基于有限脊波变换的图像哈希认证技术的研究
|
摘要
图像哈希在多媒体内容认证、数据库检索和数字水印中有着广泛的应用前景,近年来受到了高度的关注。传统的基于密码学的哈希在对图像进行压缩、过滤、几何变换等保持内容的操作时,对认证信息中每个比特的变化都非常敏感,并不适用于图像内容的认证。因此研究对内容保持操作稳健,又能够区分恶意篡改攻击的图像哈希具有重要的意义。
目前使用的数字图像哈希基本上是在变换域中进行的,尤其以基于小波变换的算法居多。但是小波一般只适合于表征零维点奇异性,而图像中广泛存在的一维奇异性影响着小波特征提取的效率,同时也难以生成理想的图像哈希。
有限脊波变换是在有限Radon变换域中沿每个方向作一维小波变换。它克服了小波的不足,在图像直线特征检测、图像降噪与复原等方面取得了良好的效果,但将其与图像哈希技术结合起来的研究还很少。本文在有限脊波变换应用于图像哈希算法方面作了一些研究和尝试。主要创新成果如下：
(1)提出一种基于有限脊波变换与傅里叶变换结合的图像哈希算法。该算法首先对原始图像预处理,再将其分割成子块,并对每个块图像进行脊波变换,然后沿每个方向作一维傅里叶变换,最后取每个脊波块系数的最大值以及每个傅里叶变换块幅值之和作为特征向量来生成哈希序列。与未采用脊波的算法相比,该方法提高了对JPEG压缩、椒盐噪声、高斯低通滤波、旋转、缩小等操作的鲁棒性。同时,图像哈希序列由密钥控制生成,因此具有较好的安全性。
(2)为了使图像哈希具有更好的鲁棒性和安全性,提出了一种新的基于视觉特性的图像哈希方法。该方法首先将原始图像预处理,然后利用人类视觉特性中‘频率敏感度提取脊波变换域上的系数生成哈希值。实验结果表明,该方法能够抵抗JPEG压缩、滤波、加噪声、剪切、旋转和缩放等攻击,具有较好的鲁棒性、敏感性和安全性。
Image hash has been paid much attention in recent years for its extensive applications in content authentication, database search and watermarking. During the manipulations of content-preserving, such as compression, filtering, geometric distortion and so on, traditional cryptographic hashes are sensitive to any change of bit and not applicable to images. So it is necessary to research on the image hash to make it robust to content-preserving manipulations and able to detect the malicious attacks.
Currently, image hashing algorithms are mainly implemented in transform domains. Wavelet is mostly used as one of them. However, wavelet is usually suitable for zero degree(point) singularities and the ID singularities existed in images affect the efficiency of feature extraction in the wavelet domain making it difficult to generate an ideal image hash.
Finite ridgelet transform, which is 1D wavelet transform along each direction in the finite radon transform domain, has shown its advantage in linear detection and image reconstruction. However, papers in demonstrating applying finite ridgelet transform to image hashing algorithm are few. In this dissertation, the author has made some research and attempt to do so. The main innovations are as follows:
(1)An image hashing based on finite ridgelet transform and fourier transform is proposed. At first, it preprocessed the original image and partitioned the image into blocks. Second, it made ridgelet transform for each image block and then made 1D FFT transform along each direction in the ridgelet transform domain. Finally, it extracted the maximum value of ridgelet coefficients and the sum of FFT amplitudes to generate the hash value. Compared with some other hashing methods, the ridgelet-based hash has better robustness against JPEG compression, salt & pepper noise, gaussian lowpass filtering, rotation, scale and so on. Since a key is used in the algorithm, the hash is harder to be forged.
(2)To obtain more robust and secure image hash value, a novel image hashing scheme based on human visual system is proposed. It first preprocessed the original image, then extracted ridgelet coefficients based on frequency sensitivity in the human visual system to generate the hash value. The experimental results demonstrate that the scheme has a good performance against JPEG compression, filtering, adding noise, shearing, rotation and scale. The hash has good robustness, sensitivity and security.
