基于小波变换的图像边缘检测技术
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摘要
现代战争正在向信息化发展，作为典型信息化兵器的精确制导武器已经被广泛的应用于战争。成像制导技术是当代精确制导技术的发展主流和方向。在成像制导技术中，首先要进行目标图像的目标提取和识别。在目标图像的目标提取和识别中最基本的图像处理技术就是图像边缘检测技术。
本文以基于小波变换的边缘检测技术为基础，在小波多分辨分析的框架下构造基于边缘检测的两类B样条单正交小波基函数，并改进现有的基于小波变换的边缘检测算法。
主要工作如下：
(1)深入研究图像边缘检测技术和小波变换理论。
(2)在分析Canny边缘检测算法和LoG边缘检测算法的基础上，针对高斯滤波器存在过度光滑图像和丢失缓变边缘的问题，采用基于小波变换的边缘检测算法。
(3)根据边缘检测的评价准则，参照最佳边缘滤波器的设计要求，确定用于边缘检测的小波基函数的一般准则，并在此基础上构造两类B样条小波函数。采用自适应平滑滤波锐化图像边缘，再进行小波边缘检测算法，提出改进的基于B样条小波变换的边缘检测算法。
(4)提出基于改进的B样条小波变换的自适应阈值图像边缘检测算法。
With further requirement of the modern war, precision guided weapon has been widely used. Imaging-based guided technology is the important development direction of precision guided technology. The fundamental image processing technology of target extract and recognition is image edge detection technology.
By means of Mallat' s multiscale analysis, we construct two type of arbitrary order cardinal B-spline wavelet. In order to avoid the loss of weak edge, take adaptive filter to sharp image edge. This is the improved image edge detection based on wavelet transform.
The important work of this paper:
1. Deeply study image detection technology and wavelet analysis theory.
2. Based on studying Canny operator and LoG operator, we take wavelet edge detection in allusion to smoothing image extremely and losing weak edge existed in Gaussian filter.
3. According to the criterion of edge detection and consulting the design-aim of optimal edge-filter, this paper discussed the general rules of selecting the mother function of wavelet used in edge detection, construct two type B-spline wavelet function. Though avoiding noise disturbance, this method will lose some weak edge. So we take adaptive filter to sharp image edge in order to avoid losing image weak edge.
4. Adaptive thresholds edge detection for image based on wavelet transform was presented to avoid losing weak edge.
本文以基于小波变换的边缘检测技术为基础，在小波多分辨分析的框架下构造基于边缘检测的两类B样条单正交小波基函数，并改进现有的基于小波变换的边缘检测算法。
主要工作如下：
(1)深入研究图像边缘检测技术和小波变换理论。
(2)在分析Canny边缘检测算法和LoG边缘检测算法的基础上，针对高斯滤波器存在过度光滑图像和丢失缓变边缘的问题，采用基于小波变换的边缘检测算法。
(3)根据边缘检测的评价准则，参照最佳边缘滤波器的设计要求，确定用于边缘检测的小波基函数的一般准则，并在此基础上构造两类B样条小波函数。采用自适应平滑滤波锐化图像边缘，再进行小波边缘检测算法，提出改进的基于B样条小波变换的边缘检测算法。
(4)提出基于改进的B样条小波变换的自适应阈值图像边缘检测算法。
With further requirement of the modern war, precision guided weapon has been widely used. Imaging-based guided technology is the important development direction of precision guided technology. The fundamental image processing technology of target extract and recognition is image edge detection technology.
By means of Mallat' s multiscale analysis, we construct two type of arbitrary order cardinal B-spline wavelet. In order to avoid the loss of weak edge, take adaptive filter to sharp image edge. This is the improved image edge detection based on wavelet transform.
The important work of this paper:
1. Deeply study image detection technology and wavelet analysis theory.
2. Based on studying Canny operator and LoG operator, we take wavelet edge detection in allusion to smoothing image extremely and losing weak edge existed in Gaussian filter.
3. According to the criterion of edge detection and consulting the design-aim of optimal edge-filter, this paper discussed the general rules of selecting the mother function of wavelet used in edge detection, construct two type B-spline wavelet function. Though avoiding noise disturbance, this method will lose some weak edge. So we take adaptive filter to sharp image edge in order to avoid losing image weak edge.
