二维经验模式分解及其在图像处理中的应用
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摘要
经验模式分解(EMD)是1998年Huang提出的一种全新的信号处理方法,它从根本上改变了传统Fourier变换和小波变换的思想,实现了信号的多尺度分解,在非线性、非平稳信号处理方面具有良好的性能。二维经验模式分解(BEMD)作为一维EMD的延伸和扩展,在二维信号处理领域已经得到了广泛的应用,由于二维信号的复杂性,BEMD方法还存在一些问题有待解决。
本文对一维EMD的分解过程进行了详细的论述和介绍,分析了一维EMD中的常见问题,阐述了一维EMD的时频分析理论,给出了一维EMD方法的具体应用。
本文重点介绍了BEMD的分解原理和实现过程,讨论了BEMD分解算法中几个关键步骤的实现。对8邻域比较法和形态学重构法两种图像极值点提取方法进行了比较和分析。在包络曲面拟合方面,实现了基于Delaunay三角剖分和基于径向基函数的两种插值方法。本文采用镜像延拓的方法解决BEMD分解过程中存在的边界问题。关于筛分停止条件,本文提出了一种基于包络均值阈值和极值点差值阈值的方法来对BEMD的筛分停止条件进行约束,最后实现了两种BEMD方法对Lena图像的分解。
本文在改进BEMD分解算法的基础上,将其应用在图像处理方面。提出了一种基于IMF阈值函数的去噪方法,避免了传统BEMD方法强制去除高频分量使得图像边缘模糊的缺点,实验验证了该方法具有较好的效果。最后,将BEMD应用在图像边缘特征提取方面,将分解出的各层IMF分量逐层进行边缘特征提取,最后集合汇总输出图像边缘特征,与传统边缘特征提取算子进行比较,通过对比,验证了该方法的有效性。
Empirical Mode Decomposition (EMD) is a new signal processing method, which has been recently introduced by Huang in 1998. It is fundamentally different from the traditional Fourier transform and Wavelet transform, realize the signal multi-scale decomposing. This method is adaptive and suitable for processing non-linear and non-stationary date. Bidimensional empirical mode decomposition(BEMD) is the extension and expansion of one-dimensional EMD, which has been widely used in processing bidimensional signal. On account of the complexity in bidimensional signal, the general BEMD method has some defects which need to be resolved.
In this thesis, the decomposition process and some key characteristics of one-dimensional EMD is discussed in details, describe the Time-spectrum analysis theory of one-dimensional EMD, and give a specific application of EMD in one-dimension signal.
This thesis is mainly introduced the principle and the decompose steps of BEMD, and discuss the implement of several key algorithms in BEMD framework. Analyze and compare the two detect regional extrema methods, the 8-neighborhood comparison method and the mathematical morphology. The upper and lower envelopes of the original image are based on two methods, which are delaunay triangulation and radial basis function interpolation, the boundary effect is solved by mirror symmetry. put forward a new condition to end the sifting process, propose two thresholds based on the envelope mean and the extreme point difference to restrain IMF decomposing process. At last, using two BEMD methods to decompose Lena image.
Using the improved BEMD algorithm to process image. A noise removing method based on IMF threshold function is proposed, it avoids the shortcomings of blurred edges in using traditional BEMD method, Experiments show that the method has better results. At last, the BEMD is applied in image edge detection. Detecting the edge feature form all of the IMF, then output the final summary of image edge feature set, Experiments verify the validity of the method.
本文对一维EMD的分解过程进行了详细的论述和介绍,分析了一维EMD中的常见问题,阐述了一维EMD的时频分析理论,给出了一维EMD方法的具体应用。
本文重点介绍了BEMD的分解原理和实现过程,讨论了BEMD分解算法中几个关键步骤的实现。对8邻域比较法和形态学重构法两种图像极值点提取方法进行了比较和分析。在包络曲面拟合方面,实现了基于Delaunay三角剖分和基于径向基函数的两种插值方法。本文采用镜像延拓的方法解决BEMD分解过程中存在的边界问题。关于筛分停止条件,本文提出了一种基于包络均值阈值和极值点差值阈值的方法来对BEMD的筛分停止条件进行约束,最后实现了两种BEMD方法对Lena图像的分解。
本文在改进BEMD分解算法的基础上,将其应用在图像处理方面。提出了一种基于IMF阈值函数的去噪方法,避免了传统BEMD方法强制去除高频分量使得图像边缘模糊的缺点,实验验证了该方法具有较好的效果。最后,将BEMD应用在图像边缘特征提取方面,将分解出的各层IMF分量逐层进行边缘特征提取,最后集合汇总输出图像边缘特征,与传统边缘特征提取算子进行比较,通过对比,验证了该方法的有效性。
Empirical Mode Decomposition (EMD) is a new signal processing method, which has been recently introduced by Huang in 1998. It is fundamentally different from the traditional Fourier transform and Wavelet transform, realize the signal multi-scale decomposing. This method is adaptive and suitable for processing non-linear and non-stationary date. Bidimensional empirical mode decomposition(BEMD) is the extension and expansion of one-dimensional EMD, which has been widely used in processing bidimensional signal. On account of the complexity in bidimensional signal, the general BEMD method has some defects which need to be resolved.
