基于多维矢量DCT正交矩阵的视频流压缩算法的研究
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摘要
当今社会,随着数字通信和网络技术的飞速发展,人们对视频和图像业务的需求越来越大。视频图像作为最丰富的信息载体,已经成为构建信息环境所必须的环节。然而视频和图像的数据量庞大,这就需要对其进行压缩编码以适应存储和传输的要求。
为了更有效地压缩彩色图像,本实验室提出了四维矩阵的理论,建立了四维n阶矩阵模型,定义了一个全新的四维n阶矩阵乘法,并借助Hadamard矩阵的构成原理成功地找到了四维n阶矩阵空间中的正交方阵。该模型通过与经典离散余弦变换(DCT)相结合,可以取得良好的图像压缩效果。
本文引入了多维矢量矩阵的概念,给出了多维矢量矩阵的基本定义和乘法及转置的运算准则。并作为特例建立了四维矢量矩阵乘法的模型,定义了四维矢量矩阵的正交变换,并且创新性的提出了四维矢量DCT正交变换矩阵,并对其正交性作了详细的公式证明。在该理论的应用中,将CIF格式的视频流的YUV三帧分别建立三维数据模型,并利用四维矢量矩阵正交变换算法,将四维矢量DCT操作算子和二维DCT操作算子结合,对三维数据模型进行正交变换,以达到压缩目的。
最后以Visual C++6.0为工具,编程实现了基于多维矢量DCT正交矩阵的视频流变换压缩算法,并对实验结果进行了分析;从实验结果可以看出本文方法的可行性及有效性;同时还总结了该算法尚未完善和有待进一步发掘与研究的地方,并展望了该算法继续改进的方向。
At present, the digital video and image processing technology and the relative products and services are undergoing remarkable progress. It is almost certain that digital video and image processing technology have a significant economic impact on the computers, telecommunications, videos and image industries. But the huge data of video and image makes the storage of memory, channel transmission rate of trunk line and the speed of computer work hard, which is the bottle-neck problem of the implements of multi-video application. We have two solutions to solve the problem. Firstly, we extend the storage of the memory, increase the channel transmission rate of trunk line and improve the speed of computer, which is hardly to realize for the performance of hardware is limited. Secondly, we reduce the quantity of data, store and transmit the data in the form of compress in order to relax the technology pressure radically which the huge data brings. We get rid of the redundant information and keep the independent information so as to compress the data. Obviously, the best solution is compressing and coding the video information.
In this paper, we first introduced the video coding theory,such as Predictive Coding,Transform Coding and entropy coding. We also introduce international standards,for example:JPEG, H.26X, MPEG, AVS.
Due to the traditional encoding theory doesn’t consider the redundancy of the YUV or RGB frames. Our laboratory has proposed a new expression idea named multi-dimensional matrix theory, which is capable of expressing the three consecutive frames of a color image into a whole mathematical model to reduce its color redundancy. With the theory of 4-D nth order matrix, the model has been used in the color image compression, which has got a better effect.
In this paper, the theory of multi- dimensional vector matrix redefines the concept of multi- dimensional matrix, which makes the multiplication of the matrixes is more flexible and universal. The paper also extends the application of the color image compression to the color video compression, and proposes the 4-D vector DCT orthogonal transform matrix on the basis of 4-D nth Hadamard orthogonal transform matrix, which has more flexibility.
Finally, this paper lists out the performance of the 4-D nth order matrix orthogonal transform by using Visual C ++ 6.0 under Windows environment. The experimental results of our algorithm have shown its better concentration for energy, which definitely proves the effectiveness of our algorithm.
However, the 4-D vector DCT orthogonal transform matrix which is based on the theory of multi- dimensional vector matrix is still a new image compression algorithm and surely needs further improving. For instance, the decoded video has blocking effect, so we could use the multi-dimensional loop-filter to eliminate the blocking effect. In addition, we should find the finest scanning and encoding method to improve the compression ratio.
