基于小波变换的有噪图像多分辨率分割
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摘要
有噪图像多分辨率分割中根本问题是噪声的抑制，多分辨率分析充分利用了各分辨率互相独立的信息，具有较好的抑制噪声的能力。Mallat把小波分析与多分辨率分析结合起来，从而使得小波变换多分辨率分析在图像工程中的应用成为人们研究的焦点。
小波分析是近年来发展起来的新的研究领域。它是Fourier分析的突破和进展，是信号和图像处理强有力的工具。本文在对小波分析基本理论研究的基础上，深入探索了小波变换多分辨率分析在有噪图像分割中的应用，并且通过与经典分割方法的比较，体现了小波变换多分辨率分割的优点。
噪声的存在是图像分割的困难所在，本文着重研究了基于小波变换的多分辨率分割中噪声抑制的问题。针对小波变换多分辨率边缘检测中单一阈值难以区分边缘与噪声的问题，本文提出了一种自适应的阈值方法，并改进了边缘链接方法。
中值滤波器是一种去除噪声的非线性处理方法，中值滤波器在边缘保持上具有良好的特性。本文采用模糊Boolean函数提出了一种自适应模糊中值滤波器，并把中值滤波同小波多分辨率分割结合，在抑制噪声的同时较好的保持了边缘。
化学反应中的气液两相图分割存在目标分布紧密、信噪比低的困难，本文利用灰度-小波变换模值的二维分布中，背景、边缘和目标的二维分布之间的欧氏距离较大对图像，进行分割，我们提出了把模糊聚类结合小波变换，在气液两相图分割中取得了成功。
The basic principle of multiresolution Segmentation of noise image is suppressing noise. Multiresolution analysis makes use of the independent information in different resolution. Mallat combines wavelet analysis with multiresolution analysis, and multiresolution analysis based on wavelet transform becomes a focal field.
Wavelet analysis has been a new field in recent years. It has been accepted as a very important breakthrough of Fourier analysis, and has become a useful tool in image and signal processing. We have study the fundamental theory of Wavelet transform, and then we explore the application of multiresolution analysis based on Wavelet Transform in noise image segmentation. Through comparing between classical image segmentation algorithm and Multiresolution Analysis based on Wavelet Transform, we can know the excellence of Multiresolution Analysis.
Suppressing noise is the difficult problem in image segmentation, so we have study suppressing noise in multiresolution segmentation based on Wavelet transform. To discern edge and noise in multiresolution edge detection used single threshold, we put forward a kind of adaptive threshold and improve the method of edge linking.
Median filter is a kind of nonlinear filter, and it has good abilities of keeping edge. A new kind of adaptive fuzzy median filter defined by Boolean function is given in this paper, and this method can keeping edge very well and reduce noise at the same time.
Gas-liquid image in chemistry reaction has close object and lower signal-to-noise ratio, so gas-liquid image segmentation is very difficult. In 2-D grey-wavelet transform distribution, the Euclidean distance between background, object and edge is very far, so we can carry out image segmentation using this character. We describe a kind of method combing wavelet transform and fuzzy cluster, and succeed in gas-liquid image segmentation.
小波分析是近年来发展起来的新的研究领域。它是Fourier分析的突破和进展，是信号和图像处理强有力的工具。本文在对小波分析基本理论研究的基础上，深入探索了小波变换多分辨率分析在有噪图像分割中的应用，并且通过与经典分割方法的比较，体现了小波变换多分辨率分割的优点。
噪声的存在是图像分割的困难所在，本文着重研究了基于小波变换的多分辨率分割中噪声抑制的问题。针对小波变换多分辨率边缘检测中单一阈值难以区分边缘与噪声的问题，本文提出了一种自适应的阈值方法，并改进了边缘链接方法。
中值滤波器是一种去除噪声的非线性处理方法，中值滤波器在边缘保持上具有良好的特性。本文采用模糊Boolean函数提出了一种自适应模糊中值滤波器，并把中值滤波同小波多分辨率分割结合，在抑制噪声的同时较好的保持了边缘。
化学反应中的气液两相图分割存在目标分布紧密、信噪比低的困难，本文利用灰度-小波变换模值的二维分布中，背景、边缘和目标的二维分布之间的欧氏距离较大对图像，进行分割，我们提出了把模糊聚类结合小波变换，在气液两相图分割中取得了成功。
The basic principle of multiresolution Segmentation of noise image is suppressing noise. Multiresolution analysis makes use of the independent information in different resolution. Mallat combines wavelet analysis with multiresolution analysis, and multiresolution analysis based on wavelet transform becomes a focal field.
