基于改进二维离散希尔伯特变换的图像边缘检测方法
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摘要
提出一种新的基于二维希尔伯特变换的边缘检测方法。对于频域信号而言,希尔伯特变换不改变信号的幅值,而仅仅改变其相位,即负频率的相位作+90°相移,而正频率作-90°相移。经由傅里叶变换后,边缘特征呈极值状态,因此本文利用二维离散希尔伯特变换实现边缘检测。由于二维离散希尔伯特变换结果具有方向性,提出利用两个呈正交性的二维离散希尔伯特变换的幅度平方和来检测图像边缘特征。此外将高斯核函数引入到希尔伯特变换中,以减少图像噪声对检测结果的影响,并根据PSNR(峰值信噪比)来确定最佳参数σ,从而得到理想的边缘检测效果。为验证该方法的检测结果,将所提方法与传统边缘检测算子的检测效果进行了比较分析,并将该方法运用于卫星遥感图像中,结果表明该方法可以有效地应用于边缘检测工作中。
A novel algorithm is proposed based on 2-D discrete Hilbert transform.It has been verified that Hilbert transform can be used to detect the edge features from images.The magnitude of signal is not changed,and the phase is shifted in frequency domain after transforming by Hilbert transform.Namely,when the signal is negative,the phaseshift is +90°;when it is positive,the phaseshifit is-90°.There are peaks and valleys on features of signal after Hilbert transform.Thus,the 2-D discrete Hilbert transform to detect image edges is proposed.Because of the directionality of the 2-D discrete Hilbert transform in edge detection,the quadratic sum of two orthogonal 2-D discrete Hilbert transform is calculated to complete the edge detection.Furthermore,Gaussian function is introduced into the 2-D discrete Hilbert transform to reduce the influence from noises,and PSNR(peak signal to noise ratio) is used to determine the optimal parameter σ.An evaluation between the proposed algorithm and the others is realized to verify the result of edge detection.Remotely sensed imageries are chosen as test data in edge features detection.The results of detection show that the proposed algorithm is effective in edge features detection.
A novel algorithm is proposed based on 2-D discrete Hilbert transform.It has been verified that Hilbert transform can be used to detect the edge features from images.The magnitude of signal is not changed,and the phase is shifted in frequency domain after transforming by Hilbert transform.Namely,when the signal is negative,the phaseshift is +90°;when it is positive,the phaseshifit is-90°.There are peaks and valleys on features of signal after Hilbert transform.Thus,the 2-D discrete Hilbert transform to detect image edges is proposed.Because of the directionality of the 2-D discrete Hilbert transform in edge detection,the quadratic sum of two orthogonal 2-D discrete Hilbert transform is calculated to complete the edge detection.Furthermore,Gaussian function is introduced into the 2-D discrete Hilbert transform to reduce the influence from noises,and PSNR(peak signal to noise ratio) is used to determine the optimal parameter σ.An evaluation between the proposed algorithm and the others is realized to verify the result of edge detection.Remotely sensed imageries are chosen as test data in edge features detection.The results of detection show that the proposed algorithm is effective in edge features detection.
引文
[1]ROBERTS L G.Machine Perception of Three DimensionalSolids[C]∥Optical and Electro-optical InformationProcessing.Cambridge:Massachusetts Institute of TechnologyPress,1965:159-197.
[2]SOBEL I.Neighborhood Coding of Binary Images for FastContour Following and General Array Binary Processing[J].Computer Graphics and Image Processing,1978,8:127-135.
[3]CANNY J F.A Computational Approach to Edge Detection[J].IEEE Transactions on Pattern Analysis and MachineIntelligence,1986,8(6):679-698.
[4]MORRONE M C,OWENS R A.Feature Detection fromLocal Energy[J].Pattern Recognition Letters,1987,6(5):303-313.
[5]FIELD D J.Relations between the Statistics of NaturalImages and the Response Properties of Cortical Cells[J].Journal of the Optical Society of America A,1987,4(12):2379-2394.
[6]KOVESI P.Invariant Measures of Image Features fromPhase Information[D].Perth:The University of WesternAustralia,1996.
[7]KOVESI P.Image Features from Phase Congruency[J].A Journal of Computer Vision Research,1999,1(3):1-26.
[8]DUCOTTET C,FOURNEL T,BARAT C.Scale-adaptiveDetection and Local Characterization of Edges Based onWavelet Transform[J].Signal Processing,2004,84(11):2115-2137.
