基于小波分析的图像边缘检测算法研究
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摘要
边缘检测是图像处理领域的重要课题,小波分析是继Fourier分析、短时Fourier分析之后的新的信号分析技术。在本文中,首先简要介绍了小波理论的发展及图像的边缘检测的定义；然后给出了一些传统的边缘检测方法,并回顾了一些经典的边缘检测算子,通过实验得出这些方法对不含噪声的图像的边缘检测效果较好,但用于含有噪声的图像则并不理想；从而引入了多尺度小波边缘检测方法,但该方法会导致边缘细节的损失且边缘位置会发生偏移,即在小尺度下存在噪声剔除不干净的情况,随着尺度的增加,在去除噪声的同时把图像的边缘细节也给去掉了,针对这种情况,提出了基于边缘方向性的小波边缘检测算法,该算法先对图像进行基于边缘方向性的平滑,在处理边缘像素时可自动搜索边缘方向进行平滑,然后再用小波变换提取边缘；通过对一系列图像进行仿真实验有力地证明了该方法的有效性；形态学边缘检测算子具有抗噪性不佳的特点,本文构造了一种新的形态学滤波器,并用该滤波器和小波方法结合起来进行边缘检测,仿真实验结果证明了该算法十分有效。
Edge detection is an important topic in the field of image processing. Wavelet transform is a new signal analysis technology after the Fourier transform and short-time Fourier transform. In this thesis, we briefly introduce the development of wavelet theory and the fundamental theories of edge detection firstly, then several traditional methods of edge detection used usually are described and some classical edge detectors are reviewed.Those edge detectors have high performance in detecting the edges when there is no noise in those images, but can not deal well with noisy images, so we introduce the edge detectors based on wavelet transform that can deal well with noisy images, but it may loss some details of the edge and have the drift of edge position across different scale,the algorithm can not clear all the noise of image at small scale,with the increase of the scale,the details of the edge go with the noise, under this situation,we present a wavelet transform-based edge detection algorithm based on edge direction,this method smooth the image based on edge direction firstly,the smoothing algorithm smooth the image on the direction of the edge,then detect the image, a series of experiments for edge detection show that the algorithm is more effective.The edge detector based on morphology can not deal well with noisy images,a new morphology filter is presented in this paper,and we detect the image edge with this filter and wavelet transform,the experimental results show that the proposed alogrithm is very reliable and efficient.
Edge detection is an important topic in the field of image processing. Wavelet transform is a new signal analysis technology after the Fourier transform and short-time Fourier transform. In this thesis, we briefly introduce the development of wavelet theory and the fundamental theories of edge detection firstly, then several traditional methods of edge detection used usually are described and some classical edge detectors are reviewed.Those edge detectors have high performance in detecting the edges when there is no noise in those images, but can not deal well with noisy images, so we introduce the edge detectors based on wavelet transform that can deal well with noisy images, but it may loss some details of the edge and have the drift of edge position across different scale,the algorithm can not clear all the noise of image at small scale,with the increase of the scale,the details of the edge go with the noise, under this situation,we present a wavelet transform-based edge detection algorithm based on edge direction,this method smooth the image based on edge direction firstly,the smoothing algorithm smooth the image on the direction of the edge,then detect the image, a series of experiments for edge detection show that the algorithm is more effective.The edge detector based on morphology can not deal well with noisy images,a new morphology filter is presented in this paper,and we detect the image edge with this filter and wavelet transform,the experimental results show that the proposed alogrithm is very reliable and efficient.