In this thesis, the decomposition process and some key characteristics of one-dimensional EMD is discussed in details, describe the Time-spectrum analysis theory of one-dimensional EMD, and give a specific application of EMD in one-dimension signal.
This thesis is mainly introduced the principle and the decompose steps of BEMD, and discuss the implement of several key algorithms in BEMD framework. Analyze and compare the two detect regional extrema methods, the 8-neighborhood comparison method and the mathematical morphology. The upper and lower envelopes of the original image are based on two methods, which are delaunay triangulation and radial basis function interpolation, the boundary effect is solved by mirror symmetry. put forward a new condition to end the sifting process, propose two thresholds based on the envelope mean and the extreme point difference to restrain IMF decomposing process. At last, using two BEMD methods to decompose Lena image.
Using the improved BEMD algorithm to process image. A noise removing method based on IMF threshold function is proposed, it avoids the shortcomings of blurred edges in using traditional BEMD method, Experiments show that the method has better results. At last, the BEMD is applied in image edge detection. Detecting the edge feature form all of the IMF, then output the final summary of image edge feature set, Experiments verify the validity of the method.
引文
[1]张贤达,保铮.非平稳信号分析与处理[M].北京：国防工业出版社,1998：12-81.
[2]王宏禹,邱天爽,陈喆.非平稳随机信号分析与处理[M].北京：国防工业出版社,1999：8-259.
[3]王大凯,彭进业.小波分析及其在信号处理中的应用[M].北京：电子工业出版社,2006：8-180.
[4]N.E.Huang, Z.Shen, S.R.Long.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].ProcRoy.Soc.Lond.A, 1998,454:903-995.
[5]J.C.Nunes, Y.Bouaoune, E.Delechelle.Image analysis by bidimensional empirical mode decomposition[J].Image and Vision Computing,2003,21:1019-1026.
[6]J.C.Nunes, S.Guyot, E.Delechlle.Texture analysis based on the bidimensional empirical mode decomposition[J].Mach.Vision,2005,16:177-188.
[7]J.C.Nunes, Y.Bouaoune, E.Delechelle.Bidimensional empirical mode decomposition modified for texture analysis[C].SCIA 2003 13th Scandinavian Conference on Image Analysis, June 29-July 2 2003:171-177.
[8]Huang W, Shen Z, N.E.Huang et al.Use of intrinsic modes in biology:examples of indicial response of pulmonary blood pressure to step hypoxia.Proc.Natl Acad.Sci.USA,1998,95:12766-12771.
[9]Gloersen P, Huang N E.Comparison of interannual intrinsic modes in hemispheric sea ice covers and other geophysical parameters[J].IEEE Transactions on Geoscience and Remote Sensing,2003,41(5):1062-1074.
[10]张义平,李夕兵,赵国彦.基于HHT方法的爆破地震信号分析.工程爆破,2005,11(1)：1-7.
[11]Balocchi R, Menicucci D, Santarcangelo E.Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition [J]. Soli tons and Fractals,2004,20(1):171-177.
[12]盖强,马孝江,殷福亮.局域波多分辨分析及其在振动信号分析中的应用.仪器仪表学报[J],2006,27(6)：1744-1745.
[13]胡红英,马孝江.基于局域波的非参数瞬时频率估计[J].电子学报,2005,33(7)： 1303-1306.
[14]陈东方,吴先良.采用EMD方法消除瞬态散射回波中的高斯白噪声干扰[J].电子学报,2004,3：496-498.
[15]于德介,程军圣,杨宇Hilbert能量谱及其在齿轮故障诊断中的应用[J].湖南大学学报,2004,4：47-50.
[16]陈忠,郑时雄.基于经验模式分解(EMD)的齿轮箱齿轮故障诊断技术研究[J].振动工程学报,2003,2：229-232.
[17]杨志华,齐东旭等.基于经验模式分解的汉字字体识别方法[J].软件学报,2005,16(08)：1438-1444.
