基于突变理论的图像边缘检测技术研究
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摘要
边缘检测是图像处理、图像分析和计算机视觉领域中最经典的研究内容之一,是图像分析的基础。目前在边缘检测领域已经提出了许多方法,但是至今提出的相关理论和方法尚存在不足之处,在某些具体情况下仍然无法很好的检测出目标物体的边缘,难以找到一种普遍适应性的边缘检测方法。因此,根据具体的应用要求设计新的边缘检测方法,或者对现有的方法进行改进以得到满意的边缘检测结果,仍是目前研究的主流方向。
本文首次将控制领域的突变控制理论引入到图像边缘检测领域,利用突变理论的特性研究图像边缘的突变特性,结合实际问题的需要,找出突变模型描述系统状态变化的规律,通过尖点突变理论建立边缘模型实现了图像边缘检测。实验结果表明,本文提出的边缘检测方法克服了经典微分边缘检测算法边缘检测不完整及现代边缘检测算法运算复杂的缺点,能够准确检测到连续的图像边缘且具有较好的实时性和准确性。
Edge detection is one of the most fundamental operations in image processing, image analysis and computer vision and offers people important parameters to describe and recognize objects in an image. There have been many algorithms proposed for the edge detection of images. But the existing theories and algorithms for edge detection still have some drawbacks and can not detect edges satisfactorily in some cases. It is hard to propose a general method of edge detection applied to all cases. So, it has been the focus of current research work to find new methods for edge detection with specific application requirements or to make improvements to existing methods.
The first time we apply Catastrophe Theory to research the characteristics of mutation of image, base on need of the problem, apply of cusp catastrophe theory to build edge model to detect edge and build catastrophe model to analyze the law of systemic state. Experimental results show that the method given by this paper can accuratly detect continue edge and have good real-time.
本文首次将控制领域的突变控制理论引入到图像边缘检测领域,利用突变理论的特性研究图像边缘的突变特性,结合实际问题的需要,找出突变模型描述系统状态变化的规律,通过尖点突变理论建立边缘模型实现了图像边缘检测。实验结果表明,本文提出的边缘检测方法克服了经典微分边缘检测算法边缘检测不完整及现代边缘检测算法运算复杂的缺点,能够准确检测到连续的图像边缘且具有较好的实时性和准确性。
Edge detection is one of the most fundamental operations in image processing, image analysis and computer vision and offers people important parameters to describe and recognize objects in an image. There have been many algorithms proposed for the edge detection of images. But the existing theories and algorithms for edge detection still have some drawbacks and can not detect edges satisfactorily in some cases. It is hard to propose a general method of edge detection applied to all cases. So, it has been the focus of current research work to find new methods for edge detection with specific application requirements or to make improvements to existing methods.
The first time we apply Catastrophe Theory to research the characteristics of mutation of image, base on need of the problem, apply of cusp catastrophe theory to build edge model to detect edge and build catastrophe model to analyze the law of systemic state. Experimental results show that the method given by this paper can accuratly detect continue edge and have good real-time.
引文
[1]E.C.Zeeman.Catastrophe Theory,Scientific American,1999.
[2]Gilmore,R.Catastrophe Theory for Science and Engineers,New York,Wiley,1999,P10-35
[3]E.V.Vorozhtsov,B.Yu.Scobelev.Symbolic-numerical Method for the Stability Analysis of Difference Schemes on the Basis of the Catastrophe Theory.Journal of computation Physics 2000(16),P26-38
[4]凌复华.突变理论及其应用.上海:上海交通大学出版社,1999,P1-225
[5]桑博德[英],凌复华译.突变理论入门.上海科学技术文献出版社,1998,P1-172
[6]赵松年,于允贤.突变理论及其在生物医学中的应用.科学出版社,1999,P1-110
[7]Armstrong,M.A.著,孙以丰译,李同孚校.基础拓扑学,北京大学出版社.1999,P26-49
[8]哈肯.H.著,徐锡申译,章扬等校.协同学,原子能出版社.2000,P1-152
[9]周绍江.突变理论在环境影响评价中的应用.人民长江.2003,P52-54
[10]Marco Carricato,Joseph Duffy,Vincenzo Parenti-Castelli.Catastrophe analysis of a planar system with flexural pivots.Mechanism and Machine Theory.2002,37:P693-716
[11]孙尧.突变控制技术及其应用研究.哈尔滨工程大学博士学位论文,2002
[12]张亚平,张起森.尖点突变理论在交通流预测中的应用.系统工程学报.2001,3:P272-276
[13]柴立和,彭晓峰.非线性沸腾传热学:分叉和突变理论.自然杂志.20(5),P305
[14]项希勇,穆星,纪晓东.突变理论及其在油气检测中的应用.石油地球物理勘探.2006,3:P269-174
[15]秦四清.斜坡失稳的突变模型与混沌机制.岩石力学与工程学报.1999,4:P486-492
[16]张晓今.翼伞系统稳定性分析的分歧与突变理论法.航天返回与遥感.2004,16(4):P1-6
[17]熊正美,宋永华.突变理论在大电力系统暂态稳定分析中的应用.信息与控制.2001,2:P1-7
[18]赵正跃,项成龙.突变理论在环境预测中的应用.中国环境监测.2002
[19]曹义.突变论中的计算问题.贵州科学.2002,15(4):P309-316
[20]Diederik Aerts,Marek Czachor,Liane Gabora,Maciej Kuna,Andrzej Posiewnik,Jaroslaw Pykacz,Monika.Quantum morphogenesis:Avariation on Thom's catastrophe theory.Research report.2006,15:P1-18
[21]Jonathan Dushoff,Wenzhang Huang,Carlos Castillo-Chavez.Backwards bifurcations and catastrophe in simple models of fatal diseases.Journal of mathematical biology.2003,36:P227-248
[22]Xie Zhikang,Fan Weicheng,Wang Qing'an.Catastrophe mechanism and classification of discontinuity behavior in thermal science(Ⅰ)—fold catastro -phe.Chinese Science Bulletin.2000,45(20):P1905-1912
[23]Eiichi Muramatsu,Masao Ikeda,Takayuki Tamai.Stabilition of a multi-input multi-output plant with variable operating conditions.Nonlinear analysis,theory,methods,and applications,vol.30,no.4,1997.P2291-2296
[24]Igor V.Chernenko.Cargo cult science and the catastrophe theory.Nonlinear analysis.2000,38:P87-103
[25]Anthony N.Kounadis.Dynamic buckling of simple two-bar frames using catastrophe theory.International Journal of Nonlinear Mechanics.2002,37:P1249-1259
[26]Vladislav V.Velichenko.Variational analysis and control of catastrophic dynamical systems.Nonlinear analysis,theory,methods and applications.2001,30(4):P2065-2074
[27]Fu Chang,Jar Der Luo.System catastrophe:A distributive model for collective phenomenon.Research report.2007,13:P1-17
[28]P.T.Saunders.An Introduction to Catastrophe Theory.Cambridge university Press.2003
[29]V I.Arnold.Catastrophe Theory.Second,Revised and Expanded Edition.Springer-Verlag.2000
[30]何平,赵子都.突变理论及其应用[M].大连理工大学出版社,1988
[31]托姆[法].突变论思想和应用[M].上海译文出版社,1998
[32]阮秋琦.数字图像处理学[M].电子工业出版社 2001
[33]郭健.突变理论在复杂系统脆性理论研究中的应用[D].哈尔滨工程大学.2004
[34]甘金来.图像边缘检测算法的比较研究[D].电子科技大学.2005
[35]张晶.图像边缘检测算法的研究[D].山东大学.2006
[36]叶枫.基十灰度图像的边缘检测方法研究[D].西北土业大学.2003
[37]张亚平,张起森.尖点突变理论在交通流预测中的应用[J].系统工程学报.2000,9:P272-276
[38]K.R.Castleman著HALL出版公司.朱志刚,林学阎,电子工业出版社.石定机等译.数字图像处理.1998
[39]Ballard H.Generalizing the bough transform to detect arbitary shapes.Pattern Recognition.2001,13(2):P111-122
[40]邓航,苗雨,石俊,余松煌.用于边缘检测的Snake模型.上海交通大学学报.2000,4(6):P848-850.
[41]Cohen L Cohen I.A finite element method applied to new active contour models and 3D reconstruction from cross sections[A].Proc of 3rd Intern Conf on Computer Vision[C].Paris Ⅸ Univ.France.1999:P587-591.
[42]Braden R,zhang L(RSVP)一一Version Berson S} etal.RFC 2205Resource ReSerVation Protocol functional specification[S].2000.
[43]Howing F,Wermser D.Fuzzy Snake[A],6th Intern Conf on Image Processing and Its Application[C].Dublin.2001,P627-630.
[44]邓航,丙雨,石俊,余松煌.用于边缘检测的Snake模型.上海交通大学学报.2000,14(6):P848-850.
[45]魏立梅,张永瑞,谢维信.人脸识别中边缘检测器的改进.西安电子科技大学学报.2000,25(2):P146-151.
[46]刘宏兵,杨万海,马剑虹.图像小波边缘提取中闭值选取的一种自适应方法.西安电子科技大学学报.2000,27(3):P294-296.
[47]周德龙,潘泉.图像模糊边缘检测的改进算法.中国图象图形学报.2001,6(4):P353-358
[48]李映,焦李成一种有效的基于并行量子进化算法的图像边缘检测方法.信号处理,2003,19(1):P69-74
[49]李映,焦李成.基于自适应免疫遗传算法的边缘检测.中国图像图形学报.2003,8(6):P890-895
[50]A comparative Traps.On System,cost function approach to Man and Cybernetic.2004,edge detection.IEEE 19(6):P1337-1349.
[2]Gilmore,R.Catastrophe Theory for Science and Engineers,New York,Wiley,1999,P10-35
[3]E.V.Vorozhtsov,B.Yu.Scobelev.Symbolic-numerical Method for the Stability Analysis of Difference Schemes on the Basis of the Catastrophe Theory.Journal of computation Physics 2000(16),P26-38
[4]凌复华.突变理论及其应用.上海:上海交通大学出版社,1999,P1-225
[5]桑博德[英],凌复华译.突变理论入门.上海科学技术文献出版社,1998,P1-172
[6]赵松年,于允贤.突变理论及其在生物医学中的应用.科学出版社,1999,P1-110
[7]Armstrong,M.A.著,孙以丰译,李同孚校.基础拓扑学,北京大学出版社.1999,P26-49
[8]哈肯.H.著,徐锡申译,章扬等校.协同学,原子能出版社.2000,P1-152
[9]周绍江.突变理论在环境影响评价中的应用.人民长江.2003,P52-54
[10]Marco Carricato,Joseph Duffy,Vincenzo Parenti-Castelli.Catastrophe analysis of a planar system with flexural pivots.Mechanism and Machine Theory.2002,37:P693-716
[11]孙尧.突变控制技术及其应用研究.哈尔滨工程大学博士学位论文,2002
[12]张亚平,张起森.尖点突变理论在交通流预测中的应用.系统工程学报.2001,3:P272-276
[13]柴立和,彭晓峰.非线性沸腾传热学:分叉和突变理论.自然杂志.20(5),P305
[14]项希勇,穆星,纪晓东.突变理论及其在油气检测中的应用.石油地球物理勘探.2006,3:P269-174
[15]秦四清.斜坡失稳的突变模型与混沌机制.岩石力学与工程学报.1999,4:P486-492
[16]张晓今.翼伞系统稳定性分析的分歧与突变理论法.航天返回与遥感.2004,16(4):P1-6
[17]熊正美,宋永华.突变理论在大电力系统暂态稳定分析中的应用.信息与控制.2001,2:P1-7
[18]赵正跃,项成龙.突变理论在环境预测中的应用.中国环境监测.2002
[19]曹义.突变论中的计算问题.贵州科学.2002,15(4):P309-316
[20]Diederik Aerts,Marek Czachor,Liane Gabora,Maciej Kuna,Andrzej Posiewnik,Jaroslaw Pykacz,Monika.Quantum morphogenesis:Avariation on Thom's catastrophe theory.Research report.2006,15:P1-18
[21]Jonathan Dushoff,Wenzhang Huang,Carlos Castillo-Chavez.Backwards bifurcations and catastrophe in simple models of fatal diseases.Journal of mathematical biology.2003,36:P227-248
[22]Xie Zhikang,Fan Weicheng,Wang Qing'an.Catastrophe mechanism and classification of discontinuity behavior in thermal science(Ⅰ)—fold catastro -phe.Chinese Science Bulletin.2000,45(20):P1905-1912
[23]Eiichi Muramatsu,Masao Ikeda,Takayuki Tamai.Stabilition of a multi-input multi-output plant with variable operating conditions.Nonlinear analysis,theory,methods,and applications,vol.30,no.4,1997.P2291-2296
[24]Igor V.Chernenko.Cargo cult science and the catastrophe theory.Nonlinear analysis.2000,38:P87-103
[25]Anthony N.Kounadis.Dynamic buckling of simple two-bar frames using catastrophe theory.International Journal of Nonlinear Mechanics.2002,37:P1249-1259
[26]Vladislav V.Velichenko.Variational analysis and control of catastrophic dynamical systems.Nonlinear analysis,theory,methods and applications.2001,30(4):P2065-2074
[27]Fu Chang,Jar Der Luo.System catastrophe:A distributive model for collective phenomenon.Research report.2007,13:P1-17
[28]P.T.Saunders.An Introduction to Catastrophe Theory.Cambridge university Press.2003
[29]V I.Arnold.Catastrophe Theory.Second,Revised and Expanded Edition.Springer-Verlag.2000
[30]何平,赵子都.突变理论及其应用[M].大连理工大学出版社,1988
[31]托姆[法].突变论思想和应用[M].上海译文出版社,1998
[32]阮秋琦.数字图像处理学[M].电子工业出版社 2001
[33]郭健.突变理论在复杂系统脆性理论研究中的应用[D].哈尔滨工程大学.2004
[34]甘金来.图像边缘检测算法的比较研究[D].电子科技大学.2005
[35]张晶.图像边缘检测算法的研究[D].山东大学.2006
[36]叶枫.基十灰度图像的边缘检测方法研究[D].西北土业大学.2003
[37]张亚平,张起森.尖点突变理论在交通流预测中的应用[J].系统工程学报.2000,9:P272-276
[38]K.R.Castleman著HALL出版公司.朱志刚,林学阎,电子工业出版社.石定机等译.数字图像处理.1998
[39]Ballard H.Generalizing the bough transform to detect arbitary shapes.Pattern Recognition.2001,13(2):P111-122
[40]邓航,苗雨,石俊,余松煌.用于边缘检测的Snake模型.上海交通大学学报.2000,4(6):P848-850.
[41]Cohen L Cohen I.A finite element method applied to new active contour models and 3D reconstruction from cross sections[A].Proc of 3rd Intern Conf on Computer Vision[C].Paris Ⅸ Univ.France.1999:P587-591.
[42]Braden R,zhang L(RSVP)一一Version Berson S} etal.RFC 2205Resource ReSerVation Protocol functional specification[S].2000.
[43]Howing F,Wermser D.Fuzzy Snake[A],6th Intern Conf on Image Processing and Its Application[C].Dublin.2001,P627-630.
[44]邓航,丙雨,石俊,余松煌.用于边缘检测的Snake模型.上海交通大学学报.2000,14(6):P848-850.
[45]魏立梅,张永瑞,谢维信.人脸识别中边缘检测器的改进.西安电子科技大学学报.2000,25(2):P146-151.
[46]刘宏兵,杨万海,马剑虹.图像小波边缘提取中闭值选取的一种自适应方法.西安电子科技大学学报.2000,27(3):P294-296.
[47]周德龙,潘泉.图像模糊边缘检测的改进算法.中国图象图形学报.2001,6(4):P353-358
[48]李映,焦李成一种有效的基于并行量子进化算法的图像边缘检测方法.信号处理,2003,19(1):P69-74
[49]李映,焦李成.基于自适应免疫遗传算法的边缘检测.中国图像图形学报.2003,8(6):P890-895
[50]A comparative Traps.On System,cost function approach to Man and Cybernetic.2004,edge detection.IEEE 19(6):P1337-1349.