4. Adaptive thresholds edge detection for image based on wavelet transform was presented to avoid losing weak edge.
引文
[1] 王润生，图像理解，国防科技大学出版社，1995
[2] J. Canny:A Computational Approach to Edge Detection, IEEE Trans on PAMI, Vol. 8, No. 6,679-698,1986
[3] 周心明，兰赛，徐燕：图像处理中的几种边缘检测算法的比较，现代电力，Vol．17，No．3，2000
[4] Y. Meyer: Pseudodifferential Operators, Proc. Symp. Pure. Math.,Vol. 43, No. 2,215-235,1985
[5] P. Lemarie and Y. Meyer: Ondelettes et Bases Hilbertiennes, Revista Mathematica Ibero Americana, Vol. 2, No.1,1-18,1986
[6] S. Mallat:A Theory for Multiresolution Signal Decomposition:The wavelet Representation, IEEE Trans. On PAML, Vol. 11, No. 7,674-693,1989
[7] S. Mallat:Multifrequency Channel Decopositions of Images and Wavelet Models. IEEE Trans, on ASSP, Vlo37, No. 12,2091=2110,1989
[8] C.E. Heil ,D.F. Walnut:Continuous and Discrete Wavelet Transforms, SLAM Review, 1989, Vol. 31, No. 4,628-666,1989
[9] O. Rioul and M. Vetterti:Wavelets and Signal Processing, IEEE Trans. On SP Mag, Nov, 14-38,1991
[10] S. Semmea: Nonlinear Fourier Analysis, Bulletin (New Series) of the AMS, Vol. 20, No.1,1-19,1989
[11] 邓东皋，彭立中：小波分析，数学进展，Vol．20，No．3，194-310，1990
[12] 焦李成，保铮：子波理论与应用，系统工程与电子技术，No．11，1-13，1993
[13] 焦李成，保铮：子波理论与应用：进展与展望，电子学报，Vol．21，No．7，91-96，1993
[14] 张小平，田立生，彭应宁：从时频分布到连续子波变换，电子科学学刊，Vol．16，No．6，631-640，1994
[15] T. Poggio, H. Voorhees andA. Yuille, "A Regularized Solution to Edge Detection," Tech. ReD. MA, Rep. AIM-833, MITArtificial Intell. Lab., May, 1985
[16] Vishvjit S. Nalwa and Thomas O. Binford, "On Detecting Edged" IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 6, pp. 699-714, Nov. 1986
[17] D.C. Marr and E. Hildreth, "Theory of Edge Detection," Proc. Roy. Soc. London, vol. B275, pp. 187-217, 1980
[18] S.O. Rice, "Mathematical Analysis of Random Noise," Bell Syst Tech. J., vol. 24, pp. 46-156, 1945
[19] I. Daubechines, "Where Do Wavelets Come From?-A Personal Point of View", IEEE Trans. on Proceedings, Vol. 84, No. 4, pp. 510-513, 1996
[20] W.H. Lunscher and M.P. Beddoes, "Optimal Edge Detector Design I: Parameter Selection and Noise Effects", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, pp. 164-177, 1986
[21] W.H. Lunscher and M.P. Beddoes, "Optimal Edge Detector Design Ⅱ: Coefficient Quantization," IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, pp. 178-187, 1986
[22] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of L2, Trans. Amer. Math. Soc.,315,69-87,1989
[23] I. Daubechines:Orthonormal Bases of Compactly Supported Wavelats, Comm in Pure Applied Math.,Vol. 41, No.7,909-996,1988
[24] I. Daubechines:The Wavelet Transform, Time-Frequency Location and Sgnal Analysis. IEEE Trans. on Information Theory, Vol. 36, No. 5,961-10051990
[25] S. Mallat and S. Zhong:Characterization of Signals from Multiscale Edges IEEE Trans. On PAMI.,Vol. 14, No. 7,733-750,1992
[26] 张小洪，杨丹，刘亚威，基于Canny算子的改进型边缘检测算法，计算机工
程与应用, Vol. 29,113-115,2003
[27] Y. Meyer:Ondelettles et Functions Spline, Seminaire, EDP, Ecole Polytechnique Paris, France, Dec.,1983
[28] S. Mallat:Multiresolution Approximations and Wavelet Orthonormal Bases of L~2(R), Trans. AMS, Vol. 315, No.1,69-87,1988