为了更有效地压缩彩色图像,本实验室提出了四维矩阵的理论,建立了四维n阶矩阵模型,定义了一个全新的四维n阶矩阵乘法,并借助Hadamard矩阵的构成原理成功地找到了四维n阶矩阵空间中的正交方阵。该模型通过与经典离散余弦变换(DCT)相结合,可以取得良好的图像压缩效果。
本文引入了多维矢量矩阵的概念,给出了多维矢量矩阵的基本定义和乘法及转置的运算准则。并作为特例建立了四维矢量矩阵乘法的模型,定义了四维矢量矩阵的正交变换,并且创新性的提出了四维矢量DCT正交变换矩阵,并对其正交性作了详细的公式证明。在该理论的应用中,将CIF格式的视频流的YUV三帧分别建立三维数据模型,并利用四维矢量矩阵正交变换算法,将四维矢量DCT操作算子和二维DCT操作算子结合,对三维数据模型进行正交变换,以达到压缩目的。
最后以Visual C++6.0为工具,编程实现了基于多维矢量DCT正交矩阵的视频流变换压缩算法,并对实验结果进行了分析;从实验结果可以看出本文方法的可行性及有效性;同时还总结了该算法尚未完善和有待进一步发掘与研究的地方,并展望了该算法继续改进的方向。
At present, the digital video and image processing technology and the relative products and services are undergoing remarkable progress. It is almost certain that digital video and image processing technology have a significant economic impact on the computers, telecommunications, videos and image industries. But the huge data of video and image makes the storage of memory, channel transmission rate of trunk line and the speed of computer work hard, which is the bottle-neck problem of the implements of multi-video application. We have two solutions to solve the problem. Firstly, we extend the storage of the memory, increase the channel transmission rate of trunk line and improve the speed of computer, which is hardly to realize for the performance of hardware is limited. Secondly, we reduce the quantity of data, store and transmit the data in the form of compress in order to relax the technology pressure radically which the huge data brings. We get rid of the redundant information and keep the independent information so as to compress the data. Obviously, the best solution is compressing and coding the video information.
In this paper, we first introduced the video coding theory,such as Predictive Coding,Transform Coding and entropy coding. We also introduce international standards,for example:JPEG, H.26X, MPEG, AVS.
Due to the traditional encoding theory doesn’t consider the redundancy of the YUV or RGB frames. Our laboratory has proposed a new expression idea named multi-dimensional matrix theory, which is capable of expressing the three consecutive frames of a color image into a whole mathematical model to reduce its color redundancy. With the theory of 4-D nth order matrix, the model has been used in the color image compression, which has got a better effect.
In this paper, the theory of multi- dimensional vector matrix redefines the concept of multi- dimensional matrix, which makes the multiplication of the matrixes is more flexible and universal. The paper also extends the application of the color image compression to the color video compression, and proposes the 4-D vector DCT orthogonal transform matrix on the basis of 4-D nth Hadamard orthogonal transform matrix, which has more flexibility.
Finally, this paper lists out the performance of the 4-D nth order matrix orthogonal transform by using Visual C ++ 6.0 under Windows environment. The experimental results of our algorithm have shown its better concentration for energy, which definitely proves the effectiveness of our algorithm.
However, the 4-D vector DCT orthogonal transform matrix which is based on the theory of multi- dimensional vector matrix is still a new image compression algorithm and surely needs further improving. For instance, the decoded video has blocking effect, so we could use the multi-dimensional loop-filter to eliminate the blocking effect. In addition, we should find the finest scanning and encoding method to improve the compression ratio.
引文
[1] 毕厚杰,新一代视频压缩编码标准 H.264/AVC,人民邮电出版社,2005.5
[2] 石迎波,MPEG-4 视频编码系统的研究与实现,西安电子科技大学通信与信息系统,2005,01(01),pp:1-2
[3] 徐敏,基于聚类搜索的彩色分形图像压缩编码,复旦大学计算机应用技术,2005,20(05),pp:8-10
[4] 沈兰荪、卓力,视频编码与低速率传输,电子工业出版社,2001.12 第一版
