基于模糊方法和小波变换的图像边缘检测
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摘要
边缘是图像中重要的特征之一,反映了图像中最有价值的信息之一。小波变换具有数学显微镜的特征,使用小波变换多尺度可以很好的检测图像的边缘和细节。模糊方法可以通过设置不同的隶属度函数来检测图像的边缘。
本文将模糊方法和小波多尺度变换理论用于图像的边缘检测中,并对每种方法的边缘检测结果进行了详细的分析和比较,通过分析和比较,说明了模糊方法和小波变换与传统的边缘检测方法相比在边缘检测方面的优越性,并将模糊方法和小波变换的边缘检测效果进行了详细的比较。对模糊方法在原有的理论的基础上进行了改进,在快速模糊算法的基础上加入了阈值,使得边缘检测的效果更好,将直方图和模糊方法结合起来,运用多阈值的模糊检测方法,与双阈值的方法检测的边缘效果相比,提取的边缘信息更加丰富。为了检测模糊方法和小波变换的边缘检测的抗噪性能,在原有的图像中加入了椒盐噪声和不同类型的高斯噪声,对噪声图像的边缘检测结果进行了详细的分析和比较,并与传统的边缘检测方法的抗噪效果进行了分析和比较,显示了模糊方法和小波变换在抗噪方面的优越性。本文提出了一种新的多光谱图像的边缘检测方法,将高空间分辨率的全色图像的边缘检测结果应用于多光谱图像的边缘检测中,并用模糊方法和小波变换来检测提出的新方法的可行性,扩展了边缘检测的应用空间,也为遥感图像的解译提供了方便。
Edge, one of the most important characteristic in the image, communicates very valuable information. Fuzzy method can detect image edge by setting different subject functions. And wavelet transform has the character of math microscope which makes the detection of the edge and details perform excellent in the image processing.
This paper applied both wavelet Multi-scale transform and fuzzy method in the image detection. Then it analyzes and compares the results of both methods in detail. It shows that wavelet Multi-scale transform and fuzzy method are more advantageous than the traditional methods. This paper makes an improvement on traditional fuzzy method based on fuzzy theory by adding a restrain value in the fast fuzzy method. By combining the fuzzy method with histogram, it puts forward a multi-value fuzzy method which can detect more precise information of image edge compared with the two-value method. In order to test the new method's performance of edge detection, some salt & pepper and Gaussian noise is added to the original image, and then analyze the results of edge detection of noisy images in detail. It shows the advantage of wavelet Multi-scale transform and fuzzy method in noise resistance, compared with the traditional methods. This paper propounds an original method to detect the Multi-spectrum image's edge, which applies the edge detection result of the panchromatic image to the multi-spectrum image edge detection, and employs the wavelet transform and fuzzy method to test the new method's feasibility. This method expands the range of the edge detection means, also promotes convenience for the remote image's interpretation.
本文将模糊方法和小波多尺度变换理论用于图像的边缘检测中,并对每种方法的边缘检测结果进行了详细的分析和比较,通过分析和比较,说明了模糊方法和小波变换与传统的边缘检测方法相比在边缘检测方面的优越性,并将模糊方法和小波变换的边缘检测效果进行了详细的比较。对模糊方法在原有的理论的基础上进行了改进,在快速模糊算法的基础上加入了阈值,使得边缘检测的效果更好,将直方图和模糊方法结合起来,运用多阈值的模糊检测方法,与双阈值的方法检测的边缘效果相比,提取的边缘信息更加丰富。为了检测模糊方法和小波变换的边缘检测的抗噪性能,在原有的图像中加入了椒盐噪声和不同类型的高斯噪声,对噪声图像的边缘检测结果进行了详细的分析和比较,并与传统的边缘检测方法的抗噪效果进行了分析和比较,显示了模糊方法和小波变换在抗噪方面的优越性。本文提出了一种新的多光谱图像的边缘检测方法,将高空间分辨率的全色图像的边缘检测结果应用于多光谱图像的边缘检测中,并用模糊方法和小波变换来检测提出的新方法的可行性,扩展了边缘检测的应用空间,也为遥感图像的解译提供了方便。
Edge, one of the most important characteristic in the image, communicates very valuable information. Fuzzy method can detect image edge by setting different subject functions. And wavelet transform has the character of math microscope which makes the detection of the edge and details perform excellent in the image processing.