[18]田岩,彭复员.数字图像处理与分析[M].武汉：华中科技大学出版社,2009：259.
[19]Gabriel Rilling, Patrick Flandrin.One or Two Frequencies?The Empirical Mode Decomposition Answers.Signal Processing,2008,56(1):85-95.
[20]邓拥军.EMD方法及Hilbert变化中边界问题的处理[J].科学通报,2001,46(3)：257-263.
[21]张郁山,梁建文.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,10：1054-1059.
[22]黄大吉,赵进平.希尔伯特-黄变化的端点延拓[J].海洋学报,2003,1：1-11.
[23]盖强.局域波时频分析的理论研究与应用[D].大连：大连理工大学,2001.
[24]J.C.Nunes, Y.Bouaoune, E.Delechelle.Texture analysis based on the bidimensional empirical mode decomposition with gray-level co-occurrence models[J].Mach.Vision App,2003:633-635.
[25]Christophe Damerval.A fast algorithm for bidimensional EMD[J].Signal Processing Letters, IEEE,2005,12(10):701-704.
[26]宋平舰,张杰.二维经验模分解在海洋遥感图像信息分离中的应用[J].高技术通讯,2001,9：62-67.
[27]韩春明,郭华东,王长林.利用经验模态分解方法抑制SAR斑点噪声[J].遥感学报,2002,4：266-271.
[28]刘忠轩,彭思龙.方向EMD分解与其在纹理分割中的应用[J].中国科学E辑,2005,2：113-123.
[29]崔峰,沈滨,彭思龙.基于EMD细化四元数谱的纹理分割[J].计算机应用,2005,3：573-576.
[30]沈滨,崔峰,彭思龙.二维EMD的纹理分析及图像瞬时频率估计[J].计算机辅助设计与图形学学报,2005,10：2345-2352.
[31]Yan Tian, Ying Huang, Yongjiang Li.Image Zooming Method Using 2D EMD[C]. Technique Intelligent Control and Automation,2006.WCICA 2006.The Sixth World Congress on Volume 2,21-23 June 2006:10036-10040.
[32]徐冠雷,王孝通,徐晓刚等.基于限邻域EMD的图像增强[J].电子学报,2006,9：1635-1639.
[33]贺璐璐.二维经验模式分解及其在图像分析中的应用[D].武汉：华中科技大学,2007.
[34]高凤娇.二维EMD方法及其在图像处理中的应用研究[D].哈尔滨：哈尔滨理工大学,2008.
[35]万建,任龙涛,赵春晖.二维EMD应用在图像边缘特征提取中的仿真研究[J].系统仿真学报,2009,21(3)：799-801.
[36]徐晓刚,徐冠雷,王孝通等.经验模式分解(EMD)及其应用[J].电子学报,2009,3：581-585.
[37]谭善文.多分辨希尔伯特黄(Hilbert-Huang)变换方法的研究[D].重庆：重庆大学,2001.
[38]沈国际,陶利民,陈仲生.多频信号经验模态分解的理论研究及应用[J].振动工程学报,2005,18(1)：1-94.
[39]P.Flandrin.Some aspects of Huang's empirical mode decomposition,from interpretation to applications.Presented at the Int.Conf.Computational Harmonic Analysis(Invited Talk), Nashville, TN,2004.
[40]Gabor D.Theory of communication.[M].Inst.Elec.Eng.1946,93:429-457.
[41]B.Boashash.Estimating and Interpreting the Instantaneous Frequency of a Signal[C], Proc.IEEE, April 1992,80(4):520-538.
[42]L.Vincent.Morphological grayscale reconstruction in image analysis[C], applications and efficient algorithms.IEEE Trans.on Image Processing,1993,2(2):176-201.
[43]P.Soille.Morphological Image Analysis:principles and applications[J].Springer Verlag, 1999:170-171.
[44]S.Beucher.Geodesic reconstruction saddle zones and hierarchical segmentation[J]. Image Anal.Stereol,2001:137-141.
[45]R.C.Gonzalez, R.E.Woods.Digital Image Processing[M]北京：电子工业出版社,2002：15-28
[46]王树文,闫成新,张天序等.数学形态学在图像处理中的应用[J].计算机工程与应用,2004,32：89-92.
[47]闵卫东,唐泽圣.二维任意域内点集的Delaunay三角划分的研究[J].计算机学报,1995,18(5)：357-364.
[48]M.J.D.Powell.The theory of radial basis functions approximation[M]. London:Oxford Univ.Press,1992:105-210.