[5] 朱剑英,基于 DCT 变换的图像编码方法研究,南京理工大学通信与信息系统,2004,01(03),pp:3-5
[6] 毕厚杰,多媒体信息的传输和处理,人民邮电出版社,1999
[7] 朱秀昌,多媒体网络通信技术及应用,电子工业出版社,1998
[8] 戴逸民,段占云,郭东风,V.34 高速 Modem 的通信标准及其实现,电信科学,1998
[9] 许刚,JPEG2000 感兴趣区编码实现的研究,武汉理工大学检测技术与自动化装置,2005.05,pp:13-14
[10] Mark Nelson and Jean-loup G.Ailly, The Data Compression Book 2nd edition, IDG Books Worldwide, Inc 1995
[11] 刘玮、王红星,图像的无损压缩编码方法及 JPEG 标准模式,现代电子技术,2002 年第 5 期,pp:7-11
[12] 崔春艳、李彩霞,基于 DCT 变换的数字图像压缩技术及其 Matlab 实现,现代电子技术,2002 年第 9 期,pp:7-9
[13] 蓝波,图像无损压缩方法的研究与实现,中国科学技术大学计算机应用,2004.03,pp:22-26
[14] S.W.Golomb, Run-length encoding, IEEE trans. IT, 1996,12(3), pp:399-401
[15] W.Berghorn, T.Boskamp, M.Lang and H.O.Peitgen, Context conditioning and run –length coding for hybrid, embedded progressive image coding, IEEE trans Image processing,2001,10(12), pp:1791-1792
[16] Jinhua Yu, Advantages of Uniform Scalar Dead-zone Quantization in Image Coding System, IEEE.2004, pp:805-808
[17] M.A.Golner, W.B. Mikhael, V.Krishnan and A.Ramaswamy, Region Based Variable Quantization for JPEG Image Compression, IEEE Midwest Symposium on Circuits and Systems, Lansing MI,USA, Aug 2000, pp:8-11
[18] Gopal Lakhani, Improving DC Coding Models of JPEG Arithmetic Coder, IEEE SIGNAL PROCESSING LETTERS, May 2004, pp505-508
[19] 孙圣和、陆哲明,矢量量化技术及应用,北京:科技出版社,2002.05 第 1 版,pp.31-49
[20] 吴乐南,数据压缩的原理与应用,北京:电子工业出版社,1995.02 第 1 版,pp.21-25
[21] Gregory.K.Wallace, The JPEG Still Picture compression standard, IEEE Transactions on Consumer Electronics,1992,38(1)
[22] A.Zandi, J.D.Allen, E.L.Schwartz , M.Boliek, CREW:compression with eversible embedded wavelets, Proc.IEEE Data Compression Conf, March 1995, pp:212-221
[23] Adams.M.D, The JPEG-2000 Still Image Compression Standard, 1SO/IEC JTC I/SC 29/WGI N2412, 2001.09
[24] ISO/IECJTCl/SC29/WG1(ITU-TSG8), JPEG2000 Partl Final Committee Draft Version 1.0, 2000
[25] 焦晓、朱光喜、马明罡,JPEG2000 的编码技术,计算机仿真,2003,20(9),pp:112-114
[26] M Charrier, D .S Cruz, M Larsson, JPEG2000:the next millennium compression standard for still images, Proc IEEE Int .Conf. Multimedia Computing and Systems (ICMCS), June 1999, vol.1, pp:131-132
[27] 桑爱军、陈贺新,三维矩阵彩色图像 WDCT 压缩编码,电子学报,2002,30(4),pp:594-597
[28] 朱艳秋、陈贺新、戴逸松,彩色图像三维矩阵变换压缩编码,电子学报,1997,25(7),pp:16-21
[29] 韩晓微,彩色图像处理关键技术研究,东北大学控制理论和控制工程,2005.01,pp:35-38
[30] E.M.Granger,J.C.Heurtley,Visual chromaticity-modulation transfer function,J.Opt.Soc. Am.,1973, vol.63, pp:1173-1174
[31] K.T.Mullen, The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings, J. Physiol., 1985, vol.359, pp:381-400.
[32] Charles Poynton, Color Science and Color Appearance Models for CG, HDTV and D-Cinema, SIGGRAPH2004 course 2, 2004.05, pp:33
[33] 张鹤,基于四维n阶矩阵的彩色图像正交变换算法的研究,吉林大学通信与信息系统,2007
[34] 何东健,数字图像处理,西安电子科技大学出版社,2003.07第1版,pp:234-236
[35] 刘鹏举,基于小波变换的图像压缩技术研究,西北工业大学电路与系统,2005.01,pp:6-7
[36] 马会礼,基于小波变换的图像压缩方法研究,大连理工大学电子与通信工程,2005.03,pp:24-25
[37] 罗军、程存学,图像文件格式及其在WINDOWS环境下的使用,声学与电子工程,1995年第3期 pp:22-29
[38] Lawrence.A.Rowe, Equipment, Facilities and Transmission, Berkeley Multimedia Research Center University of California at Berkeley, Oct. 2000, pp:6-12
[39] 林福宗,图像文件格式(上)-Windows 编程,北京:清华大学出版社,1996.12第 1 版,pp:40-48
[40] 田玉敏、梁若莹,计算机彩色输入输出设备常用颜色空间及其转换,计算机工程,2002,28(9),pp:198-200
[41] 李孝安、张晓缋,神经网络与神经计算机导论,西安:西安电子工业出版社,1994.10第1版,pp:34-41
[42] W.Sweldens, The Lifting Scheme:A Custom-design Construction of orthogonal Wavelets, Appl.Comut.Harmon.Appl.,1996,3(2), pp:186-200
[43] Daubechies.I, Sweldens.W., Factoring Wavelet Transforms into Lifting Steps, Journal of Fourier Analysis and Application,1998,5(3), pp:245-267
[44] Calderbank.A.R, Daubechies.I, Sweldens.W, Wavelet transforms that map integers to integers , Applied and Computational Harmonic analysis, 1998,5(3), pp:332-369.