[9]YI S,LABATE D,EASLEY D,et al.A ShearletApproach to Edge Analysis and Detection[J].IEEETransactions on Image Processing,2009,18(5):929-941.
[10]TOIVANEN P J,ANSAMAKI J,PARKKINEN J P S,et al.Edge Detection in Multispectral Images Using theSelf-organizing Map[J].Pattern Recognition Letters,2003,24(16):2987-2994.
[11]SHEN J,CASTAN S.An Optimal Linear Operator forEdge Detection[J].CVGIP:Graphical Models and ImageProcessing,1992,54(2):112-133.
[12]BUSTINCE H,BARRENECHEA E,PAGOLA M,et al.Interval-valued Fuzzy Sets Constructed from Matrices:Appli-cation to Edge Detection[J].Fuzzy Sets and Systems,2009,160(13):1819-1840.
[13]XIAO Pengfeng,FENG Xuezhi,ZHAO Shuhe,et al.Segmentation of High-resolution Remotely Sensed ImageryBased on Phase Congruency[J].Acta Geodaetica etCartographica Sinica,2007,36(2):146-152.(肖鹏峰,冯学智,赵书河,等.基于相位一致的高分辨率遥感图像分割方法[J].测绘学报,2007,36(2):146-152.)
[14]ZHAO Xi’an,LI Deren.Constructing Two DimensionSymmetric Wavelets for Extracting Edge Features ofImage at Multiscales[J].Acta Geodaetica et CartographicaSinica,2003,32(4):113-119.(赵西安,李德仁.2维对称小波与多尺度影像边缘特征提取[J].测绘学报,2003,32(4):113-119.)
[15]KARANDE K J,TALBAR S N.Independent ComponentAnalysis of Edge Information for Face Recognition[J].International Journal of Image Processing,2009,3(3):120-130.
[16]RAMAMURTHY B,CHANDRAN K R.Content BasedImage Retrieval for Medical Image Using Canny EdgeDetection Algorithm[J].International Journal of ComputerApplications,2011,17(6):32-37.
[17]LIVADAS G M,CONSTANTINIDES A G.Image EdgeDetection and Segmentation Based on the Hilbert Trans-form[C]∥Proceedings of IEEE International Conferenceon Acoustics,Speech and Signal Processing.New York:IEEE Computer Society,1988:1152-1155.
[18]CHEN Xuehua,HE Zhenhua,HUANG Deji.Seismic DataEdge Detection Based on Higher-order Pseudo HilbertTransform[J].Progress in Geophysics,2008,23(4):1106-1110.(陈学华,贺振华,黄德济.地震资料的高阶伪希尔伯特变换边缘检[J].地球物理学进展,2008,23(4):1106-1110.)
[19]CHEN Xuehua,HE Zhenhua,HUANG Deji.High-orderPseudo Hilbert Transform and Application in EdgeDetection[J].Journal of Data Acquisition and Processing,2008,23(2):224-227.(陈学华,贺振华,黄德济.高阶伪希尔伯特变换在边缘检测中的应用[J].数据采集与处理,2008,23(2):224-227.)
[20]KOHLMANN K.Corner Detection in Natural ImagesBased on the 2-D Hilbert Transform[J].Signal Processing,1996,48:225-234.
[21]READ R R,TREITEL S.The Stabilization of Two-dimensional Recursive Filters via the Discrete HilbertTransform[J].IEEE Transactions on GeoscienceElectronics,1973,11:153-160.
[22]BOSE N K,PRABHU K A.Two-dimensional DiscreteHilbert Transforms and Computational ComplexityAspects in Its Implementation[J].IEEE Transactions onAcoustics,Speech,and Signal Processing,1979,27(4):356-360.
[23]MARR D,HILDRETH E C.Theory of Edge Detection[C]∥Proceedings of the Royal Society of London:SeriesB,Biological Sciences.London:the Royal Society,1980:187-217.
[24]Van RIJSBERGEN C J.Information Retrieval[M].2nded.London:Butterworths,1979.
[2]SOBEL I.Neighborhood Coding of Binary Images for FastContour Following and General Array Binary Processing[J].Computer Graphics and Image Processing,1978,8:127-135.
[3]CANNY J F.A Computational Approach to Edge Detection[J].IEEE Transactions on Pattern Analysis and MachineIntelligence,1986,8(6):679-698.
[4]MORRONE M C,OWENS R A.Feature Detection fromLocal Energy[J].Pattern Recognition Letters,1987,6(5):303-313.
[5]FIELD D J.Relations between the Statistics of NaturalImages and the Response Properties of Cortical Cells[J].Journal of the Optical Society of America A,1987,4(12):2379-2394.