目前使用的数字图像哈希基本上是在变换域中进行的,尤其以基于小波变换的算法居多。但是小波一般只适合于表征零维点奇异性,而图像中广泛存在的一维奇异性影响着小波特征提取的效率,同时也难以生成理想的图像哈希。
有限脊波变换是在有限Radon变换域中沿每个方向作一维小波变换。它克服了小波的不足,在图像直线特征检测、图像降噪与复原等方面取得了良好的效果,但将其与图像哈希技术结合起来的研究还很少。本文在有限脊波变换应用于图像哈希算法方面作了一些研究和尝试。主要创新成果如下：
(1)提出一种基于有限脊波变换与傅里叶变换结合的图像哈希算法。该算法首先对原始图像预处理,再将其分割成子块,并对每个块图像进行脊波变换,然后沿每个方向作一维傅里叶变换,最后取每个脊波块系数的最大值以及每个傅里叶变换块幅值之和作为特征向量来生成哈希序列。与未采用脊波的算法相比,该方法提高了对JPEG压缩、椒盐噪声、高斯低通滤波、旋转、缩小等操作的鲁棒性。同时,图像哈希序列由密钥控制生成,因此具有较好的安全性。
(2)为了使图像哈希具有更好的鲁棒性和安全性,提出了一种新的基于视觉特性的图像哈希方法。该方法首先将原始图像预处理,然后利用人类视觉特性中‘频率敏感度提取脊波变换域上的系数生成哈希值。实验结果表明,该方法能够抵抗JPEG压缩、滤波、加噪声、剪切、旋转和缩放等攻击,具有较好的鲁棒性、敏感性和安全性。
Image hash has been paid much attention in recent years for its extensive applications in content authentication, database search and watermarking. During the manipulations of content-preserving, such as compression, filtering, geometric distortion and so on, traditional cryptographic hashes are sensitive to any change of bit and not applicable to images. So it is necessary to research on the image hash to make it robust to content-preserving manipulations and able to detect the malicious attacks.
Currently, image hashing algorithms are mainly implemented in transform domains. Wavelet is mostly used as one of them. However, wavelet is usually suitable for zero degree(point) singularities and the ID singularities existed in images affect the efficiency of feature extraction in the wavelet domain making it difficult to generate an ideal image hash.
Finite ridgelet transform, which is 1D wavelet transform along each direction in the finite radon transform domain, has shown its advantage in linear detection and image reconstruction. However, papers in demonstrating applying finite ridgelet transform to image hashing algorithm are few. In this dissertation, the author has made some research and attempt to do so. The main innovations are as follows:
(1)An image hashing based on finite ridgelet transform and fourier transform is proposed. At first, it preprocessed the original image and partitioned the image into blocks. Second, it made ridgelet transform for each image block and then made 1D FFT transform along each direction in the ridgelet transform domain. Finally, it extracted the maximum value of ridgelet coefficients and the sum of FFT amplitudes to generate the hash value. Compared with some other hashing methods, the ridgelet-based hash has better robustness against JPEG compression, salt & pepper noise, gaussian lowpass filtering, rotation, scale and so on. Since a key is used in the algorithm, the hash is harder to be forged.
(2)To obtain more robust and secure image hash value, a novel image hashing scheme based on human visual system is proposed. It first preprocessed the original image, then extracted ridgelet coefficients based on frequency sensitivity in the human visual system to generate the hash value. The experimental results demonstrate that the scheme has a good performance against JPEG compression, filtering, adding noise, shearing, rotation and scale. The hash has good robustness, sensitivity and security.