[45] Mandelbrot.B.B, Fractals Form , Chance, and Dimension, W.H.Freeman and Co., San Francisco,1977
[46] Jacquin.A.E, Image coding based on a fractal theory of iterated contractive image transformations, IEEE Transactions on Image Processing, 1992,1(1), pp:18-30
[47] Woods.JW, O'Neil.S.D.,Subband coding of images, IEEE Transactions on Acoustic, Speech and Signal Processing, 1986,34(5), pp:1278-1288.
[48] Mallat.S, A Theory for Multi-resolution Signal Decomposition: the wavelet representation, IEEE Transaction on Pattern Analysis and Machine Intelligence, 1989,11(7), pp:674-693.
[49] 高雪峰,快速分形图像编码及高压缩比纹理压缩方法研究,西北工业大学计算数学,2005.03,pp:7-8.
[50] 容观澳,计算机图像处理,北京:清华大学出版社,2000.02第1版,2003.06第4次印刷,pp:98-102
[51] Andrew.B.Watson, Image Compression Using the Discrete cosine transform, Mathematical Journal, 1994,4(1), pp:81-88
[52] Syed.Ali.Khayam,The Discrete Cosine Transform: Theory and Application, ECE802-602: Information Theory and Coding, 2003.03
[2] 石迎波,MPEG-4 视频编码系统的研究与实现,西安电子科技大学通信与信息系统,2005,01(01),pp:1-2
[3] 徐敏,基于聚类搜索的彩色分形图像压缩编码,复旦大学计算机应用技术,2005,20(05),pp:8-10
[4] 沈兰荪、卓力,视频编码与低速率传输,电子工业出版社,2001.12 第一版
[5] 朱剑英,基于 DCT 变换的图像编码方法研究,南京理工大学通信与信息系统,2004,01(03),pp:3-5
[6] 毕厚杰,多媒体信息的传输和处理,人民邮电出版社,1999
[7] 朱秀昌,多媒体网络通信技术及应用,电子工业出版社,1998
[8] 戴逸民,段占云,郭东风,V.34 高速 Modem 的通信标准及其实现,电信科学,1998
[9] 许刚,JPEG2000 感兴趣区编码实现的研究,武汉理工大学检测技术与自动化装置,2005.05,pp:13-14
[10] Mark Nelson and Jean-loup G.Ailly, The Data Compression Book 2nd edition, IDG Books Worldwide, Inc 1995
[11] 刘玮、王红星,图像的无损压缩编码方法及 JPEG 标准模式,现代电子技术,2002 年第 5 期,pp:7-11
[12] 崔春艳、李彩霞,基于 DCT 变换的数字图像压缩技术及其 Matlab 实现,现代电子技术,2002 年第 9 期,pp:7-9
[13] 蓝波,图像无损压缩方法的研究与实现,中国科学技术大学计算机应用,2004.03,pp:22-26
[14] S.W.Golomb, Run-length encoding, IEEE trans. IT, 1996,12(3), pp:399-401
[15] W.Berghorn, T.Boskamp, M.Lang and H.O.Peitgen, Context conditioning and run –length coding for hybrid, embedded progressive image coding, IEEE trans Image processing,2001,10(12), pp:1791-1792
[16] Jinhua Yu, Advantages of Uniform Scalar Dead-zone Quantization in Image Coding System, IEEE.2004, pp:805-808
[17] M.A.Golner, W.B. Mikhael, V.Krishnan and A.Ramaswamy, Region Based Variable Quantization for JPEG Image Compression, IEEE Midwest Symposium on Circuits and Systems, Lansing MI,USA, Aug 2000, pp:8-11
[18] Gopal Lakhani, Improving DC Coding Models of JPEG Arithmetic Coder, IEEE SIGNAL PROCESSING LETTERS, May 2004, pp505-508
[19] 孙圣和、陆哲明,矢量量化技术及应用,北京:科技出版社,2002.05 第 1 版,pp.31-49
[20] 吴乐南,数据压缩的原理与应用,北京:电子工业出版社,1995.02 第 1 版,pp.21-25
[21] Gregory.K.Wallace, The JPEG Still Picture compression standard, IEEE Transactions on Consumer Electronics,1992,38(1)
[22] A.Zandi, J.D.Allen, E.L.Schwartz , M.Boliek, CREW:compression with eversible embedded wavelets, Proc.IEEE Data Compression Conf, March 1995, pp:212-221
[23] Adams.M.D, The JPEG-2000 Still Image Compression Standard, 1SO/IEC JTC I/SC 29/WGI N2412, 2001.09
