图像质量客观评价的研究
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摘要
视觉信息是人类获取信息的最主要途径,它通过人自身的视觉感知系统获取,其中图像信息是最主要的组成部分。随着个人计算机、数字通信、多媒体和网络技术的发展,数字图像和数字视频日益成为信息最重要的载体之一,已经深入到人们的日常生活,普及到千家万户。在数字图像的获取、处理、编码、存储、传输和重建的每一个步骤中,通常都会对图像的质量产生影响,如何评价图像质量成为图像处理、计算机视觉领域的一个基本而文富有挑战的问题。本论文研究图像的结构失真,并且充分利用图像的结构失真特性设计客观图像质量评价方法,使其能够自动精确的评价图像的质量。
本论文的研究内容主要围绕图像结构重要性表示和度量、图像投影能量和图像方向投影等关键技术进行研究工作。主要工作和创新成果总结如下:
(1)将匹配追逐算法用于图像质量评价中,并且为满足图像质量评价的需求进行了修改。匹配追逐算法是一种将图像在基函数集上进行投影提取图像结构的算法,主要应用于图像和视频编码中。为满足图像质量评价的需求,对匹配追逐算法进行了改进,使用该算法对参考图像进行分解以提取重要的结构信息。
(2)提出了一种图像结构特征表示和重要性度量方法。人眼天然具有获取图像结构的特性,一般而言,自然图像中由于各个结构所表示的内容不同,不同的结构区域往往在视觉上具有不同重要性,基于此种假设,利用改进的匹配追逐算法对图像进行结构提取,并且对结构进行特征表示和重要性度量。
(3)提出了一种基于结构重要性度量的质量评价方法。该方法提出了一种结构重要性度量的概念,并且用在图像质量客观评价中,通过对参考图像的结构进行提取,按照重要性排列获得不同图像结构信息和重要性度量,通过计算失真图像与参考图像结构信息的差异获得图像的失真度量和质量值。
(4)提出了一种基于投影能量的质量评价方法。该方法将图像的失真建模为投影值的差异,在此基础上提出了一种基于信号投影能量的图像质量客观评价方法。该方法使用了简单的投影方法,参数简单,具有高效以及低复杂度的特点,可以满足各种实时需求的应用。由于该算法简单,易于实现,期望成为基于像素统计算法比如PSNR的一个扩展。
(5)提出了一种基于方向投影的质量评价方法。图像的结构信息主要由带有方向特性的像素、边缘和形状等组成,使用图像在各个方向上的投影来表示图像的方向特性,图像质量的改变可以建模为图像在方向特性上的改变。该方法通过Radon变换来统计图像在各个方向的投影,建立方向投影矩阵来表示图像的方向特性,最后计算失真图像和参考图像方向投影矩阵之间的差异来统计图像的失真度量。
The uppermost way which human beings learn from is visual information that is received by human perceptional system,and among the visual information photos are the matters of primary importance.With the development of PC,digital communication,multimedia and network technology,as one of the most important informational intermedium,digital image/video has penetrated into individual's daily life and popularized among people.In the orocedures of image processing system,e.g., acquisition,processing,coding,storage,transmission and reproduction,digital image may be in degradation in visual quality,so evaluating image quality becomes a fundamental job in the field of image processing and computer vision.The objective of this thesis is to research on the structural distortion of the image,and further design the algorithms of objective assessment to evalue the image quality automatically and accurately by using the characteristics of structural distortion.
In this thesis,we explore which consists of the novel idea about the expression and measurement of image structural importance,the image's projection energy and directional projection.The main work and innovations are listed as follows:
(1)Introduce matching pursuit into image QA,and it is modified for the image QA applications.Matching pursuit projects the image on the basis set and extracts the image structure under the rule of the largest energy,and it is used widely in image and video coding.We modify matching pursuit to meet the image QA applications,and decompose and extract the important structural information from the reference image.
(2)Propose an approach of expression of image structural information and measurement of structural importance.Human visual perception is hilly adaptive for extracting structural information from a scene.Generally according to the differences of the characteristic which the structure represents,the different structural information is always of different importance.On such an assumption,modified matching pursuit is introduced into extracting the structural information from images,charactering the structural information and measuring its importance.
(3)Propose an image QA approach based on the importance of structural information.The proposed idea of structural importance is introduced into image QA.By extracting the structural information from the reference image, the different structural information and its importance measurement is gained.The structural distortion and quality predictive score are calculated by comparing the difference between the structural information of reference images and distortion ones.
(4)Propose an image QA approach based on projection energy.On the assumption that any image distortion could be modeled as the difference of the PEVs(projection energy vector)between the reference image and the distortion one,an image QA approach is proposed based on signal projection energy.This approach uses the simple projection operator and simple parameters and it achieves high efficiency and low computational complexity,so it is adaptive to the real-time applications.This approach is of simple parameters and easy to calculate,thus it expects to work as an expansion for those mathematically defined ones for example PSNR.
(5)Propose an image QA approach based directional projection.The image structure contains many pixels,edges and shape with directional characteristic mainly,and the directional characteristic is charactered by the images' projection on different direction.The distortion of the structural information could be modeled as the alteration of the directional characteristic.This approach is implemented by Radon transform which calculates the directional projection of images and develops the DPV (directional projection-based vector)to represent the directional characteristic.The structural distortion is calculated by comparing the difference of the DPVs between reference images and distortion ones.
