基于数学形态学和小波变换的图像边缘检测的研究
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摘要
边缘是图像的基本特征之一,边缘检测是图像分割、目标识别、区域形状提取等图像处理领域十分重要的基础。
图像边缘检测已拥有很长的研究历史,提出的方法也有很多种,但各有其优缺点,没有一种普适性方法。关键在于边缘和噪声都处于图像的高频区域,在去噪的同时,不可避免的会去除图像的细节,所以,在当前边缘检测仍是图像研究的热点和难点。因此,改进已有的方法,或根据要求设计新的方法已成为现在边缘检测研究的主要方向。
本文共分五章,第一章介绍了图像边缘检测的意义和研究现状；第二章首先介绍了图像预处理方法,提出一种基于16向的各向异性扩散方程的滤波方法,其次介绍了经典的边缘检测算法,提出了一种基于改进Sobel算子和Canny算子融合的边缘检测方法,并对各种方法的结果进行了比较；第三章介绍了形态学边缘检测的基本理论和传统的边缘检测算子,构造出一种新的形态学边缘检测算子,并与扩散方程结合,从多方位多结构的角度进行边缘检测；第四章介绍了小波变换的基本理论和小波极大值边缘检测方法,并将扩散方程与构造的形态学算子和小波变换进行结合,来检测边缘,通过试验对所提方法结果进行了比较；最后,在本文的第五章进行了总结,并对未来的研究进行了展望。
Edge is an important feature of the image, edge detection is a digital image segmentation, object recognition, shape extraction region, and is very important foundation for the field of image analysis.
The research on edge detection has a long history, and there have been lots of methods proposed for it. But all of the methods for edge detection still have some drawbacks and advantages. It is hard to propose a general method of edge detection applied to all images. Because, It is crucial that edge and noise are in the high frequency region of image. And It is inevitable that the image details will be removed, when de-noising. Therefore, edge detection is still a hot and difficult currently. So the main research orientation of edge detection is to make improvements to existing methods or to find new methods for edge detection with requirements.
The paper is organized as following five parts. Chapter one gives an introduction of the significance and development of the field of edge detection. In chapter two, firstly, it gives an introduction of the preprocessing method, and a new method based on anistropic diffusion equation is proposed. Then it introduces classical edge detection algorithm, and proposes a new fusion edge detection method based on the improved Sobel operator and Canny operator, and gives edge detection results of these methods and offers some relative analysis and comparison. The chapter three offers the basic theory of morphological edge detection and traditional edge detection operators. Meanwhile, a new morphological detection operator is constructed and combined with the diffusion equation, which is detecting edge from the perspective of multi-dimensional and more structure. In the chapter four, at first, it gives an introduction of the basic theory of wavelet transformation and edge detection method of maximum value of wavelet. Then, it is combined with anistropic diffusion equation and morphological operators, and detecting edge, and comparing with the proposed method by experiment results. At last, the paper ends with a conclusion and some further research plans mentioned in chapter five.
图像边缘检测已拥有很长的研究历史,提出的方法也有很多种,但各有其优缺点,没有一种普适性方法。关键在于边缘和噪声都处于图像的高频区域,在去噪的同时,不可避免的会去除图像的细节,所以,在当前边缘检测仍是图像研究的热点和难点。因此,改进已有的方法,或根据要求设计新的方法已成为现在边缘检测研究的主要方向。
本文共分五章,第一章介绍了图像边缘检测的意义和研究现状；第二章首先介绍了图像预处理方法,提出一种基于16向的各向异性扩散方程的滤波方法,其次介绍了经典的边缘检测算法,提出了一种基于改进Sobel算子和Canny算子融合的边缘检测方法,并对各种方法的结果进行了比较；第三章介绍了形态学边缘检测的基本理论和传统的边缘检测算子,构造出一种新的形态学边缘检测算子,并与扩散方程结合,从多方位多结构的角度进行边缘检测；第四章介绍了小波变换的基本理论和小波极大值边缘检测方法,并将扩散方程与构造的形态学算子和小波变换进行结合,来检测边缘,通过试验对所提方法结果进行了比较；最后,在本文的第五章进行了总结,并对未来的研究进行了展望。
Edge is an important feature of the image, edge detection is a digital image segmentation, object recognition, shape extraction region, and is very important foundation for the field of image analysis.