Wavelet analysis has been a new field in recent years. It has been accepted as a very important breakthrough of Fourier analysis, and has become a useful tool in image and signal processing. We have study the fundamental theory of Wavelet transform, and then we explore the application of multiresolution analysis based on Wavelet Transform in noise image segmentation. Through comparing between classical image segmentation algorithm and Multiresolution Analysis based on Wavelet Transform, we can know the excellence of Multiresolution Analysis.
Suppressing noise is the difficult problem in image segmentation, so we have study suppressing noise in multiresolution segmentation based on Wavelet transform. To discern edge and noise in multiresolution edge detection used single threshold, we put forward a kind of adaptive threshold and improve the method of edge linking.
Median filter is a kind of nonlinear filter, and it has good abilities of keeping edge. A new kind of adaptive fuzzy median filter defined by Boolean function is given in this paper, and this method can keeping edge very well and reduce noise at the same time.
Gas-liquid image in chemistry reaction has close object and lower signal-to-noise ratio, so gas-liquid image segmentation is very difficult. In 2-D grey-wavelet transform distribution, the Euclidean distance between background, object and edge is very far, so we can carry out image segmentation using this character. We describe a kind of method combing wavelet transform and fuzzy cluster, and succeed in gas-liquid image segmentation.
引文
[01]阮秋琦编著，数字图像处理学，电子工业出版社，2001
[02]夏良正主编，数字图像处理，东南大学出版社，1999
[03]章毓晋编著，图像工程上册—图像处理和分析，清华大学出版社，1999
[04]杨福生，小波变换的工程分析与应用，科学出版社，1999
[05]尹平，王润生，多尺度边缘检测技术的分类及比较，计算机工程与科学，1998，20(1)，16～21
[06]S.Mallat,Multifrequency channel decompositions of images and wavelet models,IEEE Trans.on Assp,1989,37(12),2091～2110
[07]S.Ranganath,Image filtering using multiresolution representation,IEEE Trans.on PAMI,1991,13(5),426～440
[08]P.J.Burt,The laplacian pyramid as a compact image code,IEEE Trans.on COM,1983,31(4),532～540
[09]P.H.Westerink,D.E.Boekee,Subband coding of images using vector quantization IEEE Trans.on COM,1988,36(6),713～719
[10]P.Vaidyanathan,Quadrature mirror filter banks,m-band extensions and perfect-reconstruction techniques,IEEE ASSP magazine,1987,(7),4～37
[11]A.N.Akansu,The binomial QMF-wavelet transform for multiresolution signal decomposition,IEEE Trans.on SP,1993,41(1),13～19
[12]罗会国，朱耀庭，朱光喜，信号的一种快速子波分解，电子学报，1994，22(7)，17～22
[13]M.B.Ruskai,G.Beylkin,R.Coifman,I.Daubechies,S.Mallat,Wavelets and their applications,Jones and Bartlett publicshers,1992
[14]毛建昌，王成道，万嘉若，多分辨率自回归纹理模型，电子学报，1988，16(6)，64～68
[15]Zhang YE,Qian Guohui,Wavelet transform and multiresolution synthesis of texture image,IEEE Tencon'93,1993,442～446
[16]H.Caulfield,Parallel discrete and continuous wavelet transforms(appendix),Optical Eng,1992,31(9),1835～1839
[17]S.Mallat,A theory of multiresolution signal decomposition:The wavelet transform,IEEE Trans.PAMI,1989,11(7),674～693
[18]Combes,J.M,A.Grossmann,P.Tchamitchian,wavelet:time-frequency methods and phase space,Proc.First Intern.Conf.on Wavelet,Springer-Verlag,1991
[19]I.Daubechies,The wavelet transform,time-frequency localization and signal analysis,IEEE Trans.IT,1990,36(5),961～1005
[20]崔锦泰，小波分析导论，西安交通大学出版社，1995
[21]C.K.Chui,An introduction to wavelets,Academic Press,Inc,1992
[22]I.Daubechies,Ten lectures on wavelets,Society for Industrial and Applied Mathematics,Philadephia Pennsylvania,1992