本论文的研究内容主要围绕图像结构重要性表示和度量、图像投影能量和图像方向投影等关键技术进行研究工作。主要工作和创新成果总结如下:
(1)将匹配追逐算法用于图像质量评价中,并且为满足图像质量评价的需求进行了修改。匹配追逐算法是一种将图像在基函数集上进行投影提取图像结构的算法,主要应用于图像和视频编码中。为满足图像质量评价的需求,对匹配追逐算法进行了改进,使用该算法对参考图像进行分解以提取重要的结构信息。
(2)提出了一种图像结构特征表示和重要性度量方法。人眼天然具有获取图像结构的特性,一般而言,自然图像中由于各个结构所表示的内容不同,不同的结构区域往往在视觉上具有不同重要性,基于此种假设,利用改进的匹配追逐算法对图像进行结构提取,并且对结构进行特征表示和重要性度量。
(3)提出了一种基于结构重要性度量的质量评价方法。该方法提出了一种结构重要性度量的概念,并且用在图像质量客观评价中,通过对参考图像的结构进行提取,按照重要性排列获得不同图像结构信息和重要性度量,通过计算失真图像与参考图像结构信息的差异获得图像的失真度量和质量值。
(4)提出了一种基于投影能量的质量评价方法。该方法将图像的失真建模为投影值的差异,在此基础上提出了一种基于信号投影能量的图像质量客观评价方法。该方法使用了简单的投影方法,参数简单,具有高效以及低复杂度的特点,可以满足各种实时需求的应用。由于该算法简单,易于实现,期望成为基于像素统计算法比如PSNR的一个扩展。
(5)提出了一种基于方向投影的质量评价方法。图像的结构信息主要由带有方向特性的像素、边缘和形状等组成,使用图像在各个方向上的投影来表示图像的方向特性,图像质量的改变可以建模为图像在方向特性上的改变。该方法通过Radon变换来统计图像在各个方向的投影,建立方向投影矩阵来表示图像的方向特性,最后计算失真图像和参考图像方向投影矩阵之间的差异来统计图像的失真度量。
The uppermost way which human beings learn from is visual information that is received by human perceptional system,and among the visual information photos are the matters of primary importance.With the development of PC,digital communication,multimedia and network technology,as one of the most important informational intermedium,digital image/video has penetrated into individual's daily life and popularized among people.In the orocedures of image processing system,e.g., acquisition,processing,coding,storage,transmission and reproduction,digital image may be in degradation in visual quality,so evaluating image quality becomes a fundamental job in the field of image processing and computer vision.The objective of this thesis is to research on the structural distortion of the image,and further design the algorithms of objective assessment to evalue the image quality automatically and accurately by using the characteristics of structural distortion.
In this thesis,we explore which consists of the novel idea about the expression and measurement of image structural importance,the image's projection energy and directional projection.The main work and innovations are listed as follows:
(1)Introduce matching pursuit into image QA,and it is modified for the image QA applications.Matching pursuit projects the image on the basis set and extracts the image structure under the rule of the largest energy,and it is used widely in image and video coding.We modify matching pursuit to meet the image QA applications,and decompose and extract the important structural information from the reference image.
(2)Propose an approach of expression of image structural information and measurement of structural importance.Human visual perception is hilly adaptive for extracting structural information from a scene.Generally according to the differences of the characteristic which the structure represents,the different structural information is always of different importance.On such an assumption,modified matching pursuit is introduced into extracting the structural information from images,charactering the structural information and measuring its importance.
(3)Propose an image QA approach based on the importance of structural information.The proposed idea of structural importance is introduced into image QA.By extracting the structural information from the reference image, the different structural information and its importance measurement is gained.The structural distortion and quality predictive score are calculated by comparing the difference between the structural information of reference images and distortion ones.
(4)Propose an image QA approach based on projection energy.On the assumption that any image distortion could be modeled as the difference of the PEVs(projection energy vector)between the reference image and the distortion one,an image QA approach is proposed based on signal projection energy.This approach uses the simple projection operator and simple parameters and it achieves high efficiency and low computational complexity,so it is adaptive to the real-time applications.This approach is of simple parameters and easy to calculate,thus it expects to work as an expansion for those mathematically defined ones for example PSNR.
(5)Propose an image QA approach based directional projection.The image structure contains many pixels,edges and shape with directional characteristic mainly,and the directional characteristic is charactered by the images' projection on different direction.The distortion of the structural information could be modeled as the alteration of the directional characteristic.This approach is implemented by Radon transform which calculates the directional projection of images and develops the DPV (directional projection-based vector)to represent the directional characteristic.The structural distortion is calculated by comparing the difference of the DPVs between reference images and distortion ones.
引文
[1]毕厚杰等.图像通信工程,北京:人民邮电出版礼,1991
[2]Wang Z.,Bovik A.C.,Sheikh H.R.,Simoncelli E.P.,Image Quality Assessment:From Error Visibility to Structural Similarity.IEEE Trans.Image Processing,vol.13,No.4,pp.600-612,April 2004.
[3]Wang Z.,Bovik A.C.,Lu L..Why is Image Quality Assessment so Difficult.Proceeding of IEEE Int.Conf Acoust,Speech,and Signal Processing,vol.4(3313-3316),May 2002.
[4]Mannos J.L.,Sakrison D.J.,The Effects of a Visual Fidelity Criterion on the Encoding of Images.IEEE Trans.Information Theory,vol.20,No.4(525-536),1974
[5]Watson A.B.,DCT Quantization Matrices Visually Optimized for Individual Images.Presented at Human Vision,Visual Processing,and Digital Display IV,Bellingham,WA,1993.
[6]Google,Available:www.google.com.
[7]VQEG:Video Quality Experts Group,Available:http://www.vqeg.org/.
[8]Wu H.R.,Rao K.R.,Digital Video Image Quality and Perceptual Coding.Presented at Signal Processing and Communications,CRC Press,2006
[9]李均利,陈刚,池哲儒,张直.客观评价图像质量编码新方法.中国图象图形学报,vol.11,no.9,pp.1348-1355,2004.
[10]Pappas T.N.,Safranek R.J.,Chen J.,Perceptual criteria for image quality evaluation.Chapter 8.2 in The Handbook of Image and Video Processing,Second Edition,A.C.Bovik,(Ed.),New York:Elsevier Academic Press,pp.939-960,2005.
[11]VQEG,Final VQEG Report on the Validation of Objective quality metrics for video quality assessment.Available:http://www.its.bidrdoe.gov/vqeg/projects/frtv phasel/index.php.
[12]Beegan A.P.,Iyer L.R.,Bell A.E.,Maher V.R.,Ross M.A.,Design and Evaluation of Perceptual Masks for Wavelet Image Compression.Proceeding of IEEE Digital Signal Processing Workshop,pp.88-93,2002.
[13]Eskicioglu A.M.,Fisher P.S.,Image Quality Measures and Their Performance.IEEE Transactions on Communications,vol.43,no.12,pp.2959-2965,Dec.1995.
[14] Beaton R.J., Quantitative Models of Image Quality. Proceeding of the Human Factors Society-27~(th) Annual Meeting, pp.41-45, 1983
[15] Franti P., Blockwise Distortion Measure for Statistical and Structural Errors in Digital Images. Signal Processing: Image communication, Vol.13, pp.89-98, 1998
[16] Winkler S., Issues in Vision Modeling for Perceptual Video Quality Assessment. Signal Processing, vol.78, no.2, pp.231-252, 1999
[17] Eskicioglu A. M., Quality Measurement for Monochrome Compressed Images in the Past 25 years. Proceeding of IEEE Int. Conf. Acoustics, Speech, Signal Processing, vol. 4, pp. 1907-1910, Istanbul, Turkey, Jun. 2000
[18] Wang Z., Bovik A. C, A Universal Image Quality Index. IEEE Signal Processing Letters, vol. 9, pp. 81-84, Mar. 2002
[19] Shnayderman A., Gusev A., Eskicioglu A. M., An SVD-based Grayscale Image Quality Measure for Local and Global Assessment. IEEE Trans. Image Processing, vol. 15, no. 2, pp. 422-429, Feb. 2006.