[49]R.Schaback.Approximation by radial functions with finitely many centers[J]. Constr.Approx,1996,12:331-340.
[50]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,40(16)：84-86.
[51]谭冬梅,姚三,瞿伟廉.振动模态的参数识别综述[J].华中科技大学学报,2002,19(3)：73-78.
[52]胡维平,莫家玲,龚英姬等.经验模态分解中多种边界处理方法的比较研究[J].电子与信息学报,2007,29(6)：1394-1398.
[53]阮秋琦.数字图像处理学[M].北京：电子工业出版社,2007：204-214.
[54]许录平.数字图像处理[M].北京：科学出版社,2007：190-204.
[55]D.L.DONOHO, J.I.STONE.Ideal spatial adaptation via wavelet shrinkage[J]. Biometrika,1994,81:425-455.
[56]DONOHO D.L, STONE J.I.Wavelet Shrinkage Aaymptopia[J].Jouranl of Royal Statistical Society,1995,57(2):315-369.
[2]王宏禹,邱天爽,陈喆.非平稳随机信号分析与处理[M].北京：国防工业出版社,1999：8-259.
[3]王大凯,彭进业.小波分析及其在信号处理中的应用[M].北京：电子工业出版社,2006：8-180.
[4]N.E.Huang, Z.Shen, S.R.Long.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].ProcRoy.Soc.Lond.A, 1998,454:903-995.
[5]J.C.Nunes, Y.Bouaoune, E.Delechelle.Image analysis by bidimensional empirical mode decomposition[J].Image and Vision Computing,2003,21:1019-1026.
[6]J.C.Nunes, S.Guyot, E.Delechlle.Texture analysis based on the bidimensional empirical mode decomposition[J].Mach.Vision,2005,16:177-188.
[7]J.C.Nunes, Y.Bouaoune, E.Delechelle.Bidimensional empirical mode decomposition modified for texture analysis[C].SCIA 2003 13th Scandinavian Conference on Image Analysis, June 29-July 2 2003:171-177.
[8]Huang W, Shen Z, N.E.Huang et al.Use of intrinsic modes in biology:examples of indicial response of pulmonary blood pressure to step hypoxia.Proc.Natl Acad.Sci.USA,1998,95:12766-12771.
[9]Gloersen P, Huang N E.Comparison of interannual intrinsic modes in hemispheric sea ice covers and other geophysical parameters[J].IEEE Transactions on Geoscience and Remote Sensing,2003,41(5):1062-1074.
[10]张义平,李夕兵,赵国彦.基于HHT方法的爆破地震信号分析.工程爆破,2005,11(1)：1-7.
[11]Balocchi R, Menicucci D, Santarcangelo E.Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition [J]. Soli tons and Fractals,2004,20(1):171-177.
[12]盖强,马孝江,殷福亮.局域波多分辨分析及其在振动信号分析中的应用.仪器仪表学报[J],2006,27(6)：1744-1745.
[13]胡红英,马孝江.基于局域波的非参数瞬时频率估计[J].电子学报,2005,33(7)： 1303-1306.
[14]陈东方,吴先良.采用EMD方法消除瞬态散射回波中的高斯白噪声干扰[J].电子学报,2004,3：496-498.
[15]于德介,程军圣,杨宇Hilbert能量谱及其在齿轮故障诊断中的应用[J].湖南大学学报,2004,4：47-50.
[16]陈忠,郑时雄.基于经验模式分解(EMD)的齿轮箱齿轮故障诊断技术研究[J].振动工程学报,2003,2：229-232.
[17]杨志华,齐东旭等.基于经验模式分解的汉字字体识别方法[J].软件学报,2005,16(08)：1438-1444.
[18]田岩,彭复员.数字图像处理与分析[M].武汉：华中科技大学出版社,2009：259.
[19]Gabriel Rilling, Patrick Flandrin.One or Two Frequencies?The Empirical Mode Decomposition Answers.Signal Processing,2008,56(1):85-95.
[20]邓拥军.EMD方法及Hilbert变化中边界问题的处理[J].科学通报,2001,46(3)：257-263.
[21]张郁山,梁建文.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,10：1054-1059.
[22]黄大吉,赵进平.希尔伯特-黄变化的端点延拓[J].海洋学报,2003,1：1-11.
[23]盖强.局域波时频分析的理论研究与应用[D].大连：大连理工大学,2001.
[24]J.C.Nunes, Y.Bouaoune, E.Delechelle.Texture analysis based on the bidimensional empirical mode decomposition with gray-level co-occurrence models[J].Mach.Vision App,2003:633-635.
