增强奇异值分解的自适应零水印
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摘要
目的针对增强奇异值分解(BN-SVD)中引入最抗攻击缩放比例的参数β,需要进行大量的实验来获取且存在随机性的问题,提出一种增强奇异值分解的自适应零水印算法。方法首先对原始图像进行不重叠分块,每一个子块都做斜变换处理,再分别对斜变换后得到的每一个块矩阵进行增强奇异值分解,依据每一个块矩阵的最大奇异值与整体最大奇异值均值的大小关系构成特征向量;对水印图像进行Arnold变换和混沌映射得到二次加密的水印图像;最后利用特征向量与二次加密后的水印图像做异或运算构造零水印;利用天牛须优化算法(BAS)中的适应度函数循环迭代自适应确定参数β,更好地解决奇异值分解(SVD)算法在水印的提取时存在的虚警率和对角线失真的问题。结果仿真实验结果表明,在JPEG压缩、噪声、滤波、旋转、剪切以及混合攻击下,提取水印图像与原水印图像的归一化系数NC值均可达到98%以上,性能较好。结论利用BAS算法自适应地确定BN-SVD中参数β,找到最佳抗攻击缩放比例,增强了图像的奇异值,降低了图像矩阵在受到攻击时的敏感性。有效地解决奇异值分解带来的对角线失真和虚警错误的问题,最终提高了算法的鲁棒性。
Objective Parameter β is the most commonly used anti-attack scaling ratio in boost normed singular value decomposition( BN-SVD). However,it requires numerous experiments to obtain and has randomness. Thus,an adaptive zero-watermarking algorithm based on BN-SVD was proposed. Using this parameter presents three advantages. First,the singular value of the image is enlarged,the sensitivity of the image to attacks is reduced,and the robustness of the algorithm is improved to some extent. Second,singular values are limited to a certain range. The diagonal distortion problem can be solved by equalizing the grayscale in the diagonal direction. Third,a singular value vector is specialized,and the corresponding relation between a singular value vector and an image is specialized to one,such that singular values can represent the features of the image. Thus,the problem of false alarm error is solved. Method First,the original image was divided into non-overlapping blocks. Then,slant transform( ST) was performed on each block matrix. BN-SVD was used on each block matrix after ST to achieve a maximum singular value,and a feature vector was created by comparing the maximum singular value with the average maximum singular value. The watermarked image was processed by Arnold transfor-mation and logistic mapping to obtain an encrypted and scrambled double-encrypted watermarked image. Finally,the zero watermark was constructed using the feature vector,and the double-encrypted watermarked image was used for XOR operation. During optimization,parameter β was determined by training and updating continuously through the BAS fitness function. Similar to genetic algorithm,particle swarm optimization,and so on,the proposed algorithm does not need to know the specific function form and gradient information. The optimization process can be realized independently,and its characteristics were single individual,less computation,and faster optimization speed. The algorithm was inspired by beetle search behavior. The biological principle is as follows: the beetle relies on the strength of the food smell to find food. Two antennae were randomly used to search nearby areas. When the antennae on one side detected a higher concentration of odors,the beetles turn in that direction. According to this simple principle,the beetle can effectively find food. Results Under JPEG compression,rotation,filtering,clipping,and other attacks,the normalized coefficients of the extracted watermarked images and the original watermarked exceeded 98%. Lena,Baboon,and Bridge were selected as the original grayscale image,and two different sizes of "Liaoning Technical University"were chosen as binary watermarking images.Several sets of experiments were conducted. In the experiment,a normalized correlation coefficient( NC) was used to analyze the similarity between the original watermark and the extracted watermark,and the optimal parameters β for the 16 × 16 pixels and 32 × 32 pixels watermarked images were found by the BAS optimization algorithm. The optimum parameter β values of the three gray images of Lena,Baboon,and Bridge were 0. 298 3,0. 642 4,and 0. 533 2 for the 16 × 16 pixels watermarked images and 0. 737 0,0. 991 4,and 0. 873 5 for the 32 × 32 pixels watermarked images. The experimental results revealed that with the increase in attack intensity and mixed attacks,the NC value of the watermark is affected. However,most NC values exceeded 0. 99. The NC value of the watermark extracted after geometric attacks,such as clipping and rotation,was close to 1. Given that the original gray image was rotated,and some pixels were lost in the clipping process,the watermark generated was incomplete. A larger compression attack parameter corresponded to a larger NC value,indicating that the algorithm had better resistance to JPEG compression. For all kinds of noise attacks,the NC value of the extracted watermark can exceed 0. 99. Conclusion BAS algorithm can be used to adaptively determine parameters β in BN-SVD. The optimal scale of scaling enhanced the singular value of the image and reduced the sensitivity of the image matrix when attacked. The problems of diagonal distortion and false alarm error caused by singular value decomposition were solved effectively,and the robustness of the watermarking algorithm was improved. Compared with other traditional optimization algorithms,the BAS algorithm presented the advantages of short training time,fast convergence speed,and good robustness.By integrating the concept of zero watermark,the contradiction between robustness and invisibility of the watermark is solved. Thus,the robustness of the watermarking algorithm was improved.