[20] Sheikh H.R., Bovik A.C., Image Information and Visual Quality. IEEE Trans. Image Processing, vol.15, no.2, pp. 430- 444, Feb. 2006
[21] Li J. L., Chen G, Chi Z. R., Lu C. G, Image Coding Quality Assessment Using Fuzzy Integrals With a Three-Component Image Model. IEEE Transactions on Fuzzy Systems, 2004, vol.12, no. 1, pp.99-106
[22] Wang S., Zheng D, Zhao J. Y., Tarn W. J., Speranza F., An Image Quality Evaluation Method Based on Digital Watermarking. IEEE Trans. Circuits and Systems for Video Technology, Vol. 17, No. 1, January 2007.
[23] Campisi P., Carli M., Giunta G., Neri A., Blind Quality Assessment System for Multimedia Communications Using Tracing Watermarking. IEEE Trans. Signal Processing. vol. 51, no. 4, pp. 996-1002, Apr. 2003.
[24] Zhai GT., Zhang W. J. Yang X.K., Xu Y, Image Quality Assessment Metrics based on Multi-Scale Edge Presentation. Proceeding of IEEE Workshop on Signal Processing Systems Design and Implementation, pp. 331- 336,2005.
[25] Wang Z., Wu G., Sheikh H. R., Simoncelli E. P., Yang E.-H., Bovik A. C., Quality-aware Images. IEEE Transactions on Image Processing, vol. 15, no. 6, pp. 1680-1689, June 2006
[26] Bovik A. C., New Directions in Image and Video Quality Assessment. Processings of IEEE Signal Processing Society International Workshop on Multimedia Signal Processing, Crete, Greece, 2007
[27] Wang Z., Lu L., Bovik A. C., Video Quality Assessment based on Structural Distortion Measurement. Signal Processing: Image Communication, special issue on "Objective video quality metrics", vol. 19, no. 2, pp. 121-132, Feb. 2004.
[28] Seshadrinathan K., Bovik A. C., A Structural Similarity Metric for Video based on Motion Models. Proceeding of IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 15-20, 2007
[29] Wang Z., Li Q., Shang X., Perceptual Image Coding based on a Maximum of Minimal Structural Similarity Criterion. Proceeding of IEEE Int. Conf. Image Processing, San Antonio, TX,Sept. 16-19,2007
[30] Wang Z., Bovik A. C., Simoncelli E. P., Structural Approaches to Image Quality Assessment. Handbook of Image and Video Processing (Al Bovik, eds.), second edition, Academic Press, June 2005
[31] Seshadrinathan K., Sheikh H. R., Wang Z., Bovik A. C., Structural and information theoretical approaches to image quality assessment. Multi-Sensor Image Fusion and Its Applications (R. S. Blum and Z. Liu, eds.), CRC Press, July 2005.
[32] Silverstein D.A., Farrell J.E., The Relationship between Image Fidelity and Image Quality. Proceeding of IEEE Int. Conf. Image Processing, pp. 881-884,1996.
[33] Eckert M. P., Bradley A. P., Perceptual Quality Metrics Applied to Still Image Compression. Signal Processing, vol.70, no. 1, pp. 177-200,1998.
[34] Simoncelli E.P., Statistical Models for Images: Compression, Restoration and Synthesis. Proceeding of 31th Asilomar Conf. Signals, Systems and Computers, pp. 673-678, Nov. 1997.
[35] Liu J., Moulin P., Information-theoretic Analysis of Interscale and Intrascale Dependencies between Image Wavelet Coefficients. IEEE Trans. Image Processing, vol. 10, pp. 1647-1658, Nov.2001.
[36] Shapiro J.M., Embedded Image Coding using Zerotrees of Wavelets Coefficients. IEEE Trans. Signal Processing, vol.41, pp. 3445-3462, Dec.1993.
[37]Said A.,Pearlman W.A.,A New,Fast,and Efficient Image Codec based on Set Partitioning in Hierarchical Trees.IEEE Trans.Circuits Syst.Video Technol.,vol.6,pp.243-250,June 1996.
[38]Hermiston K.J.,Booth D.M.,Image Quality Measurement using Integer Wavelet Transformations.Proceeding of IEEE Int.Conf.Image Processing,vol.2,pp.293-297,1999.
[39]Beghdadi A.,Popescu B.P.,A New Image Distortion Measure based on Wavelet Decomposition,proceedings of Int.Symposium on Signal Processing and Its Applications,vol.1,pp.485-488,July 2003.
[40]Zheng D.,Zhao J.Y.,Tam W.J.,Speranza F.,Image Quality Measurement by Using Digital Watermarking.Proceedings of IEEE Int.Workshop on Haptic,Audio and Visual Environments and Their Applications,pp.65-70,Sept.2003.
[41]熊兴华,张丽,一种基于灰度预测误差统计的影像质量评价方法.中国图象图形学报,vol.9,no.3,pp.302-307,2003.