[25]Christophe Damerval.A fast algorithm for bidimensional EMD[J].Signal Processing Letters, IEEE,2005,12(10):701-704.
[26]宋平舰,张杰.二维经验模分解在海洋遥感图像信息分离中的应用[J].高技术通讯,2001,9：62-67.
[27]韩春明,郭华东,王长林.利用经验模态分解方法抑制SAR斑点噪声[J].遥感学报,2002,4：266-271.
[28]刘忠轩,彭思龙.方向EMD分解与其在纹理分割中的应用[J].中国科学E辑,2005,2：113-123.
[29]崔峰,沈滨,彭思龙.基于EMD细化四元数谱的纹理分割[J].计算机应用,2005,3：573-576.
[30]沈滨,崔峰,彭思龙.二维EMD的纹理分析及图像瞬时频率估计[J].计算机辅助设计与图形学学报,2005,10：2345-2352.
[31]Yan Tian, Ying Huang, Yongjiang Li.Image Zooming Method Using 2D EMD[C]. Technique Intelligent Control and Automation,2006.WCICA 2006.The Sixth World Congress on Volume 2,21-23 June 2006:10036-10040.
[32]徐冠雷,王孝通,徐晓刚等.基于限邻域EMD的图像增强[J].电子学报,2006,9：1635-1639.
[33]贺璐璐.二维经验模式分解及其在图像分析中的应用[D].武汉：华中科技大学,2007.
[34]高凤娇.二维EMD方法及其在图像处理中的应用研究[D].哈尔滨：哈尔滨理工大学,2008.
[35]万建,任龙涛,赵春晖.二维EMD应用在图像边缘特征提取中的仿真研究[J].系统仿真学报,2009,21(3)：799-801.
[36]徐晓刚,徐冠雷,王孝通等.经验模式分解(EMD)及其应用[J].电子学报,2009,3：581-585.
[37]谭善文.多分辨希尔伯特黄(Hilbert-Huang)变换方法的研究[D].重庆：重庆大学,2001.
[38]沈国际,陶利民,陈仲生.多频信号经验模态分解的理论研究及应用[J].振动工程学报,2005,18(1)：1-94.
[39]P.Flandrin.Some aspects of Huang's empirical mode decomposition,from interpretation to applications.Presented at the Int.Conf.Computational Harmonic Analysis(Invited Talk), Nashville, TN,2004.
[40]Gabor D.Theory of communication.[M].Inst.Elec.Eng.1946,93:429-457.
[41]B.Boashash.Estimating and Interpreting the Instantaneous Frequency of a Signal[C], Proc.IEEE, April 1992,80(4):520-538.
[42]L.Vincent.Morphological grayscale reconstruction in image analysis[C], applications and efficient algorithms.IEEE Trans.on Image Processing,1993,2(2):176-201.
[43]P.Soille.Morphological Image Analysis:principles and applications[J].Springer Verlag, 1999:170-171.
[44]S.Beucher.Geodesic reconstruction saddle zones and hierarchical segmentation[J]. Image Anal.Stereol,2001:137-141.
[45]R.C.Gonzalez, R.E.Woods.Digital Image Processing[M]北京：电子工业出版社,2002：15-28
[46]王树文,闫成新,张天序等.数学形态学在图像处理中的应用[J].计算机工程与应用,2004,32：89-92.
[47]闵卫东,唐泽圣.二维任意域内点集的Delaunay三角划分的研究[J].计算机学报,1995,18(5)：357-364.
[48]M.J.D.Powell.The theory of radial basis functions approximation[M]. London:Oxford Univ.Press,1992:105-210.
[49]R.Schaback.Approximation by radial functions with finitely many centers[J]. Constr.Approx,1996,12:331-340.
[50]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,40(16)：84-86.
[51]谭冬梅,姚三,瞿伟廉.振动模态的参数识别综述[J].华中科技大学学报,2002,19(3)：73-78.
[52]胡维平,莫家玲,龚英姬等.经验模态分解中多种边界处理方法的比较研究[J].电子与信息学报,2007,29(6)：1394-1398.
[53]阮秋琦.数字图像处理学[M].北京：电子工业出版社,2007：204-214.
[54]许录平.数字图像处理[M].北京：科学出版社,2007：190-204.
[55]D.L.DONOHO, J.I.STONE.Ideal spatial adaptation via wavelet shrinkage[J]. Biometrika,1994,81:425-455.
[56]DONOHO D.L, STONE J.I.Wavelet Shrinkage Aaymptopia[J].Jouranl of Royal Statistical Society,1995,57(2):315-369.