M, the binary matrix W is sorted according to Index2. f Perform chaotic interleaving operation to obtain the processed binary watermark image W g , this process can be expressed by the following formula:

[0053]

[0054] Where BK r K r The sequence obtained after ascending order, Index2 is the position index vector, Index2(n) and Index2(n+1) are the nth and n+1th positions of Index2 respectively, W f (:,n) and W g (:,n) are binary matrices W f And the processed watermark image W g The nth column of By W f (:,n) Arrange the resulting column vector in reverse order.

[0055] S120, in the original color binocular stereo image left and right viewpoints I L and I R Extract the invariant feature region image C L and C R , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri .

[0056] For example, the low frequency mean subband D is obtained Liand D Ri You can use the following methods:

[0057] The left and right viewpoints I of the original color binocular stereo image L and I R Extract the invariant feature region image C L and C R ,include:

[0058] In the original color binocular stereo image, the left and right viewpoints I L and I R Draw inscribed circles in the left and right viewpoints to obtain the inscribed circle images B L and B R , then inscribe the circle image B in the left and right viewpoints L and B R Make inscribed squares in the image and get the square invariant feature region image C with the size of Q×Q L and C R ;

[0059] The non-subsampled dual-tree complex wavelet transform is used to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri , where i = R, G, B, including:

[0060] The invariant feature region image C L and C R Perform l-level non-subsampled dual-tree complex wavelet transform on each channel, and obtain 4 low-frequency subbands for each channel, which are respectively recorded as low-frequency subbands L Lij and L Rij , where i = R, G, B, j = 1, 2, 3, 4;

[0061] The low frequency sub-band L Lij and L Rij Take the average value to get the low frequency mean subband D Li and D Ri , where i = R, G, B. This process is expressed by the following formula:

[0062]

[0063] S130, the low frequency mean subband D Li and D Ri The system is divided into non-overlapping blocks of size T×T, and then the 3DDuffing chaotic system is used to generate three scrambled sequences S1~S3, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li and D RiPerform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li and E Ri .

[0064] Exemplarily, obtain the scrambled low-frequency mean subband E Li and E Ri You can use the following methods:

[0065] A 3D Duffing chaotic system is used to generate three waves with length (Q / T) 2 The scrambled sequence S1~S3 is then sorted in ascending order to obtain the position indication vector Idx i , i=R,G,B, the low frequency mean subband D Li and D Ri Perform non-overlapping blocks of size T×T respectively, and each sub-block is represented by D Li (p) and D Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , using the position indicator vector Idx i Scramble the sub-blocks to get the scrambled sub-block E Li (p) and E Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , after synthesizing the scrambled sub-blocks, we can get the scrambled low-frequency mean sub-band E Li and E Ri ,include:

[0066] The 3D Duffing chaotic system is expressed by the following formula:

[0067]

[0068] Where x t ,y t ,z t are all system variables, a1, b1, c1 are all control parameters, x0, y0, z0 are the initial values ​​of the system, x t+1 ,y t+1 ,z t+1 is x t ,y t ,z t The value of the next state is recorded as the key Key2, which is composed of the above control parameters and the system initial value.

[0069] The scrambled sequences S1 to S3 are arranged in ascending order to obtain the position indication vector Idx i , i=R,G,B, this process is expressed by the following formula:

[0070]

[0071] Where BS1~BS3 are the sequences obtained by arranging the scrambled sequences S1~S3 in ascending order, Idx i is the position indicator vector;

[0072] The use position indication vector Idx i Scramble the sub-blocks to get the scrambled sub-block E Li (p) and E Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , after synthesizing the scrambled sub-blocks, we get the scrambled low-frequency sub-band E Li and E Ri , this process can be expressed as follows:

[0073]

[0074] Where Idx i (p) is the indicator vector Idx i The pth bit, E Li (p) and E Ri (p) are the low-frequency mean subband E after scrambling Li and E Ri The p-th sub-block of .

[0075] S140, the low frequency mean subband E after scrambling Li and E Ri Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) and F Ri (k), and use F Li (k) and F Ri (k) Construct octonion matrix OC k .

