基于提升小波的图像多尺度边缘检测方法及其应用研究
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摘要
二十世纪末以来，小波变换由于其所具有的优良性质，在理论、方法和应用技术方面得到了快速的发展。而提升小波作为第二代小波，以其独特的算法结构、快速运算能力和低存储需求等优点受到信息科学领域的广泛关注。本文基于提升小波理论重点研究了图像边缘检测问题，提出了一种新的图像多尺度边缘检测方法，并完成了相应的数值与应用特性研究。该检测方法适用于多种线性或非线性双正交小波，具有运算速度快、检测精度高等特点。
基于多尺度图像边缘检测技术，本文研究了飞机结构颤振的边界预测问题，给出了一种新的稳定性参数估计方法。经数字仿真及气弹模型低速风洞颤振试验数据验证，取得了满意的效果。结果表明，本文方法在预测精度及有效性等方面有明显的优势，可以满足工程应用的实际需要。
基于Matlab仿真平台和LabView虚拟仪器集成环境实现了数字仿真及分析软件的设计与开发。
Wavelet transform has been developed quickly in recent decades. Being as the second-generation wavelet with the special algorithm structure, the lifting wavelet is proposed for improving the operation speed of traditional wavelet. In this thesis, a new method of multiscale edge detection of image signal is presented based on lifting wavelet. The related characteristics of the method are studied by numerical simulation. The results show us that the method can be used to many kind of biorthogonal wavelets with the advantages of fast speed and higher precision.
According to the features and requirements of flutter test signal, the method for edge detection is used to pickup the major information of signal image, and a new technique is brought out for the flutter boundary prediction. The feasibility of the technique is examined by using compute simulation and flutter testing of aeroelastic models in low-speed wind tunnel.
All the calculation software is completed under the Matlab and LabView for windows.
基于多尺度图像边缘检测技术，本文研究了飞机结构颤振的边界预测问题，给出了一种新的稳定性参数估计方法。经数字仿真及气弹模型低速风洞颤振试验数据验证，取得了满意的效果。结果表明，本文方法在预测精度及有效性等方面有明显的优势，可以满足工程应用的实际需要。
基于Matlab仿真平台和LabView虚拟仪器集成环境实现了数字仿真及分析软件的设计与开发。
Wavelet transform has been developed quickly in recent decades. Being as the second-generation wavelet with the special algorithm structure, the lifting wavelet is proposed for improving the operation speed of traditional wavelet. In this thesis, a new method of multiscale edge detection of image signal is presented based on lifting wavelet. The related characteristics of the method are studied by numerical simulation. The results show us that the method can be used to many kind of biorthogonal wavelets with the advantages of fast speed and higher precision.
According to the features and requirements of flutter test signal, the method for edge detection is used to pickup the major information of signal image, and a new technique is brought out for the flutter boundary prediction. The feasibility of the technique is examined by using compute simulation and flutter testing of aeroelastic models in low-speed wind tunnel.
All the calculation software is completed under the Matlab and LabView for windows.
引文
[1] Morlet J. "Wave Propagation and Sampling Theory and Complex Wave," Geophysics, 47(2): 222-236, 1982.
[2] Daubechies I. "Orthonormal Bases of Compactly Supported Wavelets," Comm. On Pure and Appl. Math., 41(7): 909-996, 1988.
[3] Mallat S. "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Trans. on PAMI, 11(7): 674-693, 1989.
[4] Mallat S. "Multifrequency Channel Decompositions of Images and Wavelet Models," IEEE Trans on Acoustics, Speech, and signal Processing, 37 (12): 2091-2110, 1989.
[5] Daubechies I. "Ten Lectures on Wavelets," Communications on Pure and Applied Mathematics 41, 1992.
[6] Geronimo J S, Hardin D P, Massopust P R. "Fractal Functions and Wavelet Expansions Based on Several Scaling Functions," Journal of Approx Theory, 78:373-401, 1994.