[42]Seshadrinathan K.,Bovik A.C.,New Vistas in Image and Video Quality Assessment.SPIE Human Vision and Electronic Imaging,San Jose,California,Jan.2007
[43]ITU-R Recommendation BT.500-6.Methodology for the subjective Assesment of the Quality of Television Pictures.1995
[44]Kaiser P.,Boynton R.,Human Color Vision.Optical Society of America,1996
[45]Wandell B.,Foundations of Vision.Sinauer Associates,1995
[46]Grassmann H.G.,Zur Theorie der Farbenmischung.Poggendorffs Annalen der Physik und Chemie,vol.89,pp.69-84,1853
[47]Derrington A.M.,Krauskopf J.,Lennie P.,Chromatic Mechanisms in Lateral Geniculate Nucleus of Macaque.J Physiol.vol.357,pp.241-265,Dec 1984
[48]Shapley R.,Enroth-Cugell C.,Visual Adaptation and Retinal Gain Controls.Progr.Ret.Res.3,pp.263-346,1984
[49]Webster M.,Human Color Perception and its Adaptation.Network Computation in Neural Systems,vol.7,pp.587-634,1996
[50]CIE:Commission Internationale de l'Eclairage,Available:http://www.cie.co.at/index_ie.html
[51]Alleysson D.,The Processing of Chromatic Signal in the Retina:A Basis Model for Human Color Perception.Ph.D.thesis,UJF University Joseph fourier,1999
[52] Atick J. J., Li Z.P., Redlich A. N., Understanding Retinal Color Coding from First Principles. Neural Computation, vol.4, pp.449-572,1992
[53] Guth S. L., Model for color vision and light adaptation. J. Opt. Soc. Am. vol.8, no.6, pp.976-993,1991
[54] Valois R. D., Valois K. D., A Multi-stage Color Model. Vision Res. 33, no.8, pp. 1053-1065, 1993
[55] Winkler S., Issues in Vision Modeling for Perceptual Video Quality Assessment. Signal Processing vol.78, no.2, pp.231-252, 1999
[56] Daugman J. G., Two-dimensional Spectral Analysis of Cortical Receptive Field Profiles. Vision Res. 20, no. 10, pp.847-856,1980
[57] Garcia-Perez M. A., The Perceived Image: Efficient Modeling of Visual inhomogeneity. Spatial Vision, vol.6, no.2, pp.89-99,1992
[58] Watson A. B., The Cortex Transform: Rapid Computation of Simulated Neural Images. Computer Vision, Graphics, and Image Processing, vol.39, no.3, pp.311 -327, 1987
[59] Sweldens W., The lifting Scheme: A Construction of Second Generation Wavelets. SIAM Journal of Mathematical Ana sis. vol.29, no.2, pp.511-546, 1998
[60] Teo P. C., Heeger D. J., Perceptual Image Distortion. Proceeding of IEEE Int. Conf. Image Processing., vol.2, pp.982-986, Nov. 1994
[61] Gersho A., Gray R. M., Vector Quantization and Signal Compression. Kluwer Academic Publishers, Boston/Dordrechet/London, 1992
[62] Levine M.W., Fundamentals of sensation and perception (3rd ed.). Oxford University Press, New York, 2000
[63] Eude T, Cherifi H., On Quality Metrics for Low Bitrate Coding. SPIE Visual Communication and Image Processing, vol.3016, pp.70-81,1997
[64] Ngan K. N., Rao K. S., Singh H., Cosine Transform Coding Incorporating Human Visual System Model. SPIE fiber'86, Cambridge, MA, U.S.A., pp. 165-171, 1986
[65] Nill N. B., A Visual Model Weighted Cosine Transform for Image Compression and Quality Assessment. IEEE Trans. Communications, vol.33, no.3, pp.551-557, 1985
[66] Legge G. E., Foley J. M., Contrast Masing in Human Vision. JOSA, vol.70, no. 12, pp.1458-1471,1980
[67] Comes S., Macq B., Human Visual Quality Criterion. SPIE Visual Communication and Image Processing, vol.1360, pp.2-7, 1990
[68] Saghri J. A., Image Quality Measure based on a Human Visual System Model", Optical Engineering, vol. 28, No. 7, pp. 813-818, July 1989
[69] Daly S., The Visible Differences Predictor: An Algorithm for the Assessment of Image Fidelity. Digital Images and Human Vision, A. B. Watson Ed., Chapter 14, pp. 179-206, the MIT press, 1993
[70] Jayant N., Signal Compression: Technology Targets and Research Directions. IEEE J. Select. Areas Communications, vol. 10. pp. 314-323, June 1992
[71] Jayant N., Johnston J., Safranek R., Signal Compression based on Model of Human Perception. Proceedings of the IEEE, vol. 81, pp. 1385-1422, Oct. 1993
[72] Chou C. H., Li Y. C., A Perceptually Tuned Subband Image Coder based on the Measure of Just-Noticeable-Distortion Profile. IEEE Trans. Circuits and Systems for Video Technology, vol.5, no. 6, pp. 467-476, Dec. 1995
[73] Safranek R. J., Johnston J. D., A Perceptually Tuned Subband Image Coder with Image Dependent Quantization and Post-Quantization Data Compression. Proceedings of IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 3, pp. 1945-1948, 1989
[74] Lubin J., A Visual Discrimination Model for Imaging System Design and Evaluation. Vision Models for Target Detection and Recognition, E. Peli ed., Chapter 10, pp. 245-283, World Scientific Publishing Co. Pte. Ltd., 1995
[75] Karunasekera S.A., Kingsbury N. G., A Distortion Measure for Blocking Artifacts in Images based on Human Visual Sensitivity. IEEE Trans. Image Processing, vol. 4, no. 6, pp. 713-724, June 1995
[76] Sheikh H.R., Bovik A.C., Image Information and Visual Quality. Proceedings of IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol.3, pp.709-712, May 2004
[77] Sheikh H.R., Bovik A.C., de Veciana G., An Information Fidelity Criterion for Image Quality Assessment using Natural Scene Statistics. IEEE Trans. Image Processing, vol.14, pp.2117-2128, Dec. 2005
[78] Zhai, G. T., Zhang, W. J., Yang X., Xu Y, Image Quality Metric with an Integrated Bottom-up and Top-down HVS Approach. IEE Proceedings-Vision, Image and Signal Processing, vol.153, Iss.4, pp.456-460, Aug. 2006
[79] Rao D. V., Babu I. R., Reddy L. P., Sudhakar N., Image Quality Assessment Complemented with Visual Regions of Interest. Proceedings of Int. Conf. Computing: Theory and Applications, pp.681-687, Mar. 2007
[80] Babu R.V., Perkis A., An HVS-based No-Reference Perceptual Quality Assessment of JPEG Coded Images using Neural Networks. Proceedings of IEEE Int. Conf. Image Processing, vol.1, pp.433-436, Sept. 2005
[81] VQEG, Final Report From the Video Quality Experts Group on the Validation of Objective Models of Video Quality Assessment, Phase 11. Aug. 2003 [Online]. Available: http://www.vqeg.org/
[82] Sheikh H.R., Wang Z., Cormack L., Bovik A.C., LIVE Image Quality Assessment Database Release 2. Available: http://live.ece.utexas.edu/research/quality.