[23]I.Daubechies,Ten lectures on wavelets,Society for Industrial and Applied Mathematics,Philadephia Pennsylvania,1992
[24]G.strong,Wavelet and dilation equations,a brief introduction,SIAM Review,1989,31,614～627
[25]S.Mallat,Multiresolution approximation and wavelet orthonormal bases of L2,Trans.Amer.Math.Soc.,1989,315,69～87
[26]O.Rioul,Fast algorithm for discrete and continuous wavelet transform,IEEE Trans.IT,1993,38(2),569～586
[27]杨福生，带通信号的采样定理，信号处理，1986，2(1)，56～61
[28]J.Antoine,Image analysis With two-dimensional continuous wavelet transform,Signal Processing,1993,31,241～272
[29]J.Antoine,The space-angle representation in image analysis with 2D wavelet transform,Signal Processing,1992,(4),701～704
[30]吴一全，朱兆达，图像处理中阈值选取方法30年(1962～1992)的进展(一)，数据采集与处理，1993，8(3)，193～201
[31]吴一全，朱兆达，图像处理中阈值选取方法30年(1962～1992)的进展(二)，数据采集与处理，1993，8(4)，268～281
[32]O'gorman L,Sanderson A C,The converging square algorithm:an efficient method for locating peaks in multidimensions,IEEE Trans.on PAMI,1984,(6),280～288
[33]O'gorman L,Sanderson A C,The wedge filter technique for convex boundary estimation,IEEE Trans.on PAMI,1985,(7),326～332
[34]周凌翔，顾伟康，最佳边缘检测的准则与算子，模式识别与人工智能，1998，11(1)，54～61
[35]Y.Meyer,Wavelets Algorithms and Applications,Society for Industrial and Applied Mathematics,Philadephia,1993
[36]S.Mallat,singularity detection and processing with wavelets,IEEE Trans on IT,1992,38,617～643
[37]M.Vetterli,Wavelet and filter bank,theory and design,IEEE Trans on SP,1992,40(9),2207～2231
[38]宗孔德，多采样率滤波器一般理论，清华大学出版社，1996年
[39]M.Vetterli,Wavelet and filter bank,theory and design,IEEE Trans on SP,1992,40(9),2207～2231
[40]张晔，任广辉，孙翠莲，B-样条小波基的构造与实现算法，哈尔滨工业大学学报，1996，28(6)，27～31
[41]A.Soman,On orthonormal wavelets and paraunitary filter banks,IEEE Trans.on SP,1993,41(3),1170～1183
[42]A.Cohen,Biorthogonal bases of compactly supported wavelets,Comm on Pure and Appl,1992,3,485～560
[43]A.Cohen,Biorthogonal wavelets and dual filter,Wavelets ill Image Communication,1994,1～26
[44]A.Cohen,Biorthogonal bases of compactly supported wavelets,Comm on Pure and Appl,1992,3,485～560
[45]S.Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans on PAMI,1992,38(3),617～643
[46]聂汉军，沈永增，基于小波变换和模糊中值滤波的图像边缘检测，计算机工程与应用，2002，7(录用)
[47]M.S.Kamel,S.Z.Selim,A thresholded fuzzy C-means algorithm for semi-fuzzy clustering pattern recognition,1991,24(9),825～833
[48]L.O.Hall,A comparison of neural netware and fuzzy clustering techniques of segmenting magnetic resonance images of the brain,IEEE Trans on Neural Net Ware,1992,3(5),672～682
[49]唐立梅，气液两相图像识别的研究，浙江工业大学硕士学位论文，2001，3
[50]章毓晋，图象分割评价技术分类和比较，中国图象图形学报，1996，1(2)，151～158
[02]夏良正主编，数字图像处理，东南大学出版社，1999
[03]章毓晋编著，图像工程上册—图像处理和分析，清华大学出版社，1999
[04]杨福生，小波变换的工程分析与应用，科学出版社，1999
[05]尹平，王润生，多尺度边缘检测技术的分类及比较，计算机工程与科学，1998，20(1)，16～21
[06]S.Mallat,Multifrequency channel decompositions of images and wavelet models,IEEE Trans.on Assp,1989,37(12),2091～2110
[07]S.Ranganath,Image filtering using multiresolution representation,IEEE Trans.on PAMI,1991,13(5),426～440
[08]P.J.Burt,The laplacian pyramid as a compact image code,IEEE Trans.on COM,1983,31(4),532～540
[09]P.H.Westerink,D.E.Boekee,Subband coding of images using vector quantization IEEE Trans.on COM,1988,36(6),713～719
[10]P.Vaidyanathan,Quadrature mirror filter banks,m-band extensions and perfect-reconstruction techniques,IEEE ASSP magazine,1987,(7),4～37
[11]A.N.Akansu,The binomial QMF-wavelet transform for multiresolution signal decomposition,IEEE Trans.on SP,1993,41(1),13～19
[12]罗会国，朱耀庭，朱光喜，信号的一种快速子波分解，电子学报，1994，22(7)，17～22