[7] 何岭松等，“小波分析及其在设备故障诊断中的应用”，《华中理工大学学报》，1993，vol．21(01)：82-87。
[8] Weiss, Lora G., "Wavelet Based Signal Recovery and Denoising of Underwater Acoustic Signals," Wavelet applications in signal and inage processing, Ⅲ; Proceedings of the Meeting, San Diego, CA, July 12-14.1995.Pt 1(A96-2099804-63), Bellingham, WA, Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings. Vol. 2569), 1995.
[9] Pankaj N, Topiwala, "Wavelet Radar Target Classification," Wavelet applications Ⅱ: Proceedings of the Conference, Orlando, FL, Apr.17-21, 1995.Pt. 1(A96-1970104-63), Bellingham, WA, Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings. Vol.2491), 1994.
[10] Popinski, "Wavelet Transform and Its Application for Short Period Earth Rotation Analysis," Artificial Satellites-Planetary Geodesy (No.22) (ISSN 0208-841Ⅹ), Vol.29, No.2 1994.
[11] 刘索，“Laplace小波在颤振试验信号分析中的应用”，西北工业大学硕士论文，2002年3月。
[12] W. Sweldens, "The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions," in Proc. SPIE Wavelet Applications Signal Image
Processing Ⅲ, vol. 2569,A. F. Lain and M. unser, Eds., pp. 68-79 1995.
[13] I. Daubechies, W. Sweldens, "Factoring Wavelet Transforms into Lifting Steps," J. Fourier Anal. Appl., Vol. 4, Nr. 3, 1998.
[14] C. Valens, "The Fast Lifting Wavelet Transform," http://perso.wanadoo.fr, 1999.
[15] 王志武等，“基于自适应提升小波变换多分辨率数据融合”，《系统工程与电子技术》，2002，vol24(10)：8-11。
[16] Kenneth R. Castleman, "Digital Image Processing," Prentice Hall, Inc. 1996.
[17] R.M. Haralick and L.G. Shapiro, "Survey: Image Segmentation," Comput. Vision, Graphics, Image Proc., 29:100-132, 1985.
[18] G. S. Robinson, "Edge Detection by Compass Gradient Masks," CGIP, 6(5):492-501, 1977.
[19] L. G. Roberts, "Machine Perception of Three-Dimensional Solids," in J.T. Tippett, ed., Optical and Electro-Optical Information Procesing, 159-197, MIT Press, Cambridge, MA, 1965.
[20] L. S. Davis, "A Survey of Edge Detection Techniques," Computer Graphics Image Process, 4:248-270, 1975.
[21] J. Prewitt, "Object Enhancement and Extraction," Picture Processing and Psychopictorics, Academic Press, New York, 1970.
[22] Marr D. Hildreth E., "Theory of Edge Detection," Proceedings of R. Soc. London, B207: 187～217, 1980.
[23] Canny J., "A Computational Approach to Edge Detection," IEEE-PAMI, 8:679～698, 1986.
[24] J. M. Prewitt, M. L. Mendelsohn, "The Analysis of Cell Images," Ann. New York Acad. Sci, 128, 1035～1053, 1966.
[25] S. Mallat, S. Zhong, "Characterization of Signals from Multiscale Edges," IEEE Transactions, Pattern Analysis and Machine Intelligence, 14(7): 710-732, 1992.
[26] Norman H. Zimmerman., Jason T. Weissenbureer, "Prediction of Flutter Onset Speed Based on Flight Testing at Subcritical Speeds", J. Aircraft, Vol. 1, No.4, July-Aus. 1964.
[27] S. J. Price, B. H. K.Lee, "Development and Analysis of Flight Flutter Prediction Methods", AIAA-92-2101-CP, 1992.
[28] Yuji Matsuzaki, Yasukatsu Ando, "New Estimation Method for Flutter or
Divergence Boundary from Random Responses at Subcritical Speed", Technical Report of National Aerospace Laboratory TR-667T, 1981.