[83] Hangai S., Okamoto J., Miyauchi K., An Improvement in Picture Evaluation Measure WSNR for Monochrome Still Picture Considering Local Entropy. Journal of ITE vol.49 No.8 pp. 1078-1086,1995
[84] Kusayama, T., Hamamoto, T., Hangai, S., A Proposal of Objective Measure Considering Subjective Observation Areas. Proceedings of Int. Conf. Image Processing, vol.2, pp. 1089-1092, Oct. 2001
[85] Wang Y. J., Li J. H., Lu Y., Fu Y., Jiang Q.Z., Image Quality Evaluation based on Image Weighted Separating Block Peak Signal to Noise Ratio. Proceedings of Int. Conf. Neural Networks and Signal Processing, vol.2, pp.994-997, Dec. 2003
[86] van Dijk A. M., Jean-Bernard M., Subjective quality assessment of compressed image. Signal Processing, vol.58, pp.235-252 J 997
[87] Simoncelli E. P., Olshausen B., Natural Image Statistics and Neuralrepresentation. Annu. Rev. Neurosci., vol.24, pp. 1193-1216, Jan.2001
[88] Simoncelli E. P., Statistical Models for Images: Compression, Restoration and Synthesis. Proceedings of Asilomar Conf. on Signals, Systems & Computers, vol.1, pp.673-678,Nov 1997
[89] Robert W. B., Simoncelli E. P., Image Compression via Joint Statistical Characterization in the Wavelet Domain. IEEE Transactions on Image Processing, vol.8, no. 12, pp. 1688-1701, Dec. 1999
[90]佟雨兵,胡薇薇,杨东凯,张其善,视频质量评价方法综述.计算机辅助设计与图形学学报,vol.18,no.5,pp.735-741,May 2006
[91]Mallat S.,Zhang Z.,Matching Pursuits with Time-frequency Dictionaries.IEEE Trans.Signal Processing,vol.41,no.12,pp.3397-3415,1993.
[92]Arfken G.,Mathematical Methods for Physicists,3rd ed.Orlando,FL:Academic Press,pp.963-964,1985.
[93]Pati Y.C.,Rezaiifar R.,Krishnaprasad P.S.,Orthogonal Matching Pursuit:Recursive Function Approximation With Applications to Wavelet Decomposition.Proceedings of IEEE Annual Asilomar Conf.Signals,Systems,and Computers,vol.1,pp 40-44,1993
[94]Noff R.,Zakhor A.,Very Low Bit Rate Video Coding based on Matching Pursuits.IEEE Trans.Circuits and Systems for Video Technology,vol.7,No.1,pp.158-171,1997.
[95]Neff R.,Zakhor A.,Matching Pursuit Video Coding—Part Ⅰ:Dictionary Approximation.IEEE Trans.Circuits and Systems for Video Technology,vol.12,No.1,pp.13-26,2002.
[96]de Vleeschouwer C.,Macq B.,New Dictionaries for Matching Pursuit Video Coding.Proceedings of IEEE Int.Conf.Image Processing,pp.764-768,1998.
[97]Redmill D.W.,Bull D.R.,Czerepinki P.,Video Coding using a Fast Non-Separable Matching Pursuits Algorithm.Proceedings of IEEE Int.Conf.Image Processing,vol.1 pp.769-773,1998.
[98]Gonzalez R.C.,Woods R.E.,Digital Image Processing,Second Edition.Prentice Hall,2002.
[99]VQEG:Video Quality Experts Group,"Final Report From The Video Quality Experts Group On The Validation Of Objective Models Of Video Quality Assessment," Mar.2000.Available:http://www.vqeg.org/
[100]Taylor A.E.,Lay D.C.,Introduction to Functional Analysis.John Wiley and Sons,New York,1980.
[101]Deans S.R.,The Radon Transform and Some of Its Applications.Wiley,New York,1983.
[102]Mukundan R.,Ramakrishnan K.R.,Moment Functions in Image Analysis:Theory and Applications.World Scientific,Singpore,1998
[103]Galigekere R.R.,Holdsworth D.W.,Swamy M.N.S.,Fenster A.,Moment Patterns in the Radon Space.Optical Engineering,vol.39,no.4,pp.1088-1097,2000
[104]Galigekere R.R.,Holdsworth D.W.,Swamy M.N.S.,Fenster A.,Moment Patterns in the Radon Space:Invariance to Intensity Scaling.Optical Engineering,vol.40,no.71,pp.409-1411,2001
[105]庄天戈,CT原理与算法.上海交通大学出版社,上海,1992.
[106]Yao W.,He A.Z.,Two-dimensional Interferometric Projection Extraction by Gabor Transform.Journal of the Optical Society of America,vol.12,no.2,pp.121-125,1999
[107]宋一中,贺安之,Radon变换的计算机模拟.光电子·激光,vol.13,no.4,pp.484-487,Apr.2006
[108]史延新,一种利用Radon变换的指纹图像预处理算法.西安工业大学学报,vol.27,no.5,pp.468-470,2007
[109]安志勇,赵珊,王晓华,周利华,基于多尺度Radon变换的图像检索.光子学报,vol.36,no.6,pp.1176-1180,2007
[110]Li J.H.,Pan Q.,Zhang H.C.,et al.,Image Recognition using Radon transform.Proceedings of IEEE Int.Conf.Intelligent Transportation Systems Ⅳ:Image Analysis,vol.4,pp.741-745,2004
[111]Sheikh H.R.,Sabir M.F.,Bovik A.C.,A Statistical Evaluation of Recent Full Reference Image Quality Assessment Algorithms,IEEE Transactions on Image Processing,vol.15,no.11,pp.3440-3451,Nov.2006
[2]Wang Z.,Bovik A.C.,Sheikh H.R.,Simoncelli E.P.,Image Quality Assessment:From Error Visibility to Structural Similarity.IEEE Trans.Image Processing,vol.13,No.4,pp.600-612,April 2004.
[3]Wang Z.,Bovik A.C.,Lu L..Why is Image Quality Assessment so Difficult.Proceeding of IEEE Int.Conf Acoust,Speech,and Signal Processing,vol.4(3313-3316),May 2002.
[4]Mannos J.L.,Sakrison D.J.,The Effects of a Visual Fidelity Criterion on the Encoding of Images.IEEE Trans.Information Theory,vol.20,No.4(525-536),1974
[5]Watson A.B.,DCT Quantization Matrices Visually Optimized for Individual Images.Presented at Human Vision,Visual Processing,and Digital Display IV,Bellingham,WA,1993.
[6]Google,Available:www.google.com.
[7]VQEG:Video Quality Experts Group,Available:http://www.vqeg.org/.
[8]Wu H.R.,Rao K.R.,Digital Video Image Quality and Perceptual Coding.Presented at Signal Processing and Communications,CRC Press,2006
[9]李均利,陈刚,池哲儒,张直.客观评价图像质量编码新方法.中国图象图形学报,vol.11,no.9,pp.1348-1355,2004.
[10]Pappas T.N.,Safranek R.J.,Chen J.,Perceptual criteria for image quality evaluation.Chapter 8.2 in The Handbook of Image and Video Processing,Second Edition,A.C.Bovik,(Ed.),New York:Elsevier Academic Press,pp.939-960,2005.