The research on edge detection has a long history, and there have been lots of methods proposed for it. But all of the methods for edge detection still have some drawbacks and advantages. It is hard to propose a general method of edge detection applied to all images. Because, It is crucial that edge and noise are in the high frequency region of image. And It is inevitable that the image details will be removed, when de-noising. Therefore, edge detection is still a hot and difficult currently. So the main research orientation of edge detection is to make improvements to existing methods or to find new methods for edge detection with requirements.
The paper is organized as following five parts. Chapter one gives an introduction of the significance and development of the field of edge detection. In chapter two, firstly, it gives an introduction of the preprocessing method, and a new method based on anistropic diffusion equation is proposed. Then it introduces classical edge detection algorithm, and proposes a new fusion edge detection method based on the improved Sobel operator and Canny operator, and gives edge detection results of these methods and offers some relative analysis and comparison. The chapter three offers the basic theory of morphological edge detection and traditional edge detection operators. Meanwhile, a new morphological detection operator is constructed and combined with the diffusion equation, which is detecting edge from the perspective of multi-dimensional and more structure. In the chapter four, at first, it gives an introduction of the basic theory of wavelet transformation and edge detection method of maximum value of wavelet. Then, it is combined with anistropic diffusion equation and morphological operators, and detecting edge, and comparing with the proposed method by experiment results. At last, the paper ends with a conclusion and some further research plans mentioned in chapter five.
引文
[1]阮秋琦编著.数字图像处理学[M].北京：电子工业出版社.2001.
[2]姚敏等编著.数字图像处理[M].北京：机械工业出版社.2006.
[3]章毓晋.图像分析(第二版),图像工程[M].北京：清华大学出版社.2005,75-76.
[4]Lee J,Haralick R Shapiro L. Morphologic edge detection[J]. IEEE Transactions on Robotics and Automation,1987,3(2):142-156.
[5]甘金来,刘钊.图像边缘检测算法的比较研究[D],成都：电子科技大学,2005.
[6]冈萨雷斯著,阮秋琦,阮宇智等译.数字图像处理(第二版)[M].北京：电子工业出版社.2003,464.
[7]巴本冬,吴晓娟等.一种快速医学图像亚像素边缘检测方法[J].山东大学学报(工学版),2005,35(5)：63-67.
[8]孙红光,李勇.基于双正交小波弱目标边缘提取方法[J].长春理工大学报,2004,27(2)：53-55.
[9]金晟业,陈圣波等.遥感图像边缘提取微分方法及其应用[J].遥感技术与应用,2008,23(6)：729-734.
[10]李新,谢永智等.基于运动图像序列的啤酒瓶凸性字符快速提取方法[J].桂林工学院学报,2005,25(1)：97-100.
[11]王新,黄兆云.基于多结构元素的数学形态学图像边缘检测[J],计算机工程与应用,2008,44(7)：89-91.
[12]Yuqian Zhao, Weihua Gui. Edge Detection Based on Multi-Structure Elements Morphology[J]. IEEE,2006(2):9795-9798.
[13]孙达,刘家锋.基于概率密度梯度的边缘检测[J].计算机学报,2009：32(2),299-307.
[14]S.Konishi, A.Yuille, J.Coughlan. A statistical approach to multi scale edge detection[J]. Image and Vision computing,2003, (21):37-48.
[15]冯会真,夏哲雷等.基于神经网络的图像边缘检测方法[J].浙江：中国计量学院学报,2006,17(4)：289-291.
[16]S.C.Douglas, T.H.Y.Meng. Design of edge detection templates using a neural network[J]. Proc.Inter-national Joint Conference on Neural Networks.1990,2: 331-334.
[17]张东波,王耀南.FCM聚类算法和粗糙集在医疗图像分割中的应用[J].仪 器仪表学报,2006,27(12)：1683-1687.
[18]D.S.Kim, W.H.Lee, I.S.Kweon. Automatic edge detection using 3*3 ideal binary pixel patterns and fuzzy based edge thresholding.Pattern Recognition Letters[J],2004, (25):101-106.
[19]Henri Maitre等著,孙洪译.现代数字图像处理[M],北京：电子工业出版社,2006,156.
[20]P.Perona, J.Malik. Scale-space and edge detection using anisotropic diffusion [J]. IEEE Trans,1990, PAMI-12(7):629-639.
[21]Z.Lei, B.Paul. Edge detection by scale multiplication in wavelet domain[J]. Pattern Recognition Letters,2002,23(14):1771-1784.