[29] 肖创柏，“低速颤振模型风洞实验颤振边界预测——李亚普诺夫直接法的应用”，西北工业大学硕士论文，1986年3月。
[30] 林韵，“系统辨识的建模理论和快速算法在颤振边界预测中的应用”，西北工业大学硕士论文，1987年3月。
[31] Pei Chengming, Tan Yunhai, "A New Method in Tegrated Data Modeling and Stability Critertion for Flutter Boundary Perdiction", JSASS 31st Aircraft Symposium, #3A6, Tokyo, Japan, Aug., 1993.
[32] 翟昆，“基于神经网络专家系统的FBP方法”，西北工业大学硕士论文，1999年3月。
[33] 赵善红，“颤振边界预测的时频共振方法研究”，西北工业大学硕士论文，2002年3月。
[34] 裴承鸣，“颤振试验信号的时频共振与图像跟踪识别方法研究”，中国航空科学技术基金，项目编号01A53001，2002年。
[35] 技术合同，《某型飞机机翼／外挂风洞模型颤振试验亚临界数据处理》，中国航空第一集团公司603所，西北工业大学，2002年2月。
[36] 《某型飞机部件／全机低速颤振模型风洞试验任务书》，中国航空第一集团公司603所，2002年5月。
[37] S. Mallat, "A Wavelet Tour of Signal Processing, Second Edition," Academic Press 1999.
[38] 李建平，《小波分析与信号处理——理论、应用及软件实现》，重庆出版社，2001年。
[39] 冉启文、谭立英，《小波分析与分数傅立叶变换及应用》，国防工业出版社，2002年。
[40] 文成林、周东华，《多尺度估计理论及其应用》，清华大学出版社，2002年。
[41] 章国宝等，“基于正交小波变换的多尺度边缘提取”，《中国图像图形学报》1998，vol．3(8)：651-654。
[42] 皮明红、李德仁，“一种多尺度边缘检测的方法”，《信号处理》2000，vol．16(01)：5-8。
[43] 陈东、周大威、王炎等，“用多尺度小波变换进行边缘检测算法的研究”，《计算机工程与设计》，1998，vol．19(2)：35-37。
[44] 刘宏兵、杨万海、张群，“两类阈值对图像小波边缘提取的影响研究”，《系
统工程与电子技术》，2000，vol．22(2)：87-89。
[45] J. Goutsias and H. J. Heijmans, "Nonlinear Multiresolution Signal Decomposition Schemes—Part Ⅰ: Morphological Pyramids," IEEE Trans. Image Processing, vol. 9, pp. 1862-1876, Nov. 2000.
[46] H. J. Heijmans and J. Goutsias, "Nonlinear Multiresolution Signal Decomposition Schemes—Part Ⅱ: Morphological Wavelet," IEEE Trans. Image Processing, vol. 9, pp. 1897-1913, Nov., 2000.
[47] H. J. Heijmans, Gemma Piella, Pesquet-Popescu, "Building Adaptive 2D Wavelet Decompositions by Update Lifting," Image Processing. 2002. Proceedings. 2002 International Conference on, vol. 1, 22-25 Sep., 2002.
[48] D. L. Donoho, "De-noising by Shoft-thresholding," IEEE Trans. Inform Theory, vol. 41, pp. 613-627,1995.
[49] 张哲，“时频域滤波方法及其在颤振信号处理中的应用”，西北工业大学硕士论文，2003年3月。
[2] Daubechies I. "Orthonormal Bases of Compactly Supported Wavelets," Comm. On Pure and Appl. Math., 41(7): 909-996, 1988.
[3] Mallat S. "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Trans. on PAMI, 11(7): 674-693, 1989.
[4] Mallat S. "Multifrequency Channel Decompositions of Images and Wavelet Models," IEEE Trans on Acoustics, Speech, and signal Processing, 37 (12): 2091-2110, 1989.
