几种ESPI滤波方法的比较及基于RBF散斑信息提取方法的研究
|
摘要
光学测量技术是一种全场、非接触无损检测技术，渗透到科学和工程的多个领域。电子散斑干涉技术(ESPI)和数字散斑相关方法(DSCM)是两种最常用的光学测量方法。高精度的信息提取是这两种光学测量技术应用的基础。本文就电子散斑干涉技术和数字散斑相关方法中有关信息提取的一些关键问题进行了研究。电子散斑干涉测量以条纹图或相位图的形式表现测量结果，然而无论是条纹图还是相位图都含有大量的噪声，严重干扰了相位信息的提取。因此，如何有效地降低噪声的影响，提高条纹的对比度，成为电子散斑干涉测量技术的关键问题之一。数字散斑相关法通过相关搜索算法获得被测试件的位移场，搜索算法的性能将直接影响测量精度的高低及测量的实时性。如何提高相关算法的计算精度和计算效率也成为数字散斑相关技术的关键问题之一。
本文的具体工作包括：
(1)基于偏微分方程(PDE)的滤波方法是ESPI滤波中的有效工具。本文比较分析了六个非方向偏微分方程和两个方向偏微分方程滤波模型的性能，总结了每个滤波模型的特点及各自的适应性。
(2)通过我们的分析比较，结果表明方向二阶PDE滤波模型是一种有效的PDE模型。本文进一步将该模型与几种有代表性的、新近的ESPI滤波方法进行了比较分析，包括窗傅里叶滤波法、正则化二次方向成本函数法、新近的方向模板滤波法和局域傅里叶变换滤波法，并对各方法的滤波性能进行了总结。
(3)将径向基函数引入到ESPI信息提取中，包括：针对粗宽ESPI条纹图，提出了基于径向基函数的ESPI条纹图滤波的新方法；将径向基函数应用于条纹骨架线法的条纹级数插值中；采用径向基函数对相位解包裹得到的相位进行平滑处理。利用基于径向基函数的信息提取新方法对三氧化二铝(Al2O3)陶瓷基片在激光照射下不同时刻的热变形进行了测量。
(4)提出了一种基于数字散斑相关法和径向基函数插值相结合的位移场分析新方法，径向基函数插值对散乱数据具有高精度的逼近能力，新方法的计算效率同时得到提高。由该方法获得的位移场不再需要任何平滑技术进行后处理。将该方法应用于铝片刚体位移变形场和试验梁三点弯曲变形场的测量，获得了较理想的位移场。
Optical measurement technology as a kind of whole-field, non-contactnondestructive measurement technique, has permeated into many fields of scientificand engineering. Electronic speckle pattern interferometry (ESPI) technology anddigital speckle correlation method (DSCM) are two kinds of commonly used opticalmeasurement technology. Information extraction with high accuracy is of fundamentalto optical measurement technology. In this paper some key problems to these twotechniques in information extraction are studied. ESPI measurement delive themeasurement results in the form of fringe patterns or phase patterns, both fringepatterns and phase patterns contain heavy speckle noise, which hampers the extractionof phase information seriously. Therefore, how to reduce the influence of specklenoise effectively, and improve the contrast of the fringe has become one key issue toESPI measurement technology. DSCM acquires the displacements of the testspecimen by use of correlation algorithm. The performance of the correlationalgorithm makes influence on the measurement accuracy and real-timing directly.Improving computing efficiency and accuracy is the key problem in this technique.
The work in this dissertation is as follows:
(1) The filtering model based on partial differential equation is an effective toolin ESPI filtering. Six non-orientation and two orientation partial differentialequation filtering models are analyzed and compared, and the feature of eachpartial differential equation filtering model and their respective flexibility aresummarized.
(2) By use of the analyzing and comparing the eight PDE filtering model, theresult indicates that the second-order oriented PDE model is the mosteffective model. This PDE model is analyzed and compared with severalother representative and recent ESPI filtering methods, mainly including thewindowed Fourier transform method (WFF), the oriented, regularizedquadratic cost function (ORQCF) method, the oriented spatial filter masks(OSFM) and the localized Fourier transform filter (LFF). The summary ofthe performance for these filtering methods are presented.
(3) Introducing the Radial basis function(RBF) to ESPI information extraction, mainly including: the new filtering method based on radial basis function forESPI fringe patterns with wide density; introducing the radial basis functionto interpolate the number of fringe in the fringe skeleton method; smoothingthe phase acquired by phase unwrapping algorithm by use of the radial basisfunction. By use of the information extraction method based on RBF, thethermal deformation of the Al2O3ceramic substrate at different moment ismeasured on the circumstance of laser radiation.
(4) A new method for displacement field analysis based on the combination ofDSCM with RBF interpolation is proposed. The ability to approximatescattered data make this method has the advantage with better accuracy andless computational time. Another advantage is that this method does notrequire any smoothing algorithm to process the discrete displacement fielddata obtained. Using this method, the displacement fields for rigid bodytranslation and three-point bending are analyzed, the accurate displacementfields are acquired.
本文的具体工作包括：
(1)基于偏微分方程(PDE)的滤波方法是ESPI滤波中的有效工具。本文比较分析了六个非方向偏微分方程和两个方向偏微分方程滤波模型的性能，总结了每个滤波模型的特点及各自的适应性。
(2)通过我们的分析比较，结果表明方向二阶PDE滤波模型是一种有效的PDE模型。本文进一步将该模型与几种有代表性的、新近的ESPI滤波方法进行了比较分析，包括窗傅里叶滤波法、正则化二次方向成本函数法、新近的方向模板滤波法和局域傅里叶变换滤波法，并对各方法的滤波性能进行了总结。
(3)将径向基函数引入到ESPI信息提取中，包括：针对粗宽ESPI条纹图，提出了基于径向基函数的ESPI条纹图滤波的新方法；将径向基函数应用于条纹骨架线法的条纹级数插值中；采用径向基函数对相位解包裹得到的相位进行平滑处理。利用基于径向基函数的信息提取新方法对三氧化二铝(Al2O3)陶瓷基片在激光照射下不同时刻的热变形进行了测量。
(4)提出了一种基于数字散斑相关法和径向基函数插值相结合的位移场分析新方法，径向基函数插值对散乱数据具有高精度的逼近能力，新方法的计算效率同时得到提高。由该方法获得的位移场不再需要任何平滑技术进行后处理。将该方法应用于铝片刚体位移变形场和试验梁三点弯曲变形场的测量，获得了较理想的位移场。
Optical measurement technology as a kind of whole-field, non-contactnondestructive measurement technique, has permeated into many fields of scientificand engineering. Electronic speckle pattern interferometry (ESPI) technology anddigital speckle correlation method (DSCM) are two kinds of commonly used opticalmeasurement technology. Information extraction with high accuracy is of fundamentalto optical measurement technology. In this paper some key problems to these twotechniques in information extraction are studied. ESPI measurement delive themeasurement results in the form of fringe patterns or phase patterns, both fringepatterns and phase patterns contain heavy speckle noise, which hampers the extractionof phase information seriously. Therefore, how to reduce the influence of specklenoise effectively, and improve the contrast of the fringe has become one key issue toESPI measurement technology. DSCM acquires the displacements of the testspecimen by use of correlation algorithm. The performance of the correlationalgorithm makes influence on the measurement accuracy and real-timing directly.