[22]唐敏,成礼智.基于自适应脊波变换的边缘检测[J],计算机应用,2006,26(11)：2713-2715.
[23]Candes E.J, Donoho D.L. Continuous curvelet transform I.Resolution of the wavefront set[J]. Article Applied and Computational Harmonic Analysis,2005, 19:162-197.
[24]Candes E.J, Donoho D.L. Continuous curvelet transform Ⅱ.Discretization and frames[J].Article Applied and Computational Harmonic Analysis,2005,19: 198-222.
[25]罗军辉,冯平等Matlab7.0在图像处理中的应用[M].北京：机械工业出版社,2005.
[26]张德丰等编著,MATLAB数字图像处理[M].北京：机械工业出版社,2009.
[27]Kim H.S, Yoo J.M, Park M.S, et al.An anisropic diffusion based on diagonal edges [C]:The 9th International Conference on Advanced Communication Technology.Washington, DC:IEEE,2007,1:384-388.
[28]李振恒,孙丰荣,刘芬,王庆浩,耿俊卿,秦晓红,姚桂华,张运.基于改进的各向异性扩散方程的医学超声图像降噪方法[J],计算机应用,2009,29(12)：3369-3371.
[29]蒋先刚.基于各向异性扩散的图像平滑及在三维重构预处理中的应用[J],计算机应用,2007,27(1)：0249-0251.
[30]Voci F, Eiho S, Sugimoto N, Sekiguchi H. Estimating the gradient threshold in the Perona-Malik equation[J]. IEEE Signal Processing Magazine,2004,65 (3):39-46.
[31]余庆军,谢胜利.基于人类视觉系统的各向异性扩散图像平滑方法[J].电子学报,2004,32(1)：17-20.
[32]L.G.Roberts, Machine perception of three-dimension solids, Optimal and Electro-Optimal Information Processing[D], MA:MIT Press,1965,99-197.
[33]L.Sobel, Camera models and machine perception, PhD Theses[D], Standford University, Standford, CA,1970.
[34]J.Prewitt, Object enhancement and extraction, Picture Process[D]. Psychopict, 1970,75-149.
[35]刘锋,孙大鹏,黄宇,陶然,王越.基于改进Wigner-Hough变换的多分量LFM信号特征提取[J].2008,28(10)：914-917.
[36]崔屹,图像处理与分析—数学形态学方法及应用[M].北京：科学出版社,2000.
[37]冯俊萍,赵转萍.基于数学形态学的图像边缘检测技术[J].航空计算技术,2004,34(3)：53-56.
[38]王树文,闫成新,张天序.数学形态学在图像处理中的应用[J].计算机工程与应用,2004,3：89-92.
[39]杨平先,孙兴波.一种改进多尺度形态学边缘检测算法[J].光电工程,2005,32(11)：72-75.
[40]傅茂名.基于形态灰度边缘检测算法的一种改进[J].电子科技大学学报,2005,34(2)：206-209.
[41]张德丰等编著,MATLAB小波分析[M].北京：机械工业出版社,2009.
[42]陈武凡.小波分析及其在图像处理中的应用[M].北京：科技出版社,2003.
[43]李建平.小波分析与信号处理---理论、应用及软件实现[M].重庆：重庆出版社,1997,12.
[44]Mallat Stephane. A Wavelet tour of signal processing[M]. (2nd ed). USA: Academic Press,1999.
[45]Mallat S.A Theory for Multiresolution Signal Decomposition:the Wavelet Representation[J]. IEEE Trans. On PAMI,1989,11(7):674-693.
[46]程正兴,小波分析算法与应用[M],西安：西安交通大学出版社,1998.
[47]Chang S.G, Yu.B, Vetterli M. Spative Wavelet Thresholding with Context Modeling for Image Denoising[J]. IEEE trans. On image processing,2000, 9(9):1522-1531.
[48]李建平,唐远炎.小波分析方法应用[M].重庆：重庆大学出版社,2001.
[49]尚晓清.多尺度分析在图像处理中的应用研究[M].西安：西安电子科技大学,2004.
[50]Candes E.J, Donoho D.L. Ridgelet:A Key to high-dimensional intermittency[J]. Phil Trans R Soc Lond A,1999,357:2495-2509.
[51]Donoho D.L. Ridgelet functions and Orthonormal Ridgelets[J]. Journal of Approximation Theory,2001,111:143-179.