引文
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[2]Mallat S, Hwang W L. Singularity Detection and Processing With Wavelets [J].IEEE Trans Information Theory,1992,38(2):617～643
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[8]Ji hu, Sun Ji-xiang, Shao Xiao-fang, Mao Lin.The Algorithm for Image Edge Detection and Prospect [J]. Computer Engineering and Applications,2004,14:70～73
[9]Zhang Shu-ling, Zhang Xiao-hua. Edge Detection based on Wavelet Transform [J]. Journal of Northwest University (Natural Science Edition),2000,30(2):93～97
[10]张书玲,张小华.基于小波变换的边缘检测[J].西北大学学报,2000,30(2)：93～97
[11]程正兴,林勇平.小波分析在图像处理中的应用[J].工程数学学报,2001,18(F12)：57～86
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[16]Dong Weijun, Zhou mingquan, Li Xiao. Research of the Edge Detection Based on Wavelet Analysis [J]. Computer Engineering and Applications,2004,25:38～40
[17]Guo Weiwei, Huang Xianwu, Ge yimin. A Method for outline Detection of Image with Noise Based on Spline Wavelet [J]. Journal of Computer Applications,2003,21(10):47～48
[18]周学海,张伍.基于Sobel算子的多尺度边缘提取算法 [J].微电子学与计算机,2006,23(12)：12～18
[19]唐良瑞.基于高频分量的边缘检测方法 [J].北方工业大学学报,2002,14(1)：13～16
[20]张权,张晶,王欣.在小波域边缘检测的新算法 [J].信号处理与模式识别,2006,3：126～127
[21]张宇伟,王耀明.基于小波变换的Canny算子边缘检测方法 [J].上海师范大学学报,2006,35(3)：35～38
[22]高国荣,刘冉,羿旭明.一种改进的基于小波变换的图像边缘提取算法[J].武汉大学学报,2005,51(5)：615～619
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[25]Donoho D L. Denosing by Soft-thresholding [J]. IEEE Trans. on IT,1995,41(3):613～627
[26]Pei S C, Chen F C. Hierarchical Image Representation by Mathematical Morphology Subband Decomposition [J]. Pattern Recogit Lettm,1995,16:183～192
[27]夏庆观,路红,陈桂.基于小波神经网络的零件图像特征提取和识别[J].仪器仪表学报,2005,26(8)：611～613
[28]夏哲雷.一种基于神经网络图像边缘检测的方法[J].量子电子学报,2001,18(5)：408～410
[29]王坤鹏,杨东勇双正交小波滤波器构造及其应用于图像边缘检测[J].微计算机信息,2005,21(10)：100～101
[30]李骞,陈占伟.图像边缘检测新技术及应用[J].许昌学院院报,2006,25(2)：42～46
[31]覃征,鲍复民,李爱国,等.数字图像融合[M].西安：西安交通大学出版社,2004
[32]Jeong H, Kim C. Adaptive determination of filter scales for edge detection [J].IEEE Trans on pattern Analysis and Machine Intelligence,1992,14(5):579～585
[33]Turgut A Y, Yemez E A, Bulem S. Multidirectional and multiscale edge detection via wavelet transform [J].IEEE Trans Image Processing, 1996,5(9):1370～1377
[34]杨蒙召,李朝峰,许磊.基于复数小波变换和HCurve准则对图像的去噪[J].计算机应用,2005,25(4)：769～774
[35]唐常青,吕宏伯,黄铮等.数学形态学方法及其应用[M].北京：科学出版社,1993
[36]龚炜,石青云,程民德.数学空间的数学形态学理论与应用[M].北京：科学出版社,2000
[37]王咏胜.基于数学形态学的灰度图像的边缘检测技术研究[硕士学位论文].哈尔滨：哈尔滨工业大学,2005
[38]柳薇,马争鸣.基于边缘检测的图像小波阀值去噪方法[J].中国图像图形学报,2002,17(8)：788～793
[39]宫武鹏,王永仲,黎全.B条小波进行图像的多尺度边缘检测[J].红外技术,2000,22(2)：15～22
[40]张雪,肖旺新,吴坚,吴斌.用二次B样条小波进行图像的自适应阐值边缘检测[J].红外与毫米波,2003,25(1)：19～24
[41]蔡云译,文成林.一种新的基于多尺度分析的滤波算法[J]工程数学学报,2000,17(4)：50～54
[42]杨述斌.图像边缘检测技术概述[J].武汉化工学院报,2003,25(1)：73～76
[43]王玉平,蔡元龙.多尺度B样条小波边缘检测算子[J].中国科学,1995,25(4)：426～437
[44]尹平,王润生.自适应多尺度边缘检测[J].软件学报,2000,11(7)：990～994