Objective Parameter β is the most commonly used anti-attack scaling ratio in boost normed singular value decomposition( BN-SVD). However,it requires numerous experiments to obtain and has randomness. Thus,an adaptive zero-watermarking algorithm based on BN-SVD was proposed. Using this parameter presents three advantages. First,the singular value of the image is enlarged,the sensitivity of the image to attacks is reduced,and the robustness of the algorithm is improved to some extent. Second,singular values are limited to a certain range. The diagonal distortion problem can be solved by equalizing the grayscale in the diagonal direction. Third,a singular value vector is specialized,and the corresponding relation between a singular value vector and an image is specialized to one,such that singular values can represent the features of the image. Thus,the problem of false alarm error is solved. Method First,the original image was divided into non-overlapping blocks. Then,slant transform( ST) was performed on each block matrix. BN-SVD was used on each block matrix after ST to achieve a maximum singular value,and a feature vector was created by comparing the maximum singular value with the average maximum singular value. The watermarked image was processed by Arnold transfor-mation and logistic mapping to obtain an encrypted and scrambled double-encrypted watermarked image. Finally,the zero watermark was constructed using the feature vector,and the double-encrypted watermarked image was used for XOR operation. During optimization,parameter β was determined by training and updating continuously through the BAS fitness function. Similar to genetic algorithm,particle swarm optimization,and so on,the proposed algorithm does not need to know the specific function form and gradient information. The optimization process can be realized independently,and its characteristics were single individual,less computation,and faster optimization speed. The algorithm was inspired by beetle search behavior. The biological principle is as follows: the beetle relies on the strength of the food smell to find food. Two antennae were randomly used to search nearby areas. When the antennae on one side detected a higher concentration of odors,the beetles turn in that direction. According to this simple principle,the beetle can effectively find food. Results Under JPEG compression,rotation,filtering,clipping,and other attacks,the normalized coefficients of the extracted watermarked images and the original watermarked exceeded 98%. Lena,Baboon,and Bridge were selected as the original grayscale image,and two different sizes of "Liaoning Technical University"were chosen as binary watermarking images.Several sets of experiments were conducted. In the experiment,a normalized correlation coefficient( NC) was used to analyze the similarity between the original watermark and the extracted watermark,and the optimal parameters β for the 16 × 16 pixels and 32 × 32 pixels watermarked images were found by the BAS optimization algorithm. The optimum parameter β values of the three gray images of Lena,Baboon,and Bridge were 0. 298 3,0. 642 4,and 0. 533 2 for the 16 × 16 pixels watermarked images and 0. 737 0,0. 991 4,and 0. 873 5 for the 32 × 32 pixels watermarked images. The experimental results revealed that with the increase in attack intensity and mixed attacks,the NC value of the watermark is affected. However,most NC values exceeded 0. 99. The NC value of the watermark extracted after geometric attacks,such as clipping and rotation,was close to 1. Given that the original gray image was rotated,and some pixels were lost in the clipping process,the watermark generated was incomplete. A larger compression attack parameter corresponded to a larger NC value,indicating that the algorithm had better resistance to JPEG compression. For all kinds of noise attacks,the NC value of the extracted watermark can exceed 0. 99. Conclusion BAS algorithm can be used to adaptively determine parameters β in BN-SVD. The optimal scale of scaling enhanced the singular value of the image and reduced the sensitivity of the image matrix when attacked. The problems of diagonal distortion and false alarm error caused by singular value decomposition were solved effectively,and the robustness of the watermarking algorithm was improved. Compared with other traditional optimization algorithms,the BAS algorithm presented the advantages of short training time,fast convergence speed,and good robustness.By integrating the concept of zero watermark,the contradiction between robustness and invisibility of the watermark is solved. Thus,the robustness of the watermarking algorithm was improved.
引文
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[14]Bao R,Zhang T Q,Tan F Q,et al.Semi-fragile watermark algorithm of color image based on slant transform[J].Computer Engineering,2012,38(5):122-125.[包锐,张天骐,谭方青,等.基于斜变换的半脆弱彩色图像水印算法[J].计算机工程,2012,38(5):122-125.][DOI:10.3969/j.issn.1000-3428.2012.05.037]
[15]Jiang X Y,Li S.BAS:beetle antennae search algorithm for optimization problems[EB/OL].[2018-06-25].https://arxiv.org/abs/1710.10724.