引文
[1]胡军全,黄继武,张龙军等.结合数字签名和数字水印的多媒体认证系统.软件学报,2003,14(6)：1157-1163
[2]焦李成,谭山.图像的多尺度几何分析：回顾和展望.电子学报,2003,31(12A)：1975-1981
[3]焦李成,谭山,刘芳.脊波理论：从脊波变换到Curvelet变换.工程数学学报,2005,22(5)：761-772
[4]Schneider M, Chang S F. A Robust Content Based Digital Dignature for Image Authentication. In:Proc of Int Conf on Image Processing. Lausanne,1996, 227-230
[5]Xiang S J, Kim H J, Huang J W. Histogram-based Image Hashing Scheme Robust Against Geometric Deformations. In:Proc of 9th ACM Multimedia and Security Workshop. USA,2007,121-128
[6]Ferman A M, Tekalp A M, Mehrotra R. Robust Color Histogram Descriptors for Video Segment Retrieval and Identification. IEEE Transactions on Image Processing,2002,11(5):497-508
[7]Jing F, Li M, Zhang H J. An Efficient and Effective Region-based Image Retrieval Framework. IEEE Transactions on Image Processing,2004,5(13): 699-709.
[8]Lou D C, Liu J L. Fault Resilient and Compression Tolerant Digital Signature for Image Authentication. IEEE Transactions on Consumer Eletronics,2000, 46(1):31-39
[9]Queluz M P. Authentication of Digital Images and Video:Generic Models and A New Contribution. Signal Processing:Image Communication,2001,16(5): 461-475
[10]Kailasanathan C, Naini R S. Image Authentication Surviving Acceptable Modifications Using Statistiacl Measures and K-mean Segmentation. In:Proc of EURASIP Workshop on Nonlinear Signal and Image Processing. USA,2001, 325-330
[11]Lin C Y, Chang S F. A Robust Image Authentication Method Distinguishing JPEG Compression from Malicious Anipulation. IEEE Transactions on Circuits and Systems for Video Technology,2001,11(2):153-168
[12]Fridrich J, Goljan M. Robust Hash Functions for Digital Watermarking. In:Proc of Int Conf on Information Technology:Coding Computing. Las Vegas,2000, 178-183
[13]Swaminathan A, Mao Y N, Wu M. Robust and Secure Image Hashing. IEEE Transactions on Information Forensics and Security,2006,1(2):215-230
[14]Kang X G, Zhong Xiong, Huang J W. An Efficient Print-scanning Resilient Data Hiding Scheme Based on A Novel LPM. In:Proc of Int Conf on Image Processing. San Diego,2008,2080-2083
[15]Mihcak M K, Venkatesan R. New Iterative Geometric Metheods for Robust Perceptual Image Hashing. In:Proc of Int Conf on ACM Workshop Security and Privacy in Digital Rights Management. Philadelphia, PA,2001,13-21
[16]Lu C S, Liao H Y. Structural Digital Signature for Image Authentication:An Incidental Distortion Resistant Scheme. IEEE Transactions on Multimedia,2003, 5(2):161-173
[17]Zhang H B, Yang C, Quan X M. Image Authentication Based on Digital Signature and Semi-Fragile Watermarking. Journal of Computer Science and Technology,2004,19(6):121-126