[11]VQEG,Final VQEG Report on the Validation of Objective quality metrics for video quality assessment.Available:http://www.its.bidrdoe.gov/vqeg/projects/frtv phasel/index.php.
[12]Beegan A.P.,Iyer L.R.,Bell A.E.,Maher V.R.,Ross M.A.,Design and Evaluation of Perceptual Masks for Wavelet Image Compression.Proceeding of IEEE Digital Signal Processing Workshop,pp.88-93,2002.
[13]Eskicioglu A.M.,Fisher P.S.,Image Quality Measures and Their Performance.IEEE Transactions on Communications,vol.43,no.12,pp.2959-2965,Dec.1995.
[14] Beaton R.J., Quantitative Models of Image Quality. Proceeding of the Human Factors Society-27~(th) Annual Meeting, pp.41-45, 1983
[15] Franti P., Blockwise Distortion Measure for Statistical and Structural Errors in Digital Images. Signal Processing: Image communication, Vol.13, pp.89-98, 1998
[16] Winkler S., Issues in Vision Modeling for Perceptual Video Quality Assessment. Signal Processing, vol.78, no.2, pp.231-252, 1999
[17] Eskicioglu A. M., Quality Measurement for Monochrome Compressed Images in the Past 25 years. Proceeding of IEEE Int. Conf. Acoustics, Speech, Signal Processing, vol. 4, pp. 1907-1910, Istanbul, Turkey, Jun. 2000
[18] Wang Z., Bovik A. C, A Universal Image Quality Index. IEEE Signal Processing Letters, vol. 9, pp. 81-84, Mar. 2002
[19] Shnayderman A., Gusev A., Eskicioglu A. M., An SVD-based Grayscale Image Quality Measure for Local and Global Assessment. IEEE Trans. Image Processing, vol. 15, no. 2, pp. 422-429, Feb. 2006.
[20] Sheikh H.R., Bovik A.C., Image Information and Visual Quality. IEEE Trans. Image Processing, vol.15, no.2, pp. 430- 444, Feb. 2006
[21] Li J. L., Chen G, Chi Z. R., Lu C. G, Image Coding Quality Assessment Using Fuzzy Integrals With a Three-Component Image Model. IEEE Transactions on Fuzzy Systems, 2004, vol.12, no. 1, pp.99-106
[22] Wang S., Zheng D, Zhao J. Y., Tarn W. J., Speranza F., An Image Quality Evaluation Method Based on Digital Watermarking. IEEE Trans. Circuits and Systems for Video Technology, Vol. 17, No. 1, January 2007.
[23] Campisi P., Carli M., Giunta G., Neri A., Blind Quality Assessment System for Multimedia Communications Using Tracing Watermarking. IEEE Trans. Signal Processing. vol. 51, no. 4, pp. 996-1002, Apr. 2003.
[24] Zhai GT., Zhang W. J. Yang X.K., Xu Y, Image Quality Assessment Metrics based on Multi-Scale Edge Presentation. Proceeding of IEEE Workshop on Signal Processing Systems Design and Implementation, pp. 331- 336,2005.
[25] Wang Z., Wu G., Sheikh H. R., Simoncelli E. P., Yang E.-H., Bovik A. C., Quality-aware Images. IEEE Transactions on Image Processing, vol. 15, no. 6, pp. 1680-1689, June 2006
[26] Bovik A. C., New Directions in Image and Video Quality Assessment. Processings of IEEE Signal Processing Society International Workshop on Multimedia Signal Processing, Crete, Greece, 2007
[27] Wang Z., Lu L., Bovik A. C., Video Quality Assessment based on Structural Distortion Measurement. Signal Processing: Image Communication, special issue on "Objective video quality metrics", vol. 19, no. 2, pp. 121-132, Feb. 2004.
[28] Seshadrinathan K., Bovik A. C., A Structural Similarity Metric for Video based on Motion Models. Proceeding of IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 15-20, 2007
[29] Wang Z., Li Q., Shang X., Perceptual Image Coding based on a Maximum of Minimal Structural Similarity Criterion. Proceeding of IEEE Int. Conf. Image Processing, San Antonio, TX,Sept. 16-19,2007
[30] Wang Z., Bovik A. C., Simoncelli E. P., Structural Approaches to Image Quality Assessment. Handbook of Image and Video Processing (Al Bovik, eds.), second edition, Academic Press, June 2005
[31] Seshadrinathan K., Sheikh H. R., Wang Z., Bovik A. C., Structural and information theoretical approaches to image quality assessment. Multi-Sensor Image Fusion and Its Applications (R. S. Blum and Z. Liu, eds.), CRC Press, July 2005.
[32] Silverstein D.A., Farrell J.E., The Relationship between Image Fidelity and Image Quality. Proceeding of IEEE Int. Conf. Image Processing, pp. 881-884,1996.
[33] Eckert M. P., Bradley A. P., Perceptual Quality Metrics Applied to Still Image Compression. Signal Processing, vol.70, no. 1, pp. 177-200,1998.
[34] Simoncelli E.P., Statistical Models for Images: Compression, Restoration and Synthesis. Proceeding of 31th Asilomar Conf. Signals, Systems and Computers, pp. 673-678, Nov. 1997.
[35] Liu J., Moulin P., Information-theoretic Analysis of Interscale and Intrascale Dependencies between Image Wavelet Coefficients. IEEE Trans. Image Processing, vol. 10, pp. 1647-1658, Nov.2001.
[36] Shapiro J.M., Embedded Image Coding using Zerotrees of Wavelets Coefficients. IEEE Trans. Signal Processing, vol.41, pp. 3445-3462, Dec.1993.
[37]Said A.,Pearlman W.A.,A New,Fast,and Efficient Image Codec based on Set Partitioning in Hierarchical Trees.IEEE Trans.Circuits Syst.Video Technol.,vol.6,pp.243-250,June 1996.
[38]Hermiston K.J.,Booth D.M.,Image Quality Measurement using Integer Wavelet Transformations.Proceeding of IEEE Int.Conf.Image Processing,vol.2,pp.293-297,1999.
[39]Beghdadi A.,Popescu B.P.,A New Image Distortion Measure based on Wavelet Decomposition,proceedings of Int.Symposium on Signal Processing and Its Applications,vol.1,pp.485-488,July 2003.
[40]Zheng D.,Zhao J.Y.,Tam W.J.,Speranza F.,Image Quality Measurement by Using Digital Watermarking.Proceedings of IEEE Int.Workshop on Haptic,Audio and Visual Environments and Their Applications,pp.65-70,Sept.2003.