[29] S.O. Rice, "Mathematical Analysis of Random Noise," Bell Syst Tech. J., vol. 24, pp. 46-156, 1945
[30] C.R. Chui and J.Z. Wang:On Compactly Supported Spline Wavelets and A Duality Principle, Trans. Amer. Math. Soc.,Vol. 330, No. 2,903-915,1992
[31] C.R. Chui and J.Z. Wang:An introduction to Wavelets, Academic Press, 1992, Bodston, USA
[32] Chui C. R.,Wang J.Z.,A general framework for compactly supported spline and wavelets, J. Approx. Theory, Vol. 71, pp. 263-307,1992
[33] M. Unser, A. Aldroubi, M. eden, Fast B-spline transforms for continuous image representation and interpolation, IEEE Trans. PAMI, Vol. 13, pp. 277-285,1991
[34] M. Unser, A. Aldroubi, M. Eden, A family of polynomial spline wavelet transforms ,Signal Processing, 1993, No. 3, pp. 141-162
[35] I.J. Schoenberg, Cardinal interpolation and spline functions, Approximation Theory, Vol. 2, pp. 167-206,1969
[36] 刘曙光，刘明远：任意阶基数B样条正交小波基的构造，CIAC’96中国智能自动化学术会议
[37] 刘曙光，刘明远：基于Canny准则的基数B样条小波边缘检测，CCC’96中国控制会议
[38] Unser M, Aldroubi A, Eden M. On the asymptotic convergence of B-spline wavelets to Gabor functions. IEEE Trans. Inf. Theory,, 1992,38(2):864-872
[39] 贾天旭，郑南宁，张元亮：中心B样条二进小波多尺度边缘提取，自动化学报，Vol．24，No．2，1998
[40] 景晓军，李剑锋，熊玉庆：图像的一种自适应平滑滤波算法，通信学报，Vol．23，No．10，2002
[41] 张书玲，张小华：基于小波变换的边缘检测，西北大学学报，Vol．30，N0．2，2000
[42] 张宏群，张雪，肖旺新：小波变换的自适应阈值图像边缘检测方法，Vol．32．No．1，2003
[43] 刘曙光：B样条小波研究及其在仪表板图像处理中的应用，西安交通大学博士论文，1998
[44] 王郑耀：数字图像的边缘检测，西安交通大学博士论文，2003
[45] 程正兴：数据拟合，西安交通大学出版社，1986年
[46] 杨福生：小波变换的工程分析与应用，科学出版社，2001年
[47] 胡昌华，张军波，夏军，张伟：基于Matlab的系统分析与设计—小波分析西安电子科技大学出版社，2001年
[2] J. Canny:A Computational Approach to Edge Detection, IEEE Trans on PAMI, Vol. 8, No. 6,679-698,1986
[3] 周心明，兰赛，徐燕：图像处理中的几种边缘检测算法的比较，现代电力，Vol．17，No．3，2000
[4] Y. Meyer: Pseudodifferential Operators, Proc. Symp. Pure. Math.,Vol. 43, No. 2,215-235,1985
[5] P. Lemarie and Y. Meyer: Ondelettes et Bases Hilbertiennes, Revista Mathematica Ibero Americana, Vol. 2, No.1,1-18,1986
[6] S. Mallat:A Theory for Multiresolution Signal Decomposition:The wavelet Representation, IEEE Trans. On PAML, Vol. 11, No. 7,674-693,1989
[7] S. Mallat:Multifrequency Channel Decopositions of Images and Wavelet Models. IEEE Trans, on ASSP, Vlo37, No. 12,2091=2110,1989
[8] C.E. Heil ,D.F. Walnut:Continuous and Discrete Wavelet Transforms, SLAM Review, 1989, Vol. 31, No. 4,628-666,1989
[9] O. Rioul and M. Vetterti:Wavelets and Signal Processing, IEEE Trans. On SP Mag, Nov, 14-38,1991
[10] S. Semmea: Nonlinear Fourier Analysis, Bulletin (New Series) of the AMS, Vol. 20, No.1,1-19,1989
[11] 邓东皋，彭立中：小波分析，数学进展，Vol．20，No．3，194-310，1990
[12] 焦李成，保铮：子波理论与应用，系统工程与电子技术，No．11，1-13，1993
[13] 焦李成，保铮：子波理论与应用：进展与展望，电子学报，Vol．21，No．7，91-96，1993
[14] 张小平，田立生，彭应宁：从时频分布到连续子波变换，电子科学学刊，Vol．16，No．6，631-640，1994
[15] T. Poggio, H. Voorhees andA. Yuille, "A Regularized Solution to Edge Detection," Tech. ReD. MA, Rep. AIM-833, MITArtificial Intell. Lab., May, 1985
[16] Vishvjit S. Nalwa and Thomas O. Binford, "On Detecting Edged" IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 6, pp. 699-714, Nov. 1986