[18]Alghoniemy M, Tewfik A H. Geometric Invariance in Image Watermarking. IEEE Transactions on Image Processing,2004,13(2):145-153
[19]Monga V, Evans B L. Perceptual Image Hashing Via Feature Points: Performance Evaluation and Tradeoffs. IEEE Transactions on Image Processing, 2006,15(11):3452-3465
[20]Malking M, Venkatesan R. The Randlet Transform:Applications to Universal Perceptual Hashing and Image Authentication. In:Proc of Int Conf on Image Processing. USA,2004,2011-2016
[21]秦川,王朔中,张新鹏.一种基于视觉特性的图像摘要算法.中国图象图形学报,2006,11(11)：1678-1681
[22]Swaminathan A, Mao Y N, Wu M. Image Hashing Resilient to Geometric and Filtering Operations. In:Proc of 6th Workshop on Multimedia Signal Processing. USA,2004,355-358
[23]Monga V, Mihcak M K. Robust and Secure Image Hashing Via Non-Negative Matrix Factorizations. IEEE Transactions on Information Forensics and Security, 2007,2(3):376-390
[24]Sujoy R, Qibin S. Robust Hash for Detecting and Locating Image Tampering. In: Proc of Int Conf on Image Processing. San Antonio,2007,117-120
[25]Kalantari N K, Ahadi S M, Vafadust M. A Robust Image Watermarking in The Ridgelet Domain Using Universally Optimum Decoder. IEEE Transactions on Circuits and Systems for Video Technology,2010,3(20):396-406
[26]何妙谊.稳健及安全的数字图像签名的研究：[中山大学硕士学位论文].广州：中山大学通信与信息系统,2007,10-12
[27]胡聪.安全图像哈希认证算法的研究：[中山大学硕士学位论文].广州：中山大学通信与信息系统,2009,8-16
[28]张鹤超.感知图像哈希技术及其在数字认证中的应用：[大连理工大学硕士学位论文].大连：大连理工大学信号与信息处理,2008,14-23
[29]孙建梅.基于内容的图像认证技术研究：[西北大学硕士学位论文].西安：西北大学电路与系统,2005,8-9
[30]叶卫国,韩水华.基于内容的图像Hash算法及其性能评估.东南大学学报,2007,37(z1)：109-113
[31]沃焱,韩国强,张波.一种新的基于特征的图像内容认证方法.计算机学报,2005,28(1)：105-112
[32]金秋明,王朔中,李茜等.基于角点检测的稳健图像摘要.中国图象图形学报,2008,13(8)：1454-1458
[33]Kozat S S, Venkatesan R, Mihcak M K. Robust perceptual Image Hashing Via Matrix Invariants. In:Proc of Int Conf on Image Processing,2004,3443-3446
[34]Schneider M, Chang S F. A Robust Content Based Digital Signature for Image Authentication. In:Proc of Int Conf on Image Processing. Lausanne,1996, 227-230
[35]Venkatesan R, Koon S M, Jakubowski M H, et al. Robust Image Hashing. In: Proc of Int Conf on Image Processing. Vancouver B C,2000,664-666
[36]Monga V, Baneriee A, Evans B L. A Clustering Based Approach to Perceptual Image Hashing. IEEE Transactions on Information Forensics and Security,2006, 1(1):68-79
[37]Wu M, Mao Y N, Swaminathan A. A Signal Processing and Randomization Perspective of Robust and Secure Image Hashing. In:Proc of 14th Int Conf on Statistical Signal Processing. Madison W I,2007,166-170
[38]Yang O, Kyung H R. A Key-dependent Secure Image Hashing Scheme by Using Radon Transform. In:Proc of Int Symposium on Intelligent Signal Processing and Communication Systems. Kanazawa,2009,595-598