[41]熊兴华,张丽,一种基于灰度预测误差统计的影像质量评价方法.中国图象图形学报,vol.9,no.3,pp.302-307,2003.
[42]Seshadrinathan K.,Bovik A.C.,New Vistas in Image and Video Quality Assessment.SPIE Human Vision and Electronic Imaging,San Jose,California,Jan.2007
[43]ITU-R Recommendation BT.500-6.Methodology for the subjective Assesment of the Quality of Television Pictures.1995
[44]Kaiser P.,Boynton R.,Human Color Vision.Optical Society of America,1996
[45]Wandell B.,Foundations of Vision.Sinauer Associates,1995
[46]Grassmann H.G.,Zur Theorie der Farbenmischung.Poggendorffs Annalen der Physik und Chemie,vol.89,pp.69-84,1853
[47]Derrington A.M.,Krauskopf J.,Lennie P.,Chromatic Mechanisms in Lateral Geniculate Nucleus of Macaque.J Physiol.vol.357,pp.241-265,Dec 1984
[48]Shapley R.,Enroth-Cugell C.,Visual Adaptation and Retinal Gain Controls.Progr.Ret.Res.3,pp.263-346,1984
[49]Webster M.,Human Color Perception and its Adaptation.Network Computation in Neural Systems,vol.7,pp.587-634,1996
[50]CIE:Commission Internationale de l'Eclairage,Available:http://www.cie.co.at/index_ie.html
[51]Alleysson D.,The Processing of Chromatic Signal in the Retina:A Basis Model for Human Color Perception.Ph.D.thesis,UJF University Joseph fourier,1999
[52] Atick J. J., Li Z.P., Redlich A. N., Understanding Retinal Color Coding from First Principles. Neural Computation, vol.4, pp.449-572,1992
[53] Guth S. L., Model for color vision and light adaptation. J. Opt. Soc. Am. vol.8, no.6, pp.976-993,1991
[54] Valois R. D., Valois K. D., A Multi-stage Color Model. Vision Res. 33, no.8, pp. 1053-1065, 1993
[55] Winkler S., Issues in Vision Modeling for Perceptual Video Quality Assessment. Signal Processing vol.78, no.2, pp.231-252, 1999
[56] Daugman J. G., Two-dimensional Spectral Analysis of Cortical Receptive Field Profiles. Vision Res. 20, no. 10, pp.847-856,1980
[57] Garcia-Perez M. A., The Perceived Image: Efficient Modeling of Visual inhomogeneity. Spatial Vision, vol.6, no.2, pp.89-99,1992
[58] Watson A. B., The Cortex Transform: Rapid Computation of Simulated Neural Images. Computer Vision, Graphics, and Image Processing, vol.39, no.3, pp.311 -327, 1987
[59] Sweldens W., The lifting Scheme: A Construction of Second Generation Wavelets. SIAM Journal of Mathematical Ana sis. vol.29, no.2, pp.511-546, 1998
[60] Teo P. C., Heeger D. J., Perceptual Image Distortion. Proceeding of IEEE Int. Conf. Image Processing., vol.2, pp.982-986, Nov. 1994
[61] Gersho A., Gray R. M., Vector Quantization and Signal Compression. Kluwer Academic Publishers, Boston/Dordrechet/London, 1992
[62] Levine M.W., Fundamentals of sensation and perception (3rd ed.). Oxford University Press, New York, 2000
[63] Eude T, Cherifi H., On Quality Metrics for Low Bitrate Coding. SPIE Visual Communication and Image Processing, vol.3016, pp.70-81,1997
[64] Ngan K. N., Rao K. S., Singh H., Cosine Transform Coding Incorporating Human Visual System Model. SPIE fiber'86, Cambridge, MA, U.S.A., pp. 165-171, 1986
[65] Nill N. B., A Visual Model Weighted Cosine Transform for Image Compression and Quality Assessment. IEEE Trans. Communications, vol.33, no.3, pp.551-557, 1985
[66] Legge G. E., Foley J. M., Contrast Masing in Human Vision. JOSA, vol.70, no. 12, pp.1458-1471,1980
[67] Comes S., Macq B., Human Visual Quality Criterion. SPIE Visual Communication and Image Processing, vol.1360, pp.2-7, 1990
[68] Saghri J. A., Image Quality Measure based on a Human Visual System Model", Optical Engineering, vol. 28, No. 7, pp. 813-818, July 1989
[69] Daly S., The Visible Differences Predictor: An Algorithm for the Assessment of Image Fidelity. Digital Images and Human Vision, A. B. Watson Ed., Chapter 14, pp. 179-206, the MIT press, 1993
[70] Jayant N., Signal Compression: Technology Targets and Research Directions. IEEE J. Select. Areas Communications, vol. 10. pp. 314-323, June 1992
[71] Jayant N., Johnston J., Safranek R., Signal Compression based on Model of Human Perception. Proceedings of the IEEE, vol. 81, pp. 1385-1422, Oct. 1993
[72] Chou C. H., Li Y. C., A Perceptually Tuned Subband Image Coder based on the Measure of Just-Noticeable-Distortion Profile. IEEE Trans. Circuits and Systems for Video Technology, vol.5, no. 6, pp. 467-476, Dec. 1995
[73] Safranek R. J., Johnston J. D., A Perceptually Tuned Subband Image Coder with Image Dependent Quantization and Post-Quantization Data Compression. Proceedings of IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 3, pp. 1945-1948, 1989
[74] Lubin J., A Visual Discrimination Model for Imaging System Design and Evaluation. Vision Models for Target Detection and Recognition, E. Peli ed., Chapter 10, pp. 245-283, World Scientific Publishing Co. Pte. Ltd., 1995
[75] Karunasekera S.A., Kingsbury N. G., A Distortion Measure for Blocking Artifacts in Images based on Human Visual Sensitivity. IEEE Trans. Image Processing, vol. 4, no. 6, pp. 713-724, June 1995
[76] Sheikh H.R., Bovik A.C., Image Information and Visual Quality. Proceedings of IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol.3, pp.709-712, May 2004
[77] Sheikh H.R., Bovik A.C., de Veciana G., An Information Fidelity Criterion for Image Quality Assessment using Natural Scene Statistics. IEEE Trans. Image Processing, vol.14, pp.2117-2128, Dec. 2005
[78] Zhai, G. T., Zhang, W. J., Yang X., Xu Y, Image Quality Metric with an Integrated Bottom-up and Top-down HVS Approach. IEE Proceedings-Vision, Image and Signal Processing, vol.153, Iss.4, pp.456-460, Aug. 2006
[79] Rao D. V., Babu I. R., Reddy L. P., Sudhakar N., Image Quality Assessment Complemented with Visual Regions of Interest. Proceedings of Int. Conf. Computing: Theory and Applications, pp.681-687, Mar. 2007
[80] Babu R.V., Perkis A., An HVS-based No-Reference Perceptual Quality Assessment of JPEG Coded Images using Neural Networks. Proceedings of IEEE Int. Conf. Image Processing, vol.1, pp.433-436, Sept. 2005
[81] VQEG, Final Report From the Video Quality Experts Group on the Validation of Objective Models of Video Quality Assessment, Phase 11. Aug. 2003 [Online]. Available: http://www.vqeg.org/
[82] Sheikh H.R., Wang Z., Cormack L., Bovik A.C., LIVE Image Quality Assessment Database Release 2. Available: http://live.ece.utexas.edu/research/quality.