[0076] For example, get the octonion matrix OC k You can use the following methods:

[0077] The use of F Li (k) and F Ri (k) Construct octonion matrix OC k , expressed using the following formula:

[0078] OC k =F LR (k)e1+F LG (k)e2+F LB (k)e3+F RR (k)e4+F RG (k)e5+FRB (k)e6

[0079] Where e1~e6 are unit octonion matrices, F LR (k),F LG (k),F LB (k) are the sub-block matrices of the three channels R, G, and B from the left viewpoint of the stereo image, respectively, and F RR (k),F RG (k),F RB (k) are the sub-block matrices of the R, G, and B channels from the right viewpoint of the stereo image.

[0080] S150, octonion matrix OC k Perform singular value decomposition of the real domain octonion to obtain the maximum singular value matrix SS of size P×M. After binarizing SS by calculating the mean of SS, the robust binary feature matrix J is obtained.

[0081] Exemplarily, the robust binary feature matrix J can be obtained in the following manner:

[0082] The octonion matrix OC k Perform singular value decomposition of real-domain octonions to obtain the maximum singular value matrix SS of size P×M, including:

[0083] The octonion matrix OC k Combine the imaginary components of to obtain the real representation matrix OC k R , this process is expressed by the following formula:

[0084]

[0085] Where Z is a zero matrix of size U×U, F LR (k),F LG (k),F LB (k) are the sub-block matrices of the three channels R, G, and B from the left viewpoint of the stereo image, respectively, and F RR (k),F RG (k),F RB (k) are the sub-block matrices of the R, G, and B channels from the right viewpoint of the stereo image;

[0086] Let the real matrix OC k R Perform singular value decomposition and obtain the maximum singular value sequence S m (k), this process is expressed by the following formula:

[0087]

[0088] Where svd() is the singular value decomposition function, OUk is the left singular vector matrix, OS k is the singular value diagonal matrix, OV k is the right singular vector matrix, OS k [1,1] is OS k The element in the first row and first column of the matrix;

[0089] The maximum singular value sequence S m (k) Use Zigzag inverse scan to obtain the P×M maximum singular value matrix SS;

[0090] The robust binary feature matrix J is obtained by calculating the mean of SS and binarizing SS, which is expressed by the following formula:

[0091]

[0092] Where mean2() is the matrix mean function, J(q,s) and SS(q,s) represent the qth row and sth column element of the maximum singular value matrix SS and the robust binary feature matrix J, respectively.

[0093] S160, the robust binary feature matrix J is combined with the processed binary watermark image W g Perform an XOR operation to obtain a zero watermark image ZW, save ZW to the watermark database of a third-party registration agency, and save the control parameters and process parameters used in the binary zero watermark embedding process as keys.

[0094] Through the above steps, the zero watermark image ZW and the related keys Key1 and Key2 in the zero watermark embedding process are obtained, which are used by the final watermark extraction end to identify the copyright ownership of the color binocular stereo image to be authenticated.

[0095] In addition, this embodiment also provides an extraction method in a color stereo image zero watermark processing method based on octonion matrix decomposition, such as Figure 2 As shown, the specific steps include:

[0096] S210, using KAZE feature matching algorithm to authenticate the validity of the color binocular stereo image left and right viewpoints I L * and I R * Perform geometric attack correction to obtain the corrected left and right viewpoint ICs L * and IC R * , after correction of left and right viewpoint IC L * and IC R * Extract the invariant feature image CL * and C R * , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L * and C R * The low-frequency mean subband D corresponding to each color channel Li * and D Ri * .

[0097] S220, the low frequency mean subband D Li * and D Ri * The system is divided into non-overlapping blocks of size T×T, and then the 3DDuffing chaotic system is used to generate three scrambled sequences S1~S3, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li * and D Ri * Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li * and E Ri * .

[0098] S230, the low frequency mean subband E after scrambling Li * and E Ri * Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) * and F Ri (k) * , and use F Li (k) * and F Ri (k) * Construct octonion matrix OC k * ;

[0099] S240, octonion matrix OC k * Perform singular value decomposition of real field octonion to obtain the maximum singular value matrix SS of size P×M * , by calculating the maximum singular value matrix SS * The mean of SS * After binarization, the robust binary feature matrix J is obtained * .