[39]Khelifi F, Jiang J M. Analysis of the Security of Perceptual Image Hashing Based on Non-negative Matrix Factorization. Signal Processing Letters,2010, 1(17):43-46
[40]Candes E J, Donoho D L. Ridgelets:A Key to Higher-dimensional Intermittency. Phil Transactions,1999,2495-2595
[41]Kelley B T, Madisetti V K. The Fast Discrete Radon Transform-Ⅰ:Theory. IEEE Transactions on Image Processing,1993,2(3):382-400
[42]Minh N D, Martin V. The Finite Ridgelet Transform for Image Representation. IEEE Transactions on Image Processing,2003,12(1):16-28
[43]张金沙.基于有限脊波变换的图像水印算法研究：[电子科技大学硕士学位论文].成都：电子科技大学信号与信息处理,2003,27-37
[44]Joshi M S, Manthalkar R R, Joshi Y V. Joint Compression and Classification for Textures in The Wavelet and Ridgelet Domain. In:Proc of 3th Int Conf on Signal-Image Technologies and Internet-Based System. Shanghai,2007, 563-569
[45]宋文蕾,赵艳华,谢慕君.基于脊波变换的数字图像处理.长春大学学报,2007,17(1)：49-53
[46]Guo S Q, Cao H Q, Deng C Z. Content-Based Adaptive Watermarking Algorithm in Ridgelet Domain. In:Proc of Int Conf on Audio, Language and Image Processing. Shanghai,2008,619-623
[47]刘伶俐.脊波变换在图像处理中的应用研究：[西安电子科技大学硕士学位论文].西安：西安电子科技大学物理电子学,2008,19-20
[48]徐金星.基于小波变换和人类视觉特性的数字水印技术：[天津大学硕士学位论文].天津：天津大学模式识别与智能系统,2007,33-34
[49]李照烽.基于分数阶傅立叶变换的图像Hash算法研究：[西安科技大学硕士论文学位].西安：西安科技大学信号与信息处理,2008,11-13
[50]Huang K, Aviyente S. Rotation Invariant Texture Classification with Ridgelet Transform and Fourier Transform. In:Proc of Int Conf on Image Processing. Atlanta G A,2006,2141-2144
[51]赵玉鑫,刘光杰等.一种新的视觉Hash算法.光学精密工程,2008,16(3)：551-557
[52]Xiao L, Wu H Z, Wei Z H. Research and Application of A New Computational Model of Human Vision System Based on Ridgelet Transform. In:Proc of Int Conf on Machine Learning and Cybernetics. Guangzhou,2005,18-21
[53]房辉.基于人类视觉特性的视频质量评价模型：[北京邮电大学硕士学位论文].北京：北京邮电大学计算机科学与技术,2009,16-17
[54]孙钱锋,温泉,王树勋.基于人类视觉的混沌阵列图像上的水印算法,电子学报,2003,31(1)：149-155
[2]焦李成,谭山.图像的多尺度几何分析：回顾和展望.电子学报,2003,31(12A)：1975-1981
[3]焦李成,谭山,刘芳.脊波理论：从脊波变换到Curvelet变换.工程数学学报,2005,22(5)：761-772
[4]Schneider M, Chang S F. A Robust Content Based Digital Dignature for Image Authentication. In:Proc of Int Conf on Image Processing. Lausanne,1996, 227-230
[5]Xiang S J, Kim H J, Huang J W. Histogram-based Image Hashing Scheme Robust Against Geometric Deformations. In:Proc of 9th ACM Multimedia and Security Workshop. USA,2007,121-128
[6]Ferman A M, Tekalp A M, Mehrotra R. Robust Color Histogram Descriptors for Video Segment Retrieval and Identification. IEEE Transactions on Image Processing,2002,11(5):497-508
[7]Jing F, Li M, Zhang H J. An Efficient and Effective Region-based Image Retrieval Framework. IEEE Transactions on Image Processing,2004,5(13): 699-709.