This paper applied both wavelet Multi-scale transform and fuzzy method in the image detection. Then it analyzes and compares the results of both methods in detail. It shows that wavelet Multi-scale transform and fuzzy method are more advantageous than the traditional methods. This paper makes an improvement on traditional fuzzy method based on fuzzy theory by adding a restrain value in the fast fuzzy method. By combining the fuzzy method with histogram, it puts forward a multi-value fuzzy method which can detect more precise information of image edge compared with the two-value method. In order to test the new method's performance of edge detection, some salt & pepper and Gaussian noise is added to the original image, and then analyze the results of edge detection of noisy images in detail. It shows the advantage of wavelet Multi-scale transform and fuzzy method in noise resistance, compared with the traditional methods. This paper propounds an original method to detect the Multi-spectrum image's edge, which applies the edge detection result of the panchromatic image to the multi-spectrum image edge detection, and employs the wavelet transform and fuzzy method to test the new method's feasibility. This method expands the range of the edge detection means, also promotes convenience for the remote image's interpretation.
引文
[1]程正兴,杨守志,冯晓霞等.小波分析的理论算法进展和应用[M].北京:国防工业出版社,2007
[2]Moon Hankyu,Chellappa Rama and Rosenfeld Azriel.Optimal Edge_based Shape Detection[J].IEEETrans.on ImageProcessing,2002,11(11):1209-1227
[3]高秀娟.图像分割的理论方法及应用[D].吉林:吉林大学,2005
[4]李建平.小波分析与信号处理[M].重庆:重庆出版社,1997
[5]崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1997
[6]Mallat S,Hwang W L.Singularity detection and processing with wavelets[J].IEEE Transations on Information Theory,1998,38(2):617-643
[7]梁学章.小波分析[M].北京:国防工业出版社,2005
[8]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
[9]MING-SUEN SHYU,JIN-JANG LEOU.A genetic algorithm approach to color image enhancement[J].Pattern Recongnition,1998,31(7):871-880
[10]Saito,M.A,Cunningham.Generalized E-Filter and Its Application to Edge Detection[J].IEEE Trans Pattern Anal MachineIn tell,1990,12(8):814-817
[11]季虎,孙即祥,邵晓芳等.图像边缘提取方法及展望[J].计算机工程与应用.2004,14:70-75
[12]L.G Roberts,J.Tippet,et al.Machine Perception of three-dimensional Solids[J].In:Optica and Electro-Optical Information Processing,1965,51:159-197
[13]D.Marr and E.C.Hildreth.Theory of Edge Detection[J].Proc.Royal Soc.of London,1980,B207:187-217
[14]徐建华.图像处理与分析[M].北京:科学出版社,1992
[15]乐宋进,武和雷,胡咏芬.图像分割方法的研究现状与展望[J].南昌水专学报,2004,6(23):15-20
[16]Wang JW.Framework combined face segementation with recognition[J].Optical Engineering,2009,48(4):58-64
[17]董鸿雁,沈振康等.自适应模糊边缘减宽增强算法[J].中国图象图形学报,2009,14(2):255-259
[18]S.K.Pal,R.A.King.Image Enhancement using Fuzzy Set[J].IEEE Electronics Letters,1980,16:376-378
[19]Pal S K,King P A.On Edge Detection of X-ray Images using Fuzzy Sets[J].IEEE Trans.Patt.Analysis and Machine Intelligence,1983,5(1):69-77
[20]尚晋,施成湘.小波多尺度模糊竞争边缘检测[J].计算机科学,2005,32(7):182-184
[21]徐蔚然,孔祥维.基于语法、语义信息德多滤波器集成边缘检测[J].模式识别与人工智能,2001,14(4):481-485
[22]刘增良.模糊技术与神经网络技术选编[M].北京:北京航空航天大学出版社,1999