[16]Jiang X Y,Li S.Beetle antennae search without parameter tuning(BAS-WPT)for multi-objective optimization[EB/OL].[2018-06-25].https://arxiv.org/abs/1811.02395.
[17]Zhu Z Y,Zhang Z Y,Man W S,et al.A new beetle antennae search algorithm for multi-objective energy management in microgrid[C]//Proceedings of the 13th IEEE Conference on Industrial Electronics and Applications.Wuhan,China:IEEE,2018:1599-1603.[DOI:10.1109/ICIEA.2018.8397965]
[18]Xu Y,Zhang S W.Encryption algorithm of image blocking and double adaptive diffusion with Arnold mapping[J].Journal of Image and Graphics,2015,20(6):740-748.[徐亚,张绍武.基于Arnold映射的分块双层自适应扩散图像加密算法[J].中国图象图形学报,2015,20(6):740-748.][DOI:10.11834/jig.20150602]
[19]Dhoka M S,Patki A.Robust and dynamic image zero watermarking using hessian laplace detector and logistic map[C]//Proceedings of 2015 IEEE International Advance Computing Conference.Banglore,India:IEEE,2015:930-935.[DOI:10.1109/IADCC.2015.7154841]
[20]Fan Y J,Sun X H,Yan X D,et al.An image-scrambling a lgorithm Based on mixed chaotic sequences[J].Journal of Image and Graphics,2006,11(3):387-393.[范延军,孙燮华,阎晓东,等.一种基于混合混沌序列的图像置乱加密算法[J].中国图象图形学报,2006,11(3):387-393.][DOI:10.11834/jig.20060363]
[21]Liu L,Zhou Y J,Zhang B,et al.Digital watermarking method for QR code images based on DCT and SVD[J].Infrared and Laser Engineering,2013,42(S2):304-311.[刘丽,周亚建,张斌,等.基于DCT和SVD的QR码数字水印算法[J].红外与继光工程,2013,42(S2):304-311.][DOI:10.3969/j.issn.1007-2276.2013.z2.005]
[2]Ye T Y.Perfectly blind self-embedding robust quantization-based watermarking scheme in DWT-SVD domain[J].Journal of Image and Graphics,2012,17(6):644-650.[叶天语.DWT-SVD域全盲自嵌入鲁棒量化水印算法[J].中国图象图形学报,2012,17(6):644-650.][DOI:10.11834/jig.20120605]
[3]Zhu X,Ho A T S.A slant transform watermarking for copyright protection of satellite images[C]//Proceedings of the 4th International Conference on Information,Communications and Signal Processing,2003 and the Fourth Pacific Rim Conference on Multimedia.Singapore:IEEE,2003:1178-1181.[DOI:10.1109/ICICS.2003.1292646]
[4]Sikder I,Dhar P K,Shimamura T.A semi-fragile watermarking method using slant transform and LU decomposition for image authentication[C]//Proceedings of 2017 International Conference on Electrical,Computer and Communication Engineering.Cox's Bazar,Bangladesh:IEEE,2017:881-885.[DOI:10.1109/ECACE.2017.7913027]
[5]Xiao Z J,Li N,Wang Y B,et al.Strong robust digital watermark algorithm based on contourlet singular value decomposition[J].Computer Engineering,2016,42(9):138-143.[肖振久,李南,王永滨,等.基于Contourlet奇异值分解的强鲁棒数字水印算法[J].计算机工程,2016,42(9):138-143.][DOI:10.3969/j.issn.1000-3428.2016.09.025]
[6]Chen L,Ma X H.Blind watermarking algorithm based on DWTand SVD[J].Software Guide,2014,13(1):51-53.[陈璐,马小虎.基于离散小波变换和奇异值分解的盲水印算法[J].软件导刊,2014,13(1):51-53.]