[6]KOVESI P.Invariant Measures of Image Features fromPhase Information[D].Perth:The University of WesternAustralia,1996.
[7]KOVESI P.Image Features from Phase Congruency[J].A Journal of Computer Vision Research,1999,1(3):1-26.
[8]DUCOTTET C,FOURNEL T,BARAT C.Scale-adaptiveDetection and Local Characterization of Edges Based onWavelet Transform[J].Signal Processing,2004,84(11):2115-2137.
[9]YI S,LABATE D,EASLEY D,et al.A ShearletApproach to Edge Analysis and Detection[J].IEEETransactions on Image Processing,2009,18(5):929-941.
[10]TOIVANEN P J,ANSAMAKI J,PARKKINEN J P S,et al.Edge Detection in Multispectral Images Using theSelf-organizing Map[J].Pattern Recognition Letters,2003,24(16):2987-2994.
[11]SHEN J,CASTAN S.An Optimal Linear Operator forEdge Detection[J].CVGIP:Graphical Models and ImageProcessing,1992,54(2):112-133.
[12]BUSTINCE H,BARRENECHEA E,PAGOLA M,et al.Interval-valued Fuzzy Sets Constructed from Matrices:Appli-cation to Edge Detection[J].Fuzzy Sets and Systems,2009,160(13):1819-1840.
[13]XIAO Pengfeng,FENG Xuezhi,ZHAO Shuhe,et al.Segmentation of High-resolution Remotely Sensed ImageryBased on Phase Congruency[J].Acta Geodaetica etCartographica Sinica,2007,36(2):146-152.(肖鹏峰,冯学智,赵书河,等.基于相位一致的高分辨率遥感图像分割方法[J].测绘学报,2007,36(2):146-152.)
[14]ZHAO Xi’an,LI Deren.Constructing Two DimensionSymmetric Wavelets for Extracting Edge Features ofImage at Multiscales[J].Acta Geodaetica et CartographicaSinica,2003,32(4):113-119.(赵西安,李德仁.2维对称小波与多尺度影像边缘特征提取[J].测绘学报,2003,32(4):113-119.)
[15]KARANDE K J,TALBAR S N.Independent ComponentAnalysis of Edge Information for Face Recognition[J].International Journal of Image Processing,2009,3(3):120-130.
[16]RAMAMURTHY B,CHANDRAN K R.Content BasedImage Retrieval for Medical Image Using Canny EdgeDetection Algorithm[J].International Journal of ComputerApplications,2011,17(6):32-37.
[17]LIVADAS G M,CONSTANTINIDES A G.Image EdgeDetection and Segmentation Based on the Hilbert Trans-form[C]∥Proceedings of IEEE International Conferenceon Acoustics,Speech and Signal Processing.New York:IEEE Computer Society,1988:1152-1155.
[18]CHEN Xuehua,HE Zhenhua,HUANG Deji.Seismic DataEdge Detection Based on Higher-order Pseudo HilbertTransform[J].Progress in Geophysics,2008,23(4):1106-1110.(陈学华,贺振华,黄德济.地震资料的高阶伪希尔伯特变换边缘检[J].地球物理学进展,2008,23(4):1106-1110.)
[19]CHEN Xuehua,HE Zhenhua,HUANG Deji.High-orderPseudo Hilbert Transform and Application in EdgeDetection[J].Journal of Data Acquisition and Processing,2008,23(2):224-227.(陈学华,贺振华,黄德济.高阶伪希尔伯特变换在边缘检测中的应用[J].数据采集与处理,2008,23(2):224-227.)
[20]KOHLMANN K.Corner Detection in Natural ImagesBased on the 2-D Hilbert Transform[J].Signal Processing,1996,48:225-234.
[21]READ R R,TREITEL S.The Stabilization of Two-dimensional Recursive Filters via the Discrete HilbertTransform[J].IEEE Transactions on GeoscienceElectronics,1973,11:153-160.
[22]BOSE N K,PRABHU K A.Two-dimensional DiscreteHilbert Transforms and Computational ComplexityAspects in Its Implementation[J].IEEE Transactions onAcoustics,Speech,and Signal Processing,1979,27(4):356-360.
[23]MARR D,HILDRETH E C.Theory of Edge Detection[C]∥Proceedings of the Royal Society of London:SeriesB,Biological Sciences.London:the Royal Society,1980:187-217.
[24]Van RIJSBERGEN C J.Information Retrieval[M].2nded.London:Butterworths,1979.
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