[0100] S250, take out the zero watermark image ZW stored in the watermark database of the third-party registration agency, and compare it with the robust binary image feature matrix J * Perform XOR operation to obtain the binary watermark image W to be restored g * .

[0101] S260, using four-wing chaotic system and cyclic code to restore the binary watermark image W g * Perform decryption and descrambling operations to obtain the extracted binary watermark image W * , and finally according to W * The displayed content information is used to identify the color binocular stereo image I to be authenticated L * and I R * Copyright belongs to .

[0102] Exemplarily, the decryption and descrambling operations may be performed as follows:

[0103] Using the key Key1, a four-wing chaotic system is used to generate four chaotic sequences K1 to K4 of length M×M, and then K1 to K4 are modulo each other to obtain the sequence K e and K r , using sequence K r The binary watermark image W to be restored g * Perform chaotic deinterleaving to obtain the matrix to be decoded W e * , treat the decoding matrix W according to the (7,4) cyclic code decoding rule e * Perform cyclic code decoding to obtain the binary watermark sequence W2 to be decrypted * , using sequence K e To be decrypted binary watermark sequence W2 * After decryption, the extracted binary watermark image W is obtained * ,include:

[0104] The use sequence K r The binary watermark image W to be restored g * Perform chaotic deinterleaving to obtain the matrix to be decoded W e * , this process is expressed by the following formula:

[0105]

[0106] Where W f * (:,n) and W g* (:,n) are binary matrices W f * and the binary watermark image W to be restored g * The nth column of By W g * (:,n) Arrange the resulting column vector in reverse order, W f *T is a binary matrix W f * The transposed matrix of

[0107] The decoding matrix W is treated according to the (7,4) cyclic code decoding rule. e * Perform cyclic code decoding to obtain the binary watermark sequence W2 to be decrypted * include:

[0108] The matrix to be decoded W e * After Zigzag scanning, the watermark sequence W3 is obtained * , the watermark sequence W3 * Group them into 7 bits each, and decode each group of sequences according to the (7,4) cyclic code decoding rule. After decoding, connect each group of sequences in order to obtain the binary watermark sequence W2 to be decrypted. * ;

[0109] The use sequence K e To be decrypted binary watermark sequence W2 * After decryption, the extracted binary watermark image W is obtained * include:

[0110] Use sequence K e The position index vector Index1 obtained by ascending order is used to decrypt the binary watermark sequence W2 * Decrypt to get the watermark sequence W1 * , this process is expressed by the following formula:

[0111] W1 * (n) = W2 * (Index1(n))

[0112] Where W1 * (n) is the watermark sequence W1 * , Index1(n) is the nth bit of Index1;

[0113] The watermark sequence W1 * The extracted binary watermark image W is obtained by Zigzag inverse scanning into a square matrix * .

[0114] This embodiment provides a zero-watermark processing method for color stereo images based on octonion matrix decomposition. The four-wing chaotic system and the 3D Duffing chaotic system are used to ensure the security of the zero-watermark algorithm. At the same time, the scrambled watermark is encoded using cyclic codes to improve the robustness of the zero-watermark algorithm. The low-frequency mean subband image of each channel of the left and right viewpoints of the color stereo image is obtained by non-subsampled dual-tree complex wavelet transform, and a robust binary feature matrix is ​​constructed by real-domain octonion singular value decomposition for zero-watermark generation. This effectively utilizes the correlation between the channels of the left and right viewpoints of the color stereo image and ensures the robustness of the algorithm. In addition, before the zero-watermark is extracted, the KAZE feature matching algorithm is used to perform geometric attack correction on the color binocular stereo image to be authenticated for legitimacy, ensuring that the algorithm has good resistance to both common non-geometric attacks and geometric attacks.

[0115] The process and effect of the zero-watermark processing method for color stereoscopic images based on octonion matrix decomposition provided by the present invention are described in detail below with reference to specific examples.