[13]M.B.Ruskai,G.Beylkin,R.Coifman,I.Daubechies,S.Mallat,Wavelets and their applications,Jones and Bartlett publicshers,1992
[14]毛建昌，王成道，万嘉若，多分辨率自回归纹理模型，电子学报，1988，16(6)，64～68
[15]Zhang YE,Qian Guohui,Wavelet transform and multiresolution synthesis of texture image,IEEE Tencon'93,1993,442～446
[16]H.Caulfield,Parallel discrete and continuous wavelet transforms(appendix),Optical Eng,1992,31(9),1835～1839
[17]S.Mallat,A theory of multiresolution signal decomposition:The wavelet transform,IEEE Trans.PAMI,1989,11(7),674～693
[18]Combes,J.M,A.Grossmann,P.Tchamitchian,wavelet:time-frequency methods and phase space,Proc.First Intern.Conf.on Wavelet,Springer-Verlag,1991
[19]I.Daubechies,The wavelet transform,time-frequency localization and signal analysis,IEEE Trans.IT,1990,36(5),961～1005
[20]崔锦泰，小波分析导论，西安交通大学出版社，1995
[21]C.K.Chui,An introduction to wavelets,Academic Press,Inc,1992
[22]I.Daubechies,Ten lectures on wavelets,Society for Industrial and Applied Mathematics,Philadephia Pennsylvania,1992
[23]I.Daubechies,Ten lectures on wavelets,Society for Industrial and Applied Mathematics,Philadephia Pennsylvania,1992
[24]G.strong,Wavelet and dilation equations,a brief introduction,SIAM Review,1989,31,614～627
[25]S.Mallat,Multiresolution approximation and wavelet orthonormal bases of L2,Trans.Amer.Math.Soc.,1989,315,69～87
[26]O.Rioul,Fast algorithm for discrete and continuous wavelet transform,IEEE Trans.IT,1993,38(2),569～586
[27]杨福生，带通信号的采样定理，信号处理，1986，2(1)，56～61
[28]J.Antoine,Image analysis With two-dimensional continuous wavelet transform,Signal Processing,1993,31,241～272
[29]J.Antoine,The space-angle representation in image analysis with 2D wavelet transform,Signal Processing,1992,(4),701～704
[30]吴一全，朱兆达，图像处理中阈值选取方法30年(1962～1992)的进展(一)，数据采集与处理，1993，8(3)，193～201
[31]吴一全，朱兆达，图像处理中阈值选取方法30年(1962～1992)的进展(二)，数据采集与处理，1993，8(4)，268～281
[32]O'gorman L,Sanderson A C,The converging square algorithm:an efficient method for locating peaks in multidimensions,IEEE Trans.on PAMI,1984,(6),280～288
[33]O'gorman L,Sanderson A C,The wedge filter technique for convex boundary estimation,IEEE Trans.on PAMI,1985,(7),326～332
[34]周凌翔，顾伟康，最佳边缘检测的准则与算子，模式识别与人工智能，1998，11(1)，54～61
[35]Y.Meyer,Wavelets Algorithms and Applications,Society for Industrial and Applied Mathematics,Philadephia,1993
[36]S.Mallat,singularity detection and processing with wavelets,IEEE Trans on IT,1992,38,617～643
[37]M.Vetterli,Wavelet and filter bank,theory and design,IEEE Trans on SP,1992,40(9),2207～2231
[38]宗孔德，多采样率滤波器一般理论，清华大学出版社，1996年
[39]M.Vetterli,Wavelet and filter bank,theory and design,IEEE Trans on SP,1992,40(9),2207～2231
[40]张晔，任广辉，孙翠莲，B-样条小波基的构造与实现算法，哈尔滨工业大学学报，1996，28(6)，27～31
[41]A.Soman,On orthonormal wavelets and paraunitary filter banks,IEEE Trans.on SP,1993,41(3),1170～1183
[42]A.Cohen,Biorthogonal bases of compactly supported wavelets,Comm on Pure and Appl,1992,3,485～560
[43]A.Cohen,Biorthogonal wavelets and dual filter,Wavelets ill Image Communication,1994,1～26
[44]A.Cohen,Biorthogonal bases of compactly supported wavelets,Comm on Pure and Appl,1992,3,485～560
[45]S.Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans on PAMI,1992,38(3),617～643
[46]聂汉军，沈永增，基于小波变换和模糊中值滤波的图像边缘检测，计算机工程与应用，2002，7(录用)
[47]M.S.Kamel,S.Z.Selim,A thresholded fuzzy C-means algorithm for semi-fuzzy clustering pattern recognition,1991,24(9),825～833
[48]L.O.Hall,A comparison of neural netware and fuzzy clustering techniques of segmenting magnetic resonance images of the brain,IEEE Trans on Neural Net Ware,1992,3(5),672～682
[49]唐立梅，气液两相图像识别的研究，浙江工业大学硕士学位论文，2001，3
[50]章毓晋，图象分割评价技术分类和比较，中国图象图形学报，1996，1(2)，151～158