[52]Candes E.J. Ridgelet:theory and application[M]. Stanford University: Department of Statistic,1998.
[53]Do M.N, Vetterli M. The finite Ridgelet Transform for Image Representation[J]. IEEE Transaction on Image Processing,2002,12(1):16-28.
[54]Starck J.L, Candes E.J, Donoho D.L. The Curvelet Transform for Image Denoising[J]. IEEE Transaction on Image Processing,2002,11(6):670-684.
[55]Candes E.J, Donoho D.L. Continuous Curvelet Transform:Resolution of the Wavefront Set[EB/OL].
[56]Candes E.J, Donoho D.L. Continuous Curvelet Transform.-Discretization and Frames[EB/OL]
[2]姚敏等编著.数字图像处理[M].北京：机械工业出版社.2006.
[3]章毓晋.图像分析(第二版),图像工程[M].北京：清华大学出版社.2005,75-76.
[4]Lee J,Haralick R Shapiro L. Morphologic edge detection[J]. IEEE Transactions on Robotics and Automation,1987,3(2):142-156.
[5]甘金来,刘钊.图像边缘检测算法的比较研究[D],成都：电子科技大学,2005.
[6]冈萨雷斯著,阮秋琦,阮宇智等译.数字图像处理(第二版)[M].北京：电子工业出版社.2003,464.
[7]巴本冬,吴晓娟等.一种快速医学图像亚像素边缘检测方法[J].山东大学学报(工学版),2005,35(5)：63-67.
[8]孙红光,李勇.基于双正交小波弱目标边缘提取方法[J].长春理工大学报,2004,27(2)：53-55.
[9]金晟业,陈圣波等.遥感图像边缘提取微分方法及其应用[J].遥感技术与应用,2008,23(6)：729-734.
[10]李新,谢永智等.基于运动图像序列的啤酒瓶凸性字符快速提取方法[J].桂林工学院学报,2005,25(1)：97-100.
[11]王新,黄兆云.基于多结构元素的数学形态学图像边缘检测[J],计算机工程与应用,2008,44(7)：89-91.
[12]Yuqian Zhao, Weihua Gui. Edge Detection Based on Multi-Structure Elements Morphology[J]. IEEE,2006(2):9795-9798.
[13]孙达,刘家锋.基于概率密度梯度的边缘检测[J].计算机学报,2009：32(2),299-307.
[14]S.Konishi, A.Yuille, J.Coughlan. A statistical approach to multi scale edge detection[J]. Image and Vision computing,2003, (21):37-48.
[15]冯会真,夏哲雷等.基于神经网络的图像边缘检测方法[J].浙江：中国计量学院学报,2006,17(4)：289-291.
[16]S.C.Douglas, T.H.Y.Meng. Design of edge detection templates using a neural network[J]. Proc.Inter-national Joint Conference on Neural Networks.1990,2: 331-334.
[17]张东波,王耀南.FCM聚类算法和粗糙集在医疗图像分割中的应用[J].仪 器仪表学报,2006,27(12)：1683-1687.
[18]D.S.Kim, W.H.Lee, I.S.Kweon. Automatic edge detection using 3*3 ideal binary pixel patterns and fuzzy based edge thresholding.Pattern Recognition Letters[J],2004, (25):101-106.
[19]Henri Maitre等著,孙洪译.现代数字图像处理[M],北京：电子工业出版社,2006,156.
[20]P.Perona, J.Malik. Scale-space and edge detection using anisotropic diffusion [J]. IEEE Trans,1990, PAMI-12(7):629-639.
[21]Z.Lei, B.Paul. Edge detection by scale multiplication in wavelet domain[J]. Pattern Recognition Letters,2002,23(14):1771-1784.
[22]唐敏,成礼智.基于自适应脊波变换的边缘检测[J],计算机应用,2006,26(11)：2713-2715.
[23]Candes E.J, Donoho D.L. Continuous curvelet transform I.Resolution of the wavefront set[J]. Article Applied and Computational Harmonic Analysis,2005, 19:162-197.
[24]Candes E.J, Donoho D.L. Continuous curvelet transform Ⅱ.Discretization and frames[J].Article Applied and Computational Harmonic Analysis,2005,19: 198-222.
[25]罗军辉,冯平等Matlab7.0在图像处理中的应用[M].北京：机械工业出版社,2005.
[26]张德丰等编著,MATLAB数字图像处理[M].北京：机械工业出版社,2009.