[0116] In order to verify the effectiveness of the present invention, the standard color stereo images of the Middlebury database are used in the simulation experiment. Figure 3 、 Figure 4 The two sets of color stereo images of Art and Teddy in the database are shown, both of which are 512×512 in size. The original binary watermark image uses a CAUC image of size 64×64, as shown in Figure 5 shown.

[0117] The present invention uses the bit error rate (BER) to evaluate the extracted binary watermark image W * The degree of similarity between the original binary watermark image W and the original binary watermark image W, BER is defined as follows:

[0118]

[0119] Among them, M 2 is the size of the original binary watermark image, W(i,j) represents the pixel value of the original watermark image at point (i,j), W * (i, j) represents the extracted binary watermark image W * The pixel value at point (i, j). The lower the BER value, the better the extracted binary watermark image W * The more similar it is to the original binary watermark image W, the more robust the method is.

[0120] Figure 6This is a table of BER values ​​of the color stereo images Art and Teddy under several symmetric non-geometric attacks in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention. Figure 6 It can be seen that when Art and Teddy images are subjected to different types of noise, filtering and compression attacks, the maximum BER value calculated by extracting the watermark is 0.0059, indicating that this method has good resistance to non-geometric attacks and is extremely robust.

[0121] Figure 7 This is a table of test BER values ​​of color images Art and Teddy under several symmetric geometric attacks in a color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention. Figure 7 It can be seen that for different color stereo images, the color stereo image zero watermark method provided by this embodiment shows excellent robustness against common geometric attacks, which further illustrates the robustness and universality of the color stereo image zero watermark processing method based on octonion matrix decomposition provided by an embodiment of the present invention in resisting several geometric attacks.

[0122] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A color stereo image zero watermark processing method based on octonion matrix decomposition, characterized in that: include: Embed zero watermark in the original color stereo image and extract zero watermark from the color stereo image to be authenticated; The embedding of a zero watermark in the original color stereo image comprises: The four-wing chaotic system and cyclic code are used to perform scrambling and encryption on the original binary watermark image W of size M×M, and the processed binary watermark image W of size P×M is obtained. g ; In the original color binocular stereo image, the left and right viewpoints I L and I R Extract the invariant feature region image C L and C R , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri , where i = R, G, B; The low frequency mean subband D Li and D Ri The non-overlapping blocks of size T×T are respectively performed, and then three scrambled sequences S1~S3 are generated using the 3D Duffing chaotic system, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li and D Ri Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li and E Ri ; The low-frequency mean subband E after scrambling Li and E Ri Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) and F Ri (k), where i = R, G, B; k = 1, 2, ..., P × M, using F Li (k) and F Ri (k) Construct octonion matrix OC k ; For the octonion matrix OC k Perform singular value decomposition of the real domain octonion to obtain the maximum singular value matrix SS of size P×M. Binarize SS by calculating the mean of SS to obtain the robust binary feature matrix J. Combine the robust binary feature matrix J with the processed binary watermark image W g Perform an XOR operation to obtain a zero watermark image ZW, save ZW to the watermark database of a third-party registration agency, and save the control parameters and process parameters used in the binary zero watermark embedding process as keys; The zero-watermark extraction of the color stereo image to be authenticated comprises: The KAZE feature matching algorithm is used to treat the left and right viewpoints of the color binocular stereo image for authentication legitimacy. L * and I R * Perform geometric attack correction to obtain the corrected left and right viewpoint ICs L * and IC R * , after correction of left and right viewpoint IC L * and IC R * Extract the invariant feature region image C L * and C R * , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L * and C R * The low-frequency mean subband D corresponding to each color channel Li * and D Ri * , where i = R, G, B; The low frequency mean subband D Li * and D Ri * The non-overlapping blocks of size T×T are respectively performed, and then three scrambled sequences S1~S3 are generated using the 3D Duffing chaotic system, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li * and D Ri * Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li * and E Ri * ; The low-frequency mean subband E after scrambling Li * and E Ri * Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) * and F Ri (k) * , where i = R, G, B; k = 1, 2, ..., P × M, using F Li (k) * and F Ri (k) * Construct octonion matrix OC k * ; For the octonion matrix OC k * Perform singular value decomposition of real field octonion to obtain the maximum singular value matrix SS of size P×M * , by calculating the maximum singular value matrix SS * The mean of SS * After binarization, the robust binary feature matrix J is obtained * ; Take out the zero watermark image ZW stored in the watermark database of the third-party registration agency and compare it with the robust binary feature matrix J * Perform XOR operation to obtain the binary watermark image W to be restored g * ; The four-wing chaotic system and cyclic code are used to restore the binary watermark image W g * Perform decryption and descrambling operations to obtain the extracted binary watermark image W * , and finally according to W * The displayed content information is used to identify the color binocular stereo image I to be authenticated L * and I R * Copyright belongs to .