[17] D.C. Marr and E. Hildreth, "Theory of Edge Detection," Proc. Roy. Soc. London, vol. B275, pp. 187-217, 1980
[18] S.O. Rice, "Mathematical Analysis of Random Noise," Bell Syst Tech. J., vol. 24, pp. 46-156, 1945
[19] I. Daubechines, "Where Do Wavelets Come From?-A Personal Point of View", IEEE Trans. on Proceedings, Vol. 84, No. 4, pp. 510-513, 1996
[20] W.H. Lunscher and M.P. Beddoes, "Optimal Edge Detector Design I: Parameter Selection and Noise Effects", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, pp. 164-177, 1986
[21] W.H. Lunscher and M.P. Beddoes, "Optimal Edge Detector Design Ⅱ: Coefficient Quantization," IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, pp. 178-187, 1986
[22] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of L2, Trans. Amer. Math. Soc.,315,69-87,1989
[23] I. Daubechines:Orthonormal Bases of Compactly Supported Wavelats, Comm in Pure Applied Math.,Vol. 41, No.7,909-996,1988
[24] I. Daubechines:The Wavelet Transform, Time-Frequency Location and Sgnal Analysis. IEEE Trans. on Information Theory, Vol. 36, No. 5,961-10051990
[25] S. Mallat and S. Zhong:Characterization of Signals from Multiscale Edges IEEE Trans. On PAMI.,Vol. 14, No. 7,733-750,1992
[26] 张小洪，杨丹，刘亚威，基于Canny算子的改进型边缘检测算法，计算机工
程与应用, Vol. 29,113-115,2003
[27] Y. Meyer:Ondelettles et Functions Spline, Seminaire, EDP, Ecole Polytechnique Paris, France, Dec.,1983
[28] S. Mallat:Multiresolution Approximations and Wavelet Orthonormal Bases of L~2(R), Trans. AMS, Vol. 315, No.1,69-87,1988
[29] S.O. Rice, "Mathematical Analysis of Random Noise," Bell Syst Tech. J., vol. 24, pp. 46-156, 1945
[30] C.R. Chui and J.Z. Wang:On Compactly Supported Spline Wavelets and A Duality Principle, Trans. Amer. Math. Soc.,Vol. 330, No. 2,903-915,1992
[31] C.R. Chui and J.Z. Wang:An introduction to Wavelets, Academic Press, 1992, Bodston, USA
[32] Chui C. R.,Wang J.Z.,A general framework for compactly supported spline and wavelets, J. Approx. Theory, Vol. 71, pp. 263-307,1992
[33] M. Unser, A. Aldroubi, M. eden, Fast B-spline transforms for continuous image representation and interpolation, IEEE Trans. PAMI, Vol. 13, pp. 277-285,1991
[34] M. Unser, A. Aldroubi, M. Eden, A family of polynomial spline wavelet transforms ,Signal Processing, 1993, No. 3, pp. 141-162
[35] I.J. Schoenberg, Cardinal interpolation and spline functions, Approximation Theory, Vol. 2, pp. 167-206,1969
[36] 刘曙光，刘明远：任意阶基数B样条正交小波基的构造，CIAC’96中国智能自动化学术会议
[37] 刘曙光，刘明远：基于Canny准则的基数B样条小波边缘检测，CCC’96中国控制会议
[38] Unser M, Aldroubi A, Eden M. On the asymptotic convergence of B-spline wavelets to Gabor functions. IEEE Trans. Inf. Theory,, 1992,38(2):864-872
[39] 贾天旭，郑南宁，张元亮：中心B样条二进小波多尺度边缘提取，自动化学报，Vol．24，No．2，1998
[40] 景晓军，李剑锋，熊玉庆：图像的一种自适应平滑滤波算法，通信学报，Vol．23，No．10，2002
[41] 张书玲，张小华：基于小波变换的边缘检测，西北大学学报，Vol．30，N0．2，2000
[42] 张宏群，张雪，肖旺新：小波变换的自适应阈值图像边缘检测方法，Vol．32．No．1，2003
[43] 刘曙光：B样条小波研究及其在仪表板图像处理中的应用，西安交通大学博士论文，1998
[44] 王郑耀：数字图像的边缘检测，西安交通大学博士论文，2003
[45] 程正兴：数据拟合，西安交通大学出版社，1986年
[46] 杨福生：小波变换的工程分析与应用，科学出版社，2001年
[47] 胡昌华，张军波，夏军，张伟：基于Matlab的系统分析与设计—小波分析西安电子科技大学出版社，2001年
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