[27]Kim H.S, Yoo J.M, Park M.S, et al.An anisropic diffusion based on diagonal edges [C]:The 9th International Conference on Advanced Communication Technology.Washington, DC:IEEE,2007,1:384-388.
[28]李振恒,孙丰荣,刘芬,王庆浩,耿俊卿,秦晓红,姚桂华,张运.基于改进的各向异性扩散方程的医学超声图像降噪方法[J],计算机应用,2009,29(12)：3369-3371.
[29]蒋先刚.基于各向异性扩散的图像平滑及在三维重构预处理中的应用[J],计算机应用,2007,27(1)：0249-0251.
[30]Voci F, Eiho S, Sugimoto N, Sekiguchi H. Estimating the gradient threshold in the Perona-Malik equation[J]. IEEE Signal Processing Magazine,2004,65 (3):39-46.
[31]余庆军,谢胜利.基于人类视觉系统的各向异性扩散图像平滑方法[J].电子学报,2004,32(1)：17-20.
[32]L.G.Roberts, Machine perception of three-dimension solids, Optimal and Electro-Optimal Information Processing[D], MA:MIT Press,1965,99-197.
[33]L.Sobel, Camera models and machine perception, PhD Theses[D], Standford University, Standford, CA,1970.
[34]J.Prewitt, Object enhancement and extraction, Picture Process[D]. Psychopict, 1970,75-149.
[35]刘锋,孙大鹏,黄宇,陶然,王越.基于改进Wigner-Hough变换的多分量LFM信号特征提取[J].2008,28(10)：914-917.
[36]崔屹,图像处理与分析—数学形态学方法及应用[M].北京：科学出版社,2000.
[37]冯俊萍,赵转萍.基于数学形态学的图像边缘检测技术[J].航空计算技术,2004,34(3)：53-56.
[38]王树文,闫成新,张天序.数学形态学在图像处理中的应用[J].计算机工程与应用,2004,3：89-92.
[39]杨平先,孙兴波.一种改进多尺度形态学边缘检测算法[J].光电工程,2005,32(11)：72-75.
[40]傅茂名.基于形态灰度边缘检测算法的一种改进[J].电子科技大学学报,2005,34(2)：206-209.
[41]张德丰等编著,MATLAB小波分析[M].北京：机械工业出版社,2009.
[42]陈武凡.小波分析及其在图像处理中的应用[M].北京：科技出版社,2003.
[43]李建平.小波分析与信号处理---理论、应用及软件实现[M].重庆：重庆出版社,1997,12.
[44]Mallat Stephane. A Wavelet tour of signal processing[M]. (2nd ed). USA: Academic Press,1999.
[45]Mallat S.A Theory for Multiresolution Signal Decomposition:the Wavelet Representation[J]. IEEE Trans. On PAMI,1989,11(7):674-693.
[46]程正兴,小波分析算法与应用[M],西安：西安交通大学出版社,1998.
[47]Chang S.G, Yu.B, Vetterli M. Spative Wavelet Thresholding with Context Modeling for Image Denoising[J]. IEEE trans. On image processing,2000, 9(9):1522-1531.
[48]李建平,唐远炎.小波分析方法应用[M].重庆：重庆大学出版社,2001.
[49]尚晓清.多尺度分析在图像处理中的应用研究[M].西安：西安电子科技大学,2004.
[50]Candes E.J, Donoho D.L. Ridgelet:A Key to high-dimensional intermittency[J]. Phil Trans R Soc Lond A,1999,357:2495-2509.
[51]Donoho D.L. Ridgelet functions and Orthonormal Ridgelets[J]. Journal of Approximation Theory,2001,111:143-179.
[52]Candes E.J. Ridgelet:theory and application[M]. Stanford University: Department of Statistic,1998.
[53]Do M.N, Vetterli M. The finite Ridgelet Transform for Image Representation[J]. IEEE Transaction on Image Processing,2002,12(1):16-28.
[54]Starck J.L, Candes E.J, Donoho D.L. The Curvelet Transform for Image Denoising[J]. IEEE Transaction on Image Processing,2002,11(6):670-684.
[55]Candes E.J, Donoho D.L. Continuous Curvelet Transform:Resolution of the Wavefront Set[EB/OL].
[56]Candes E.J, Donoho D.L. Continuous Curvelet Transform.-Discretization and Frames[EB/OL]