2. The method for processing zero watermark of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: The four-wing chaotic system and cyclic code are used to perform scrambling and encryption on the original binary watermark image W of size M×M, and the processed binary watermark image W of size P×M is obtained. g ,include: The four-wing chaotic system is used to generate four chaotic sequences K1~K4 with a length of M×M, and then the sequence K is obtained by taking the modules of K1~K4 in pairs. e and K r , using sequence K e The original binary watermark image W of size M×M is scrambled to obtain the scrambled binary watermark sequence W2, and then the scrambled binary watermark sequence W2 is encoded using a cyclic code to obtain a coding matrix W of size P×M. e , and finally use sequence K r The encoding matrix W e Perform chaotic interleaving to obtain the processed watermark image W g ,include: The four-wing chaotic system is expressed by the following formula: Where x, y, z, and u are all system variables, sinh(z) is the hyperbolic sine function, a0 and b0 are control parameters, and x0, y0, z0, and u0 are the initial values ​​of the four-wing chaotic system. The above control parameters and system initial values, a total of 6 variables, are used together as the key Key1. The four-wing chaotic system is used to generate four chaotic sequences K1 to K4 with a length of M×M, and then K1 to K4 are modulo two by two to obtain the sequence K e and K r , expressed using the following formula: Where K1~K4 are four chaotic sequences of length M×M generated by the four-wing chaotic system, K e (n) and K r (n) are the sequences K e and K r The nth position of The use sequence K e Perform a scrambling operation on the original binary watermark image W of size M×M to obtain a scrambled binary watermark sequence W2, including: The binary watermark image W is scanned into a one-dimensional vector W1 using Zigzag, and then the sequence K is used to e Perform a scrambling operation on the one-dimensional vector W1 to obtain a scrambled binary watermark sequence W2. This process is expressed by the following formula: In the formula, sort() is the ascending sort function, BK e K e The sequence obtained after ascending order, Index1 is the position index vector, W2(n) is the nth bit of the scrambled binary watermark sequence W2, and Index1(n) is the nth bit of Index1; The scrambled binary watermark sequence W2 is encoded using a cyclic code to obtain a coding matrix W of size P×M e ,include: The scrambled binary watermark sequence W2 is grouped into 4-bit groups, and each group of sequences is encoded according to the (7,4) cyclic code encoding rule. After encoding, the groups of sequences are connected in order to obtain a sequence W3 of length M×P, where P=M / 4×7. Finally, the sequence W3 is subjected to Zigzag inverse scanning to obtain a coding matrix W of size M×P. e ; The use sequence K r The encoding matrix W e Perform chaotic interleaving to obtain the processed watermark image W g ,include: The encoding matrix W e After transposition, we get a binary matrix W of size P×M f , and K r Arrange in ascending order to obtain the position indication vector Index2. When 0≤n≤M, the binary matrix W is sorted according to Index2. f Perform chaotic interleaving operation to obtain the processed binary watermark image W g , this process can be expressed by the following formula: Where BK r K r The sequence obtained after ascending order, Index2 is the position index vector, Index2(n) and Index2(n+1) are the nth and n+1th positions of Index2 respectively, W f (:,n) and W g (:,n) are binary matrices W f And the processed watermark image W g The nth column of By W f (:,n) Arrange the resulting column vector in reverse order.