[23]Cao G,Sun QS,Mao ZH,Mei Y.Detection of Core Point in Fingerprint Images Based on Edge Map[J].INTERNATIONAL CONFERENCE ON ELECTRONIC COMPUTER TECHNOLOGY,2009,126-129
[24]Peter M.and Bogdan.G Edge Detection with Embedded Confidence[J].IEEE Trans on Pattern and Machine Intelligence,2001,23(12):1351-1365
[25]A.P.Witkin.Scale-space filtering,Proc.Int.Joint Conf[J].Artificial Intelligent,1983,1019-1022
[26]S.Mallat,S.Zhong.Characterization of Signals From Multi-scale Edges[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(7):710-732
[27]Canny J.A Computational Approach to Edge Detection[J].IEEE-PAMI,1986,8:679-698
[28]Borwonwatanadelok P,Rattanapitak W,Udomhunsakul S.Multi-Focus Image Fusion based on Stationary Wavelet Transform and extended Spatial Frequency Measurement [C].INTERNATIONAL CONFERENCE ON ELECTRONIC COMPUTER TECHNOLOGY,PROCEEDINGS,2009:77-81
[29]Lei Zhang,Paul Bao.Edge Detection by Scale Multiplication in Wave-let Domain [J].Pattern Recognition Letters,2002,23:1771-1784
[30]C.Dueottet,T.Foumel,C.Barat.Scale-adaptive Detection and Local Characterization of Edges Based on Wavelet Transform[J].Signal Processing,2004,84:2115-2137
[31]Jia Li,Xiaojun Jing.Edge detection based on decision-level information fusion and application in hybrid image filtering[C].International Conference on Image Processing,2004:254-259
[32]Deriche R.Using Canny's Criteria to Derive a Recursively Implemented Optimal Edge Detection[J].International Jounral of Computer Vision,1987,(12):167-187
[33]Sarkar S,Boyer K L.Optimal Infinite Impulse Response Edge Detection Filter[J].IEEE Trans on PAMI,1991,13(11):1154-1171
[34]宋焕生,刘春阳,吴成柯等.多尺脊边缘及其在图像目标分割中的应用[J].自动化学报,1999,25(6):12-15
[35]殷德奎,张保民,柏连发等.一种热图像的多模板边缘检测方法[J].南京理工大学学报,1999,23(1):16-20
[36]曹谢东.模糊信息处理及应用[M].北京:科学出版社,2003
[37]飞思科技产品研发中心.matlab 6.5辅助图像处理[M].北京:电子工业出版社,2003
[38]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000
[39]陈幼松.模糊信息处理应用的现状和展望[J].中国计算机用户,1991,(2):16-19
[40]Timothy J.Ross,钱同惠,沈其聪等译.模糊逻辑及其工程应用[M].北京:电子工业出版社,2001
[41]王畅.基于小波变换与模糊方法的图像边缘检测[D].长沙:长沙理工大学,2007
[42]孙福利.模糊边缘检测方法研究[D].大连:大连理工大学,2004
[43]J M Molina,M J Martin.A Fuzzy Reasoning System for Boundary Detection in Radiological Image[J].IEEE,1998:45-49.
[44]Zheng Chunhong,Jiao Licheng.A New Fast Fuzzy Process-ing Method for B-Scan Image[J].IEEE,2001:23-31
[45]Chang S G,Yu Bin,Verserli M.Spatially adaptive wavelet thresholding with context modeling for image denoising[J].IEEE Trans.Image Processing,2000,9(9):522-530
[46]崔冰辉.小波的多尺度变换在图像边缘检测中的应用[D].西安:西安建筑科技大学,2000
[47]Mallat Stephane.Zero-Crossing of a Wavelet Transform[J].IEEE Trans On Information Theory,1991,37(4):1019-1033
[48]S.Mallat.A theory of multiresolution signal decomposition:The wavelet transform[J].IEEE Trans,1989,11(7):674-693
[49]王博,潘全,张洪才等.图像平滑与边缘检测的模糊向量描述[J].小型微型计算机系统,1999,20(3):218-221
[50]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005
[51]钟华.多小波理论及其在边缘检测方面的应用[D].江西:江西师范大学,2005
[52]葛哲学、沙威.小波分析与MATLAB R2007实现[M].北京:电子工业出版社,2007
[53]Mallat Stephane,Zhong Siren.Characterization of Signals from Multiscale Edges[J].IEEE Trans,on Pattern Analysis and Machine Intelligence,1992,14(7):710-733
[54]陈付华,刘纯平,夏德深.对多尺度边缘检测中边缘位移的研究[J].中国图象图形学报,2003,Vol.8(A),No.11:1247-1253.