[8]Lou D C, Liu J L. Fault Resilient and Compression Tolerant Digital Signature for Image Authentication. IEEE Transactions on Consumer Eletronics,2000, 46(1):31-39
[9]Queluz M P. Authentication of Digital Images and Video:Generic Models and A New Contribution. Signal Processing:Image Communication,2001,16(5): 461-475
[10]Kailasanathan C, Naini R S. Image Authentication Surviving Acceptable Modifications Using Statistiacl Measures and K-mean Segmentation. In:Proc of EURASIP Workshop on Nonlinear Signal and Image Processing. USA,2001, 325-330
[11]Lin C Y, Chang S F. A Robust Image Authentication Method Distinguishing JPEG Compression from Malicious Anipulation. IEEE Transactions on Circuits and Systems for Video Technology,2001,11(2):153-168
[12]Fridrich J, Goljan M. Robust Hash Functions for Digital Watermarking. In:Proc of Int Conf on Information Technology:Coding Computing. Las Vegas,2000, 178-183
[13]Swaminathan A, Mao Y N, Wu M. Robust and Secure Image Hashing. IEEE Transactions on Information Forensics and Security,2006,1(2):215-230
[14]Kang X G, Zhong Xiong, Huang J W. An Efficient Print-scanning Resilient Data Hiding Scheme Based on A Novel LPM. In:Proc of Int Conf on Image Processing. San Diego,2008,2080-2083
[15]Mihcak M K, Venkatesan R. New Iterative Geometric Metheods for Robust Perceptual Image Hashing. In:Proc of Int Conf on ACM Workshop Security and Privacy in Digital Rights Management. Philadelphia, PA,2001,13-21
[16]Lu C S, Liao H Y. Structural Digital Signature for Image Authentication:An Incidental Distortion Resistant Scheme. IEEE Transactions on Multimedia,2003, 5(2):161-173
[17]Zhang H B, Yang C, Quan X M. Image Authentication Based on Digital Signature and Semi-Fragile Watermarking. Journal of Computer Science and Technology,2004,19(6):121-126
[18]Alghoniemy M, Tewfik A H. Geometric Invariance in Image Watermarking. IEEE Transactions on Image Processing,2004,13(2):145-153
[19]Monga V, Evans B L. Perceptual Image Hashing Via Feature Points: Performance Evaluation and Tradeoffs. IEEE Transactions on Image Processing, 2006,15(11):3452-3465
[20]Malking M, Venkatesan R. The Randlet Transform:Applications to Universal Perceptual Hashing and Image Authentication. In:Proc of Int Conf on Image Processing. USA,2004,2011-2016
[21]秦川,王朔中,张新鹏.一种基于视觉特性的图像摘要算法.中国图象图形学报,2006,11(11)：1678-1681
[22]Swaminathan A, Mao Y N, Wu M. Image Hashing Resilient to Geometric and Filtering Operations. In:Proc of 6th Workshop on Multimedia Signal Processing. USA,2004,355-358
[23]Monga V, Mihcak M K. Robust and Secure Image Hashing Via Non-Negative Matrix Factorizations. IEEE Transactions on Information Forensics and Security, 2007,2(3):376-390
[24]Sujoy R, Qibin S. Robust Hash for Detecting and Locating Image Tampering. In: Proc of Int Conf on Image Processing. San Antonio,2007,117-120
[25]Kalantari N K, Ahadi S M, Vafadust M. A Robust Image Watermarking in The Ridgelet Domain Using Universally Optimum Decoder. IEEE Transactions on Circuits and Systems for Video Technology,2010,3(20):396-406
[26]何妙谊.稳健及安全的数字图像签名的研究：[中山大学硕士学位论文].广州：中山大学通信与信息系统,2007,10-12
[27]胡聪.安全图像哈希认证算法的研究：[中山大学硕士学位论文].广州：中山大学通信与信息系统,2009,8-16