[5] Daubechies I. "Ten Lectures on Wavelets," Communications on Pure and Applied Mathematics 41, 1992.
[6] Geronimo J S, Hardin D P, Massopust P R. "Fractal Functions and Wavelet Expansions Based on Several Scaling Functions," Journal of Approx Theory, 78:373-401, 1994.
[7] 何岭松等，“小波分析及其在设备故障诊断中的应用”，《华中理工大学学报》，1993，vol．21(01)：82-87。
[8] Weiss, Lora G., "Wavelet Based Signal Recovery and Denoising of Underwater Acoustic Signals," Wavelet applications in signal and inage processing, Ⅲ; Proceedings of the Meeting, San Diego, CA, July 12-14.1995.Pt 1(A96-2099804-63), Bellingham, WA, Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings. Vol. 2569), 1995.
[9] Pankaj N, Topiwala, "Wavelet Radar Target Classification," Wavelet applications Ⅱ: Proceedings of the Conference, Orlando, FL, Apr.17-21, 1995.Pt. 1(A96-1970104-63), Bellingham, WA, Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings. Vol.2491), 1994.
[10] Popinski, "Wavelet Transform and Its Application for Short Period Earth Rotation Analysis," Artificial Satellites-Planetary Geodesy (No.22) (ISSN 0208-841Ⅹ), Vol.29, No.2 1994.
[11] 刘索，“Laplace小波在颤振试验信号分析中的应用”，西北工业大学硕士论文，2002年3月。
[12] W. Sweldens, "The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions," in Proc. SPIE Wavelet Applications Signal Image
Processing Ⅲ, vol. 2569,A. F. Lain and M. unser, Eds., pp. 68-79 1995.
[13] I. Daubechies, W. Sweldens, "Factoring Wavelet Transforms into Lifting Steps," J. Fourier Anal. Appl., Vol. 4, Nr. 3, 1998.
[14] C. Valens, "The Fast Lifting Wavelet Transform," http://perso.wanadoo.fr, 1999.
[15] 王志武等，“基于自适应提升小波变换多分辨率数据融合”，《系统工程与电子技术》，2002，vol24(10)：8-11。
[16] Kenneth R. Castleman, "Digital Image Processing," Prentice Hall, Inc. 1996.
[17] R.M. Haralick and L.G. Shapiro, "Survey: Image Segmentation," Comput. Vision, Graphics, Image Proc., 29:100-132, 1985.
[18] G. S. Robinson, "Edge Detection by Compass Gradient Masks," CGIP, 6(5):492-501, 1977.
[19] L. G. Roberts, "Machine Perception of Three-Dimensional Solids," in J.T. Tippett, ed., Optical and Electro-Optical Information Procesing, 159-197, MIT Press, Cambridge, MA, 1965.
[20] L. S. Davis, "A Survey of Edge Detection Techniques," Computer Graphics Image Process, 4:248-270, 1975.
[21] J. Prewitt, "Object Enhancement and Extraction," Picture Processing and Psychopictorics, Academic Press, New York, 1970.
[22] Marr D. Hildreth E., "Theory of Edge Detection," Proceedings of R. Soc. London, B207: 187～217, 1980.
[23] Canny J., "A Computational Approach to Edge Detection," IEEE-PAMI, 8:679～698, 1986.
[24] J. M. Prewitt, M. L. Mendelsohn, "The Analysis of Cell Images," Ann. New York Acad. Sci, 128, 1035～1053, 1966.
[25] S. Mallat, S. Zhong, "Characterization of Signals from Multiscale Edges," IEEE Transactions, Pattern Analysis and Machine Intelligence, 14(7): 710-732, 1992.
[26] Norman H. Zimmerman., Jason T. Weissenbureer, "Prediction of Flutter Onset Speed Based on Flight Testing at Subcritical Speeds", J. Aircraft, Vol. 1, No.4, July-Aus. 1964.