[7]Xiao Z J,Sun J,Wang Y B,et al.Wavelet domain digital watermarking method based on fruit fly optimization algorithm[J].Journal of Computer Applications,2015,35(9):2527-2530.[肖振久,孙健,王永滨,等.基于果蝇优化算法的小波域数字水印算法[J].计算机应用,2015,35(9):2527-2530.][DOI:10.11772/j.issn.1001-9081.2015.09.2527]
[8]Yang J C,Li S X,Li L.Singular value decomposition and bee colony optimization based robust image watermark algorithm[J].Control Engineering of China,2017,24(9):1935-1941.[杨俊成,李淑霞,李亮.基于奇异值分解与蜂群优化的鲁棒图像水印算法[J].控制工程,2017,24(9):1935-1941.][DOI:10.14107/j.cnki.kzgc.160376]
[9]Wen Q,Sun T F,Wang S X.Concept and application of zerowatermark[J].Acta Electronica Sinica,2003,31(2):214-216.[温泉,孙锬锋,王树勋.零水印的概念与应用[J].电子学报,2003,31(2):214-216.][DOI:10.3321/j.issn:0372-2112.2003.02.015]
[10]Qu C B,Wang D F.Robust zero watermarking algorithm based on bit plane theory and singular value decomposition[J].Journal of Computer Applications,2014,34(12):3462-3465,3506.[曲长波,王东峰.基于位平面理论和奇异值分解的鲁棒零水印算法[J].计算机应用,2014,34(12):3462-3465,3506.][DOI:10.11772/j.issn.1001-9081.2014.12.3462]
[11]Chen W Q,Li Q.A DWT-SVD based double-zero-watermarking algorithm[J].Computer Engineering&Science,2014,36(10):1991-1996.[陈伟琦,李倩.基于DWT-SVD的图像双零水印算法[J].计算机工程与科学,2014,36(10):1991-1996.][DOI:10.3969/j.issn.1007-130X.2014.10.024]
[12]Xiao Z J,Zhang H,Chen H,et al.Zero-watermarking based on boost normed singular value decomposition and cellular neural network[J].Journal of Image and Graphics,2017,22(3):288-296.[肖振久,张晗,陈虹,等.增强奇异值分解和细胞神经网络的零水印[J].中国图象图形学报,2017,22(3):288-296.][DOI:10.11834/jig.20170302]
[13]Rao Y R,Nagabhooshanam E.A novel image zero-watermarking scheme based on DWT-BN-SVD[C]//Proceeding of 2014 International Conference on Information Communication and Embedded Systems.Chennai,India:IEEE,2014:1-6.[10.1109/ICICES.2014.7034073]
[14]Bao R,Zhang T Q,Tan F Q,et al.Semi-fragile watermark algorithm of color image based on slant transform[J].Computer Engineering,2012,38(5):122-125.[包锐,张天骐,谭方青,等.基于斜变换的半脆弱彩色图像水印算法[J].计算机工程,2012,38(5):122-125.][DOI:10.3969/j.issn.1000-3428.2012.05.037]
[15]Jiang X Y,Li S.BAS:beetle antennae search algorithm for optimization problems[EB/OL].[2018-06-25].https://arxiv.org/abs/1710.10724.
[16]Jiang X Y,Li S.Beetle antennae search without parameter tuning(BAS-WPT)for multi-objective optimization[EB/OL].[2018-06-25].https://arxiv.org/abs/1811.02395.
[17]Zhu Z Y,Zhang Z Y,Man W S,et al.A new beetle antennae search algorithm for multi-objective energy management in microgrid[C]//Proceedings of the 13th IEEE Conference on Industrial Electronics and Applications.Wuhan,China:IEEE,2018:1599-1603.[DOI:10.1109/ICIEA.2018.8397965]
[18]Xu Y,Zhang S W.Encryption algorithm of image blocking and double adaptive diffusion with Arnold mapping[J].Journal of Image and Graphics,2015,20(6):740-748.[徐亚,张绍武.基于Arnold映射的分块双层自适应扩散图像加密算法[J].中国图象图形学报,2015,20(6):740-748.][DOI:10.11834/jig.20150602]
[19]Dhoka M S,Patki A.Robust and dynamic image zero watermarking using hessian laplace detector and logistic map[C]//Proceedings of 2015 IEEE International Advance Computing Conference.Banglore,India:IEEE,2015:930-935.[DOI:10.1109/IADCC.2015.7154841]
[20]Fan Y J,Sun X H,Yan X D,et al.An image-scrambling a lgorithm Based on mixed chaotic sequences[J].Journal of Image and Graphics,2006,11(3):387-393.[范延军,孙燮华,阎晓东,等.一种基于混合混沌序列的图像置乱加密算法[J].中国图象图形学报,2006,11(3):387-393.][DOI:10.11834/jig.20060363]
[21]Liu L,Zhou Y J,Zhang B,et al.Digital watermarking method for QR code images based on DCT and SVD[J].Infrared and Laser Engineering,2013,42(S2):304-311.[刘丽,周亚建,张斌,等.基于DCT和SVD的QR码数字水印算法[J].红外与继光工程,2013,42(S2):304-311.][DOI:10.3969/j.issn.1007-2276.2013.z2.005]