[83] Hangai S., Okamoto J., Miyauchi K., An Improvement in Picture Evaluation Measure WSNR for Monochrome Still Picture Considering Local Entropy. Journal of ITE vol.49 No.8 pp. 1078-1086,1995
[84] Kusayama, T., Hamamoto, T., Hangai, S., A Proposal of Objective Measure Considering Subjective Observation Areas. Proceedings of Int. Conf. Image Processing, vol.2, pp. 1089-1092, Oct. 2001
[85] Wang Y. J., Li J. H., Lu Y., Fu Y., Jiang Q.Z., Image Quality Evaluation based on Image Weighted Separating Block Peak Signal to Noise Ratio. Proceedings of Int. Conf. Neural Networks and Signal Processing, vol.2, pp.994-997, Dec. 2003
[86] van Dijk A. M., Jean-Bernard M., Subjective quality assessment of compressed image. Signal Processing, vol.58, pp.235-252 J 997
[87] Simoncelli E. P., Olshausen B., Natural Image Statistics and Neuralrepresentation. Annu. Rev. Neurosci., vol.24, pp. 1193-1216, Jan.2001
[88] Simoncelli E. P., Statistical Models for Images: Compression, Restoration and Synthesis. Proceedings of Asilomar Conf. on Signals, Systems & Computers, vol.1, pp.673-678,Nov 1997
[89] Robert W. B., Simoncelli E. P., Image Compression via Joint Statistical Characterization in the Wavelet Domain. IEEE Transactions on Image Processing, vol.8, no. 12, pp. 1688-1701, Dec. 1999
[90]佟雨兵,胡薇薇,杨东凯,张其善,视频质量评价方法综述.计算机辅助设计与图形学学报,vol.18,no.5,pp.735-741,May 2006
[91]Mallat S.,Zhang Z.,Matching Pursuits with Time-frequency Dictionaries.IEEE Trans.Signal Processing,vol.41,no.12,pp.3397-3415,1993.
[92]Arfken G.,Mathematical Methods for Physicists,3rd ed.Orlando,FL:Academic Press,pp.963-964,1985.
[93]Pati Y.C.,Rezaiifar R.,Krishnaprasad P.S.,Orthogonal Matching Pursuit:Recursive Function Approximation With Applications to Wavelet Decomposition.Proceedings of IEEE Annual Asilomar Conf.Signals,Systems,and Computers,vol.1,pp 40-44,1993
[94]Noff R.,Zakhor A.,Very Low Bit Rate Video Coding based on Matching Pursuits.IEEE Trans.Circuits and Systems for Video Technology,vol.7,No.1,pp.158-171,1997.
[95]Neff R.,Zakhor A.,Matching Pursuit Video Coding—Part Ⅰ:Dictionary Approximation.IEEE Trans.Circuits and Systems for Video Technology,vol.12,No.1,pp.13-26,2002.
[96]de Vleeschouwer C.,Macq B.,New Dictionaries for Matching Pursuit Video Coding.Proceedings of IEEE Int.Conf.Image Processing,pp.764-768,1998.
[97]Redmill D.W.,Bull D.R.,Czerepinki P.,Video Coding using a Fast Non-Separable Matching Pursuits Algorithm.Proceedings of IEEE Int.Conf.Image Processing,vol.1 pp.769-773,1998.
[98]Gonzalez R.C.,Woods R.E.,Digital Image Processing,Second Edition.Prentice Hall,2002.
[99]VQEG:Video Quality Experts Group,"Final Report From The Video Quality Experts Group On The Validation Of Objective Models Of Video Quality Assessment," Mar.2000.Available:http://www.vqeg.org/
[100]Taylor A.E.,Lay D.C.,Introduction to Functional Analysis.John Wiley and Sons,New York,1980.
[101]Deans S.R.,The Radon Transform and Some of Its Applications.Wiley,New York,1983.
[102]Mukundan R.,Ramakrishnan K.R.,Moment Functions in Image Analysis:Theory and Applications.World Scientific,Singpore,1998
[103]Galigekere R.R.,Holdsworth D.W.,Swamy M.N.S.,Fenster A.,Moment Patterns in the Radon Space.Optical Engineering,vol.39,no.4,pp.1088-1097,2000
[104]Galigekere R.R.,Holdsworth D.W.,Swamy M.N.S.,Fenster A.,Moment Patterns in the Radon Space:Invariance to Intensity Scaling.Optical Engineering,vol.40,no.71,pp.409-1411,2001
[105]庄天戈,CT原理与算法.上海交通大学出版社,上海,1992.
[106]Yao W.,He A.Z.,Two-dimensional Interferometric Projection Extraction by Gabor Transform.Journal of the Optical Society of America,vol.12,no.2,pp.121-125,1999
[107]宋一中,贺安之,Radon变换的计算机模拟.光电子·激光,vol.13,no.4,pp.484-487,Apr.2006
[108]史延新,一种利用Radon变换的指纹图像预处理算法.西安工业大学学报,vol.27,no.5,pp.468-470,2007
[109]安志勇,赵珊,王晓华,周利华,基于多尺度Radon变换的图像检索.光子学报,vol.36,no.6,pp.1176-1180,2007
[110]Li J.H.,Pan Q.,Zhang H.C.,et al.,Image Recognition using Radon transform.Proceedings of IEEE Int.Conf.Intelligent Transportation Systems Ⅳ:Image Analysis,vol.4,pp.741-745,2004
[111]Sheikh H.R.,Sabir M.F.,Bovik A.C.,A Statistical Evaluation of Recent Full Reference Image Quality Assessment Algorithms,IEEE Transactions on Image Processing,vol.15,no.11,pp.3440-3451,Nov.2006