[27] S. J. Price, B. H. K.Lee, "Development and Analysis of Flight Flutter Prediction Methods", AIAA-92-2101-CP, 1992.
[28] Yuji Matsuzaki, Yasukatsu Ando, "New Estimation Method for Flutter or
Divergence Boundary from Random Responses at Subcritical Speed", Technical Report of National Aerospace Laboratory TR-667T, 1981.
[29] 肖创柏，“低速颤振模型风洞实验颤振边界预测——李亚普诺夫直接法的应用”，西北工业大学硕士论文，1986年3月。
[30] 林韵，“系统辨识的建模理论和快速算法在颤振边界预测中的应用”，西北工业大学硕士论文，1987年3月。
[31] Pei Chengming, Tan Yunhai, "A New Method in Tegrated Data Modeling and Stability Critertion for Flutter Boundary Perdiction", JSASS 31st Aircraft Symposium, #3A6, Tokyo, Japan, Aug., 1993.
[32] 翟昆，“基于神经网络专家系统的FBP方法”，西北工业大学硕士论文，1999年3月。
[33] 赵善红，“颤振边界预测的时频共振方法研究”，西北工业大学硕士论文，2002年3月。
[34] 裴承鸣，“颤振试验信号的时频共振与图像跟踪识别方法研究”，中国航空科学技术基金，项目编号01A53001，2002年。
[35] 技术合同，《某型飞机机翼／外挂风洞模型颤振试验亚临界数据处理》，中国航空第一集团公司603所，西北工业大学，2002年2月。
[36] 《某型飞机部件／全机低速颤振模型风洞试验任务书》，中国航空第一集团公司603所，2002年5月。
[37] S. Mallat, "A Wavelet Tour of Signal Processing, Second Edition," Academic Press 1999.
[38] 李建平，《小波分析与信号处理——理论、应用及软件实现》，重庆出版社，2001年。
[39] 冉启文、谭立英，《小波分析与分数傅立叶变换及应用》，国防工业出版社，2002年。
[40] 文成林、周东华，《多尺度估计理论及其应用》，清华大学出版社，2002年。
[41] 章国宝等，“基于正交小波变换的多尺度边缘提取”，《中国图像图形学报》1998，vol．3(8)：651-654。
[42] 皮明红、李德仁，“一种多尺度边缘检测的方法”，《信号处理》2000，vol．16(01)：5-8。
[43] 陈东、周大威、王炎等，“用多尺度小波变换进行边缘检测算法的研究”，《计算机工程与设计》，1998，vol．19(2)：35-37。
[44] 刘宏兵、杨万海、张群，“两类阈值对图像小波边缘提取的影响研究”，《系
统工程与电子技术》，2000，vol．22(2)：87-89。
[45] J. Goutsias and H. J. Heijmans, "Nonlinear Multiresolution Signal Decomposition Schemes—Part Ⅰ: Morphological Pyramids," IEEE Trans. Image Processing, vol. 9, pp. 1862-1876, Nov. 2000.
[46] H. J. Heijmans and J. Goutsias, "Nonlinear Multiresolution Signal Decomposition Schemes—Part Ⅱ: Morphological Wavelet," IEEE Trans. Image Processing, vol. 9, pp. 1897-1913, Nov., 2000.
[47] H. J. Heijmans, Gemma Piella, Pesquet-Popescu, "Building Adaptive 2D Wavelet Decompositions by Update Lifting," Image Processing. 2002. Proceedings. 2002 International Conference on, vol. 1, 22-25 Sep., 2002.
[48] D. L. Donoho, "De-noising by Shoft-thresholding," IEEE Trans. Inform Theory, vol. 41, pp. 613-627,1995.
[49] 张哲，“时频域滤波方法及其在颤振信号处理中的应用”，西北工业大学硕士论文，2003年3月。
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