[28]张鹤超.感知图像哈希技术及其在数字认证中的应用：[大连理工大学硕士学位论文].大连：大连理工大学信号与信息处理,2008,14-23
[29]孙建梅.基于内容的图像认证技术研究：[西北大学硕士学位论文].西安：西北大学电路与系统,2005,8-9
[30]叶卫国,韩水华.基于内容的图像Hash算法及其性能评估.东南大学学报,2007,37(z1)：109-113
[31]沃焱,韩国强,张波.一种新的基于特征的图像内容认证方法.计算机学报,2005,28(1)：105-112
[32]金秋明,王朔中,李茜等.基于角点检测的稳健图像摘要.中国图象图形学报,2008,13(8)：1454-1458
[33]Kozat S S, Venkatesan R, Mihcak M K. Robust perceptual Image Hashing Via Matrix Invariants. In:Proc of Int Conf on Image Processing,2004,3443-3446
[34]Schneider M, Chang S F. A Robust Content Based Digital Signature for Image Authentication. In:Proc of Int Conf on Image Processing. Lausanne,1996, 227-230
[35]Venkatesan R, Koon S M, Jakubowski M H, et al. Robust Image Hashing. In: Proc of Int Conf on Image Processing. Vancouver B C,2000,664-666
[36]Monga V, Baneriee A, Evans B L. A Clustering Based Approach to Perceptual Image Hashing. IEEE Transactions on Information Forensics and Security,2006, 1(1):68-79
[37]Wu M, Mao Y N, Swaminathan A. A Signal Processing and Randomization Perspective of Robust and Secure Image Hashing. In:Proc of 14th Int Conf on Statistical Signal Processing. Madison W I,2007,166-170
[38]Yang O, Kyung H R. A Key-dependent Secure Image Hashing Scheme by Using Radon Transform. In:Proc of Int Symposium on Intelligent Signal Processing and Communication Systems. Kanazawa,2009,595-598
[39]Khelifi F, Jiang J M. Analysis of the Security of Perceptual Image Hashing Based on Non-negative Matrix Factorization. Signal Processing Letters,2010, 1(17):43-46
[40]Candes E J, Donoho D L. Ridgelets:A Key to Higher-dimensional Intermittency. Phil Transactions,1999,2495-2595
[41]Kelley B T, Madisetti V K. The Fast Discrete Radon Transform-Ⅰ:Theory. IEEE Transactions on Image Processing,1993,2(3):382-400
[42]Minh N D, Martin V. The Finite Ridgelet Transform for Image Representation. IEEE Transactions on Image Processing,2003,12(1):16-28
[43]张金沙.基于有限脊波变换的图像水印算法研究：[电子科技大学硕士学位论文].成都：电子科技大学信号与信息处理,2003,27-37
[44]Joshi M S, Manthalkar R R, Joshi Y V. Joint Compression and Classification for Textures in The Wavelet and Ridgelet Domain. In:Proc of 3th Int Conf on Signal-Image Technologies and Internet-Based System. Shanghai,2007, 563-569
[45]宋文蕾,赵艳华,谢慕君.基于脊波变换的数字图像处理.长春大学学报,2007,17(1)：49-53
[46]Guo S Q, Cao H Q, Deng C Z. Content-Based Adaptive Watermarking Algorithm in Ridgelet Domain. In:Proc of Int Conf on Audio, Language and Image Processing. Shanghai,2008,619-623
[47]刘伶俐.脊波变换在图像处理中的应用研究：[西安电子科技大学硕士学位论文].西安：西安电子科技大学物理电子学,2008,19-20
[48]徐金星.基于小波变换和人类视觉特性的数字水印技术：[天津大学硕士学位论文].天津：天津大学模式识别与智能系统,2007,33-34
[49]李照烽.基于分数阶傅立叶变换的图像Hash算法研究：[西安科技大学硕士论文学位].西安：西安科技大学信号与信息处理,2008,11-13
[50]Huang K, Aviyente S. Rotation Invariant Texture Classification with Ridgelet Transform and Fourier Transform. In:Proc of Int Conf on Image Processing. Atlanta G A,2006,2141-2144
[51]赵玉鑫,刘光杰等.一种新的视觉Hash算法.光学精密工程,2008,16(3)：551-557
[52]Xiao L, Wu H Z, Wei Z H. Research and Application of A New Computational Model of Human Vision System Based on Ridgelet Transform. In:Proc of Int Conf on Machine Learning and Cybernetics. Guangzhou,2005,18-21
[53]房辉.基于人类视觉特性的视频质量评价模型：[北京邮电大学硕士学位论文].北京：北京邮电大学计算机科学与技术,2009,16-17
[54]孙钱锋,温泉,王树勋.基于人类视觉的混沌阵列图像上的水印算法,电子学报,2003,31(1)：149-155