[45]魏立梅,张永瑞,谢维信.人脸识别中边缘检测器的改进[J].西安电子科技大学学报.1998,25(2)：146～151
[46]肖志涛.基于相位信息的图像特征检侧和基于DSP的图像匹配处理机的研究[博士学位论文].天津：天津大学,2003
[47]傅一平.基于Gabor和小波的边缘检测理论、快速算法与实时应用研究[博士学位论文].浙江：浙江大学,2004
[48]Weyrich N.Warhola G T. Wavelet Shrinkage and Generalized Cross Validation for Image Denoising [J].IEEE Trans. Image Processing 1998,7(1):82～90
[49]Jansen M, Bultheel A. Multiple Wavelet Threshold Estimation by Generalized Cross Validation for Images With Correlated Noise [J]. IEEE Trans. Image Processing,1999,8(7):947～953
[50]秦前清,杨宗凯.实用小波分析[M].西安：西安电子科技大学出版社,1995
[51]崔屹.图像处理与分析——数学形态学与应用[M].北京：科学出版社,2000
[52]李俊山,李旭辉.数字图像处理[M].北京：清华大学出版社,2007
[53]叶斌,彭嘉雄,基于顺序形态滤波的边缘检测[J].华中理工大学学报,2000,28(8)：9～11
[54]迟健男,方帅,徐心和等,基于多结构元顺序形态变换的灰度图像边缘检测[J].中国图像图形学报,2006,11(1)：41～46
[55]龚声蓉,刘纯平,王强等.数字图像处理与分析[M].北京：清华大学出版社,2006
[56]陈天华.数字图像处理[M].北京：清华大学出版社,2007
[57]王沫然.MATLAB与科学计算[M].北京：电子工业出版社,2003
[58]张圣勤.Matlab 7.0实用教程[M].北京：机械工业出版社,2006
[59]周开利,邓春晖.MATLAB基础及其应用教程[M].北京：北京大学出版社,2007
[60]刘来福,何青等译.用Maple和MATLAB解决科学计算问题[M].北京：高等教育出版社,1995
[61]董维国,深入浅出MATLAB 7.0混合编程[M].机械工业出版社,2006
[2]Mallat S, Hwang W L. Singularity Detection and Processing With Wavelets [J].IEEE Trans Information Theory,1992,38(2):617～643
[3]I Daubechies. Where do wavelet come from?—A personal point of view [J]. Proc. IEEE,1996,84(5):510～513
[4]陈武凡.小波分析及其在图像处理中的应用[M].北京：科学出版社,2002
[5]朱虹.数字图像处理基础[M].北京：科学出版社,2005
[6]阮秋琦,阮宇智,等.数字图像处理[M].北京：电子工业出版社,2003
[7]杨福生.小波变换的工程分析与应用[M].北京：科学出版社,1999
[8]Ji hu, Sun Ji-xiang, Shao Xiao-fang, Mao Lin.The Algorithm for Image Edge Detection and Prospect [J]. Computer Engineering and Applications,2004,14:70～73
[9]Zhang Shu-ling, Zhang Xiao-hua. Edge Detection based on Wavelet Transform [J]. Journal of Northwest University (Natural Science Edition),2000,30(2):93～97
[10]张书玲,张小华.基于小波变换的边缘检测[J].西北大学学报,2000,30(2)：93～97
[11]程正兴,林勇平.小波分析在图像处理中的应用[J].工程数学学报,2001,18(F12)：57～86
[12]张弘.数字图像处理与分析[M].北京：机械工业出版社,2007
[13]冯天瑾.神经网络技术[M].青岛：青岛海洋大学出版社,1994
[14](美)冈萨雷斯等著,阮秋琦等译,数字图像处理(第二版)[M].北京,电子工业出版社,2003
[15]Xie Mei,Ma Zheng, Gu Deren. Arevised Image Edge Detection Algorithm Based on Wavelet Transform [J]. System Engineering and Electronics, 1998,10:67～70
[16]Dong Weijun, Zhou mingquan, Li Xiao. Research of the Edge Detection Based on Wavelet Analysis [J]. Computer Engineering and Applications,2004,25:38～40
[17]Guo Weiwei, Huang Xianwu, Ge yimin. A Method for outline Detection of Image with Noise Based on Spline Wavelet [J]. Journal of Computer Applications,2003,21(10):47～48
[18]周学海,张伍.基于Sobel算子的多尺度边缘提取算法 [J].微电子学与计算机,2006,23(12)：12～18
[19]唐良瑞.基于高频分量的边缘检测方法 [J].北方工业大学学报,2002,14(1)：13～16
[20]张权,张晶,王欣.在小波域边缘检测的新算法 [J].信号处理与模式识别,2006,3：126～127
[21]张宇伟,王耀明.基于小波变换的Canny算子边缘检测方法 [J].上海师范大学学报,2006,35(3)：35～38
[22]高国荣,刘冉,羿旭明.一种改进的基于小波变换的图像边缘提取算法[J].武汉大学学报,2005,51(5)：615～619