3. The method for zero watermark processing of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: In the original color binocular stereo image, the left and right viewpoints I L and I R Extract the invariant feature region image C L and C R , and use non-subsampled dual-tree complex wavelet transform to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri , where i = R, G, B, including: The left and right viewpoints I of the original color binocular stereo image L and I R Extract the invariant feature region image C L and C R ,include: In the original color binocular stereo image, the left and right viewpoints I L and I R Draw inscribed circles in the left and right viewpoints to obtain the inscribed circle images B L and B R , then inscribe the circle image B in the left and right viewpoints L and B R Make inscribed squares in the image and get the square invariant feature region image C with the size of Q×Q L and C R ; The non-subsampled dual-tree complex wavelet transform is used to obtain the invariant feature area image C L and C R The low-frequency mean subband D corresponding to each color channel Li and D Ri , where i = R, G, B, including: The invariant feature region image C L and C R Perform l-level non-subsampled dual-tree complex wavelet transform on each channel, and obtain 4 low-frequency subbands for each channel, which are respectively recorded as low-frequency subbands L Lij and L Rij , where i = R, G, B, j = 1, 2, 3, 4; The low frequency sub-band L Lij and L Rij Take the average value to get the low frequency mean subband D Li and D Ri , where i = R, G, B. This process is expressed by the following formula:

4. The method for zero-watermark processing of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: The low frequency mean subband D Li and D Ri The system is divided into non-overlapping blocks of size T×T, and then the 3DDuffing chaotic system is used to generate three scrambled sequences S1~S3, and the scrambled sequences S1~S3 are used to scramble the low-frequency mean subband D Li and D Ri Perform block scrambling by channel to obtain the scrambled low-frequency mean subband E Li and E Ri ,include: A 3D Duffing chaotic system is used to generate three waves with length (Q / T) 2 The scrambled sequence S1~S3 is then sorted in ascending order to obtain the position indication vector Idx i , i=R,G,B, the low frequency mean subband D Li and D Ri Perform non-overlapping blocks of size T×T respectively, and each sub-block is represented by D Li (p) and D Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , using the position indicator vector Idx i Scramble the sub-blocks to get the scrambled sub-block E Li (p) and E Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , after synthesizing the scrambled sub-blocks, we can get the scrambled low-frequency mean sub-band E Li and E Ri ,include: The 3D Duffing chaotic system is expressed by the following formula: Where x t ,y t ,z t are all system variables, a1, b1, c1 are all control parameters, x0, y0, z0 are the initial values ​​of the system, x t+1 ,y t+1 ,z t+1 is x t ,y t ,z t The value of the next state is recorded as the key Key2, which is composed of the above control parameters and the system initial value. The scrambled sequences S1 to S3 are arranged in ascending order to obtain the position indication vector Idx i , i=R,G,B, this process is expressed by the following formula: Where BS1~BS3 are the sequences obtained by arranging the scrambled sequences S1~S3 in ascending order, Idx i is the position indicator vector; The use position indication vector Idx i Scramble the sub-blocks to get the scrambled sub-block E Li (p) and E Ri (p), where i = R, G, B, p = 1, 2, ..., (Q / T) 2 , after synthesizing the scrambled sub-blocks, we can get the scrambled low-frequency mean sub-band E Li and E Ri , this process can be expressed as follows: Where Idx i (p) is the indicator vector Idx i The pth bit, E Li (p) and E Ri (p) are the low-frequency mean subband E after scrambling Li and E Ri The p-th sub-block of .

5. The method for processing zero watermark of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: The low-frequency mean subband E after scrambling Li and E Ri Perform non-overlapping blocks of size U×U respectively, and then select the first P×M sub-blocks in each channel in order, which are recorded as F Li (k) and F Ri (k), where i = R, G, B; k = 1, 2, ..., P × M, using F Li (k) and F Ri (k) Construct octonion matrix OC k ,include: The use of F Li (k) and F Ri (k) Construct octonion matrix OC k , expressed using the following formula: OC k =F LR (k)e1+F LG (k)e2+F LB (k)e3+F RR (k)e4+F RG (k)e5+F RB (k)e6 Where e1~e6 are unit octonion matrices, F LR (k),F LG (k),F LB (k) are the sub-block matrices of the three channels R, G, and B from the left viewpoint of the stereo image, respectively, and F RR (k),F RG (k),F RB (k) are the sub-block matrices of the R, G, and B channels from the right viewpoint of the stereo image.