[24] ISO/IECJTCl/SC29/WG1(ITU-TSG8), JPEG2000 Partl Final Committee Draft Version 1.0, 2000
[25] 焦晓、朱光喜、马明罡,JPEG2000 的编码技术,计算机仿真,2003,20(9),pp:112-114
[26] M Charrier, D .S Cruz, M Larsson, JPEG2000:the next millennium compression standard for still images, Proc IEEE Int .Conf. Multimedia Computing and Systems (ICMCS), June 1999, vol.1, pp:131-132
[27] 桑爱军、陈贺新,三维矩阵彩色图像 WDCT 压缩编码,电子学报,2002,30(4),pp:594-597
[28] 朱艳秋、陈贺新、戴逸松,彩色图像三维矩阵变换压缩编码,电子学报,1997,25(7),pp:16-21
[29] 韩晓微,彩色图像处理关键技术研究,东北大学控制理论和控制工程,2005.01,pp:35-38
[30] E.M.Granger,J.C.Heurtley,Visual chromaticity-modulation transfer function,J.Opt.Soc. Am.,1973, vol.63, pp:1173-1174
[31] K.T.Mullen, The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings, J. Physiol., 1985, vol.359, pp:381-400.
[32] Charles Poynton, Color Science and Color Appearance Models for CG, HDTV and D-Cinema, SIGGRAPH2004 course 2, 2004.05, pp:33
[33] 张鹤,基于四维n阶矩阵的彩色图像正交变换算法的研究,吉林大学通信与信息系统,2007
[34] 何东健,数字图像处理,西安电子科技大学出版社,2003.07第1版,pp:234-236
[35] 刘鹏举,基于小波变换的图像压缩技术研究,西北工业大学电路与系统,2005.01,pp:6-7
[36] 马会礼,基于小波变换的图像压缩方法研究,大连理工大学电子与通信工程,2005.03,pp:24-25
[37] 罗军、程存学,图像文件格式及其在WINDOWS环境下的使用,声学与电子工程,1995年第3期 pp:22-29
[38] Lawrence.A.Rowe, Equipment, Facilities and Transmission, Berkeley Multimedia Research Center University of California at Berkeley, Oct. 2000, pp:6-12
[39] 林福宗,图像文件格式(上)-Windows 编程,北京:清华大学出版社,1996.12第 1 版,pp:40-48
[40] 田玉敏、梁若莹,计算机彩色输入输出设备常用颜色空间及其转换,计算机工程,2002,28(9),pp:198-200
[41] 李孝安、张晓缋,神经网络与神经计算机导论,西安:西安电子工业出版社,1994.10第1版,pp:34-41
[42] W.Sweldens, The Lifting Scheme:A Custom-design Construction of orthogonal Wavelets, Appl.Comut.Harmon.Appl.,1996,3(2), pp:186-200
[43] Daubechies.I, Sweldens.W., Factoring Wavelet Transforms into Lifting Steps, Journal of Fourier Analysis and Application,1998,5(3), pp:245-267
[44] Calderbank.A.R, Daubechies.I, Sweldens.W, Wavelet transforms that map integers to integers , Applied and Computational Harmonic analysis, 1998,5(3), pp:332-369.
[45] Mandelbrot.B.B, Fractals Form , Chance, and Dimension, W.H.Freeman and Co., San Francisco,1977
[46] Jacquin.A.E, Image coding based on a fractal theory of iterated contractive image transformations, IEEE Transactions on Image Processing, 1992,1(1), pp:18-30
[47] Woods.JW, O'Neil.S.D.,Subband coding of images, IEEE Transactions on Acoustic, Speech and Signal Processing, 1986,34(5), pp:1278-1288.
[48] Mallat.S, A Theory for Multi-resolution Signal Decomposition: the wavelet representation, IEEE Transaction on Pattern Analysis and Machine Intelligence, 1989,11(7), pp:674-693.
[49] 高雪峰,快速分形图像编码及高压缩比纹理压缩方法研究,西北工业大学计算数学,2005.03,pp:7-8.
[50] 容观澳,计算机图像处理,北京:清华大学出版社,2000.02第1版,2003.06第4次印刷,pp:98-102
[51] Andrew.B.Watson, Image Compression Using the Discrete cosine transform, Mathematical Journal, 1994,4(1), pp:81-88
[52] Syed.Ali.Khayam,The Discrete Cosine Transform: Theory and Application, ECE802-602: Information Theory and Coding, 2003.03