[23]Maragos P, Schafer R W. Morphological Filter-Part Ⅰ：Their Set-theoretic Analysis and Relations to Linear Shift-invariant Filters [J].IEEE Trans,1987, ASSP-35(8):1153～1169
[24]Maragos P, Schafer R W. Morphological Filter-Part Ⅱ：Their Relations to Median, Order Statistic, and Stack Filter [J].IEEE Trans, 1987, ASSP-35(8):1170～1184
[25]Donoho D L. Denosing by Soft-thresholding [J]. IEEE Trans. on IT,1995,41(3):613～627
[26]Pei S C, Chen F C. Hierarchical Image Representation by Mathematical Morphology Subband Decomposition [J]. Pattern Recogit Lettm,1995,16:183～192
[27]夏庆观,路红,陈桂.基于小波神经网络的零件图像特征提取和识别[J].仪器仪表学报,2005,26(8)：611～613
[28]夏哲雷.一种基于神经网络图像边缘检测的方法[J].量子电子学报,2001,18(5)：408～410
[29]王坤鹏,杨东勇双正交小波滤波器构造及其应用于图像边缘检测[J].微计算机信息,2005,21(10)：100～101
[30]李骞,陈占伟.图像边缘检测新技术及应用[J].许昌学院院报,2006,25(2)：42～46
[31]覃征,鲍复民,李爱国,等.数字图像融合[M].西安：西安交通大学出版社,2004
[32]Jeong H, Kim C. Adaptive determination of filter scales for edge detection [J].IEEE Trans on pattern Analysis and Machine Intelligence,1992,14(5):579～585
[33]Turgut A Y, Yemez E A, Bulem S. Multidirectional and multiscale edge detection via wavelet transform [J].IEEE Trans Image Processing, 1996,5(9):1370～1377
[34]杨蒙召,李朝峰,许磊.基于复数小波变换和HCurve准则对图像的去噪[J].计算机应用,2005,25(4)：769～774
[35]唐常青,吕宏伯,黄铮等.数学形态学方法及其应用[M].北京：科学出版社,1993
[36]龚炜,石青云,程民德.数学空间的数学形态学理论与应用[M].北京：科学出版社,2000
[37]王咏胜.基于数学形态学的灰度图像的边缘检测技术研究[硕士学位论文].哈尔滨：哈尔滨工业大学,2005
[38]柳薇,马争鸣.基于边缘检测的图像小波阀值去噪方法[J].中国图像图形学报,2002,17(8)：788～793
[39]宫武鹏,王永仲,黎全.B条小波进行图像的多尺度边缘检测[J].红外技术,2000,22(2)：15～22
[40]张雪,肖旺新,吴坚,吴斌.用二次B样条小波进行图像的自适应阐值边缘检测[J].红外与毫米波,2003,25(1)：19～24
[41]蔡云译,文成林.一种新的基于多尺度分析的滤波算法[J]工程数学学报,2000,17(4)：50～54
[42]杨述斌.图像边缘检测技术概述[J].武汉化工学院报,2003,25(1)：73～76
[43]王玉平,蔡元龙.多尺度B样条小波边缘检测算子[J].中国科学,1995,25(4)：426～437
[44]尹平,王润生.自适应多尺度边缘检测[J].软件学报,2000,11(7)：990～994
[45]魏立梅,张永瑞,谢维信.人脸识别中边缘检测器的改进[J].西安电子科技大学学报.1998,25(2)：146～151
[46]肖志涛.基于相位信息的图像特征检侧和基于DSP的图像匹配处理机的研究[博士学位论文].天津：天津大学,2003
[47]傅一平.基于Gabor和小波的边缘检测理论、快速算法与实时应用研究[博士学位论文].浙江：浙江大学,2004
[48]Weyrich N.Warhola G T. Wavelet Shrinkage and Generalized Cross Validation for Image Denoising [J].IEEE Trans. Image Processing 1998,7(1):82～90
[49]Jansen M, Bultheel A. Multiple Wavelet Threshold Estimation by Generalized Cross Validation for Images With Correlated Noise [J]. IEEE Trans. Image Processing,1999,8(7):947～953
[50]秦前清,杨宗凯.实用小波分析[M].西安：西安电子科技大学出版社,1995
[51]崔屹.图像处理与分析——数学形态学与应用[M].北京：科学出版社,2000
[52]李俊山,李旭辉.数字图像处理[M].北京：清华大学出版社,2007
[53]叶斌,彭嘉雄,基于顺序形态滤波的边缘检测[J].华中理工大学学报,2000,28(8)：9～11
[54]迟健男,方帅,徐心和等,基于多结构元顺序形态变换的灰度图像边缘检测[J].中国图像图形学报,2006,11(1)：41～46
[55]龚声蓉,刘纯平,王强等.数字图像处理与分析[M].北京：清华大学出版社,2006
[56]陈天华.数字图像处理[M].北京：清华大学出版社,2007
[57]王沫然.MATLAB与科学计算[M].北京：电子工业出版社,2003
[58]张圣勤.Matlab 7.0实用教程[M].北京：机械工业出版社,2006
[59]周开利,邓春晖.MATLAB基础及其应用教程[M].北京：北京大学出版社,2007
[60]刘来福,何青等译.用Maple和MATLAB解决科学计算问题[M].北京：高等教育出版社,1995
[61]董维国,深入浅出MATLAB 7.0混合编程[M].机械工业出版社,2006