[55]Xiong Huilin,Zhang Tianxu,Moon Y S.A translation-and Scale-invariant adaptive wavelet transform[J].IEEE Transacitons on Image Processing,2000,9(12):2100-1208
[56]杨煊,梁德群.基于图像信息测度多尺度边缘检测方法[J].模式识别与人工智能,1998,11(4):442-446
[57]耿彦峰等.快速模糊边缘检测算法[J].人工智能及技术识别,2002,10(28):26-27
[58]薛丽霞.基于对象云的遥感图像模糊边缘检测研究[D].成都:西南交通大学,2004
[59]A.Rosenfeld,M.Thurston.Edge and Curve Detection for Visual Scene Analysis[J].IEEE T-Computers,1997:10-20
[60]Yuqian Zhao,Weihua Gui,Zhencheng Chen.Edge detection based on multi-structure elements morphology[C].Sixth World Congress on Intelligent Control and Automation,2006:21-23
[61]杨冰冰.基于小波分析的图像边缘检测算法研究[D].南京:东南大学,2005
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[2]Moon Hankyu,Chellappa Rama and Rosenfeld Azriel.Optimal Edge_based Shape Detection[J].IEEETrans.on ImageProcessing,2002,11(11):1209-1227
[3]高秀娟.图像分割的理论方法及应用[D].吉林:吉林大学,2005
[4]李建平.小波分析与信号处理[M].重庆:重庆出版社,1997
[5]崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1997
[6]Mallat S,Hwang W L.Singularity detection and processing with wavelets[J].IEEE Transations on Information Theory,1998,38(2):617-643
[7]梁学章.小波分析[M].北京:国防工业出版社,2005
[8]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
[9]MING-SUEN SHYU,JIN-JANG LEOU.A genetic algorithm approach to color image enhancement[J].Pattern Recongnition,1998,31(7):871-880
[10]Saito,M.A,Cunningham.Generalized E-Filter and Its Application to Edge Detection[J].IEEE Trans Pattern Anal MachineIn tell,1990,12(8):814-817
[11]季虎,孙即祥,邵晓芳等.图像边缘提取方法及展望[J].计算机工程与应用.2004,14:70-75
[12]L.G Roberts,J.Tippet,et al.Machine Perception of three-dimensional Solids[J].In:Optica and Electro-Optical Information Processing,1965,51:159-197
[13]D.Marr and E.C.Hildreth.Theory of Edge Detection[J].Proc.Royal Soc.of London,1980,B207:187-217
[14]徐建华.图像处理与分析[M].北京:科学出版社,1992
[15]乐宋进,武和雷,胡咏芬.图像分割方法的研究现状与展望[J].南昌水专学报,2004,6(23):15-20
[16]Wang JW.Framework combined face segementation with recognition[J].Optical Engineering,2009,48(4):58-64
[17]董鸿雁,沈振康等.自适应模糊边缘减宽增强算法[J].中国图象图形学报,2009,14(2):255-259
[18]S.K.Pal,R.A.King.Image Enhancement using Fuzzy Set[J].IEEE Electronics Letters,1980,16:376-378
[19]Pal S K,King P A.On Edge Detection of X-ray Images using Fuzzy Sets[J].IEEE Trans.Patt.Analysis and Machine Intelligence,1983,5(1):69-77
[20]尚晋,施成湘.小波多尺度模糊竞争边缘检测[J].计算机科学,2005,32(7):182-184
[21]徐蔚然,孔祥维.基于语法、语义信息德多滤波器集成边缘检测[J].模式识别与人工智能,2001,14(4):481-485
[22]刘增良.模糊技术与神经网络技术选编[M].北京:北京航空航天大学出版社,1999
[23]Cao G,Sun QS,Mao ZH,Mei Y.Detection of Core Point in Fingerprint Images Based on Edge Map[J].INTERNATIONAL CONFERENCE ON ELECTRONIC COMPUTER TECHNOLOGY,2009,126-129
[24]Peter M.and Bogdan.G Edge Detection with Embedded Confidence[J].IEEE Trans on Pattern and Machine Intelligence,2001,23(12):1351-1365
[25]A.P.Witkin.Scale-space filtering,Proc.Int.Joint Conf[J].Artificial Intelligent,1983,1019-1022
[26]S.Mallat,S.Zhong.Characterization of Signals From Multi-scale Edges[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(7):710-732