6. The method for processing zero watermark of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: For the octonion matrix OC k Perform singular value decomposition of the real field octonion to obtain the maximum singular value matrix SS of size P×M. After binarizing SS by calculating the mean of SS, the robust binary feature matrix J is obtained, including: The octonion matrix OC k Perform singular value decomposition of real-domain octonions to obtain the maximum singular value matrix SS of size P×M, including: The octonion matrix OC k Combine the imaginary components of to obtain the real representation matrix OC k R , this process is expressed by the following formula: Where Z is a zero matrix of size U×U, F LR (k),F LG (k),F LB (k) are the sub-block matrices of the three channels R, G, and B from the left viewpoint of the stereo image, respectively, and F RR (k),F RG (k),F RB (k) are the sub-block matrices of the R, G, and B channels from the right viewpoint of the stereo image; Let the real matrix OC k R Perform singular value decomposition and obtain the maximum singular value sequence S m (k), this process is expressed by the following formula: Where svd() is the singular value decomposition function, OU k is the left singular vector matrix, OS k is the singular value diagonal matrix, OV k is the right singular vector matrix, OS k [1,1] is OS k The element in the first row and first column of the matrix; The maximum singular value sequence S m (k) Use Zigzag inverse scan to obtain the P×M maximum singular value matrix SS; The robust binary feature matrix J is obtained by calculating the mean of SS and binarizing SS, which is expressed by the following formula: Where mean2() is the matrix mean function, J(q,s) and SS(q,s) represent the qth row and sth column element of the maximum singular value matrix SS and the robust binary feature matrix J, respectively.

7. The method for processing zero watermark of color stereo images based on octonion matrix decomposition according to claim 1, characterized in that: The four-wing chaotic system and cyclic code are used to restore the binary watermark image W g * Perform decryption and descrambling operations to obtain the extracted binary watermark image W * , and finally according to W * The displayed content information is used to identify the color binocular stereo image I to be authenticated L * and I R * The copyright of the Using the key Key1, a four-wing chaotic system is used to generate four chaotic sequences K1 to K4 of length M×M, and then K1 to K4 are modulo each other to obtain the sequence K e and K r , using sequence K r The binary watermark image W to be restored g * Perform chaotic deinterleaving to obtain the matrix to be decoded W e * , treat the decoding matrix W according to the (7,4) cyclic code decoding rule e * Perform cyclic code decoding to obtain the binary watermark sequence W2 to be decrypted * , using sequence K e To be decrypted binary watermark sequence W2 * After decryption, the extracted binary watermark image W is obtained * ,include: The use sequence K r The binary watermark image W to be restored g * Perform chaotic deinterleaving to obtain the matrix to be decoded W e * , this process is expressed by the following formula: In the formula and W g * (:,n) are binary matrices and the binary watermark image W to be restored g * The nth column of By W g * (:,n) Arrange the resulting column vector in reverse order, is a binary matrix The transposed matrix of The decoding matrix W is treated according to the (7,4) cyclic code decoding rule. e * Perform cyclic code decoding to obtain the binary watermark sequence W2 to be decrypted * include: The matrix to be decoded W e * After Zigzag scanning, the watermark sequence W3 is obtained * , the watermark sequence W3 * Group them into 7 bits each, and decode each group of sequences according to the (7,4) cyclic code decoding rule. After decoding, connect each group of sequences in order to obtain the binary watermark sequence W2 to be decrypted. * ; The use sequence K e To be decrypted binary watermark sequence W2 * After decryption, the extracted binary watermark image W is obtained * include: Use sequence K e The position index vector Index1 obtained by ascending order is used to decrypt the binary watermark sequence W2 * Decrypt to get the watermark sequence W1 * , this process is expressed by the following formula: W1 * (n)=W2 * (Index1(n)) Where W1 * (n) is the watermark sequence W1 * , Index1(n) is the nth bit of Index1; The watermark sequence W1 * The extracted binary watermark image W is obtained by Zigzag inverse scanning into a square matrix * .

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