[27]Canny J.A Computational Approach to Edge Detection[J].IEEE-PAMI,1986,8:679-698
[28]Borwonwatanadelok P,Rattanapitak W,Udomhunsakul S.Multi-Focus Image Fusion based on Stationary Wavelet Transform and extended Spatial Frequency Measurement [C].INTERNATIONAL CONFERENCE ON ELECTRONIC COMPUTER TECHNOLOGY,PROCEEDINGS,2009:77-81
[29]Lei Zhang,Paul Bao.Edge Detection by Scale Multiplication in Wave-let Domain [J].Pattern Recognition Letters,2002,23:1771-1784
[30]C.Dueottet,T.Foumel,C.Barat.Scale-adaptive Detection and Local Characterization of Edges Based on Wavelet Transform[J].Signal Processing,2004,84:2115-2137
[31]Jia Li,Xiaojun Jing.Edge detection based on decision-level information fusion and application in hybrid image filtering[C].International Conference on Image Processing,2004:254-259
[32]Deriche R.Using Canny's Criteria to Derive a Recursively Implemented Optimal Edge Detection[J].International Jounral of Computer Vision,1987,(12):167-187
[33]Sarkar S,Boyer K L.Optimal Infinite Impulse Response Edge Detection Filter[J].IEEE Trans on PAMI,1991,13(11):1154-1171
[34]宋焕生,刘春阳,吴成柯等.多尺脊边缘及其在图像目标分割中的应用[J].自动化学报,1999,25(6):12-15
[35]殷德奎,张保民,柏连发等.一种热图像的多模板边缘检测方法[J].南京理工大学学报,1999,23(1):16-20
[36]曹谢东.模糊信息处理及应用[M].北京:科学出版社,2003
[37]飞思科技产品研发中心.matlab 6.5辅助图像处理[M].北京:电子工业出版社,2003
[38]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000
[39]陈幼松.模糊信息处理应用的现状和展望[J].中国计算机用户,1991,(2):16-19
[40]Timothy J.Ross,钱同惠,沈其聪等译.模糊逻辑及其工程应用[M].北京:电子工业出版社,2001
[41]王畅.基于小波变换与模糊方法的图像边缘检测[D].长沙:长沙理工大学,2007
[42]孙福利.模糊边缘检测方法研究[D].大连:大连理工大学,2004
[43]J M Molina,M J Martin.A Fuzzy Reasoning System for Boundary Detection in Radiological Image[J].IEEE,1998:45-49.
[44]Zheng Chunhong,Jiao Licheng.A New Fast Fuzzy Process-ing Method for B-Scan Image[J].IEEE,2001:23-31
[45]Chang S G,Yu Bin,Verserli M.Spatially adaptive wavelet thresholding with context modeling for image denoising[J].IEEE Trans.Image Processing,2000,9(9):522-530
[46]崔冰辉.小波的多尺度变换在图像边缘检测中的应用[D].西安:西安建筑科技大学,2000
[47]Mallat Stephane.Zero-Crossing of a Wavelet Transform[J].IEEE Trans On Information Theory,1991,37(4):1019-1033
[48]S.Mallat.A theory of multiresolution signal decomposition:The wavelet transform[J].IEEE Trans,1989,11(7):674-693
[49]王博,潘全,张洪才等.图像平滑与边缘检测的模糊向量描述[J].小型微型计算机系统,1999,20(3):218-221
[50]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005
[51]钟华.多小波理论及其在边缘检测方面的应用[D].江西:江西师范大学,2005
[52]葛哲学、沙威.小波分析与MATLAB R2007实现[M].北京:电子工业出版社,2007
[53]Mallat Stephane,Zhong Siren.Characterization of Signals from Multiscale Edges[J].IEEE Trans,on Pattern Analysis and Machine Intelligence,1992,14(7):710-733
[54]陈付华,刘纯平,夏德深.对多尺度边缘检测中边缘位移的研究[J].中国图象图形学报,2003,Vol.8(A),No.11:1247-1253.
[55]Xiong Huilin,Zhang Tianxu,Moon Y S.A translation-and Scale-invariant adaptive wavelet transform[J].IEEE Transacitons on Image Processing,2000,9(12):2100-1208
[56]杨煊,梁德群.基于图像信息测度多尺度边缘检测方法[J].模式识别与人工智能,1998,11(4):442-446
[57]耿彦峰等.快速模糊边缘检测算法[J].人工智能及技术识别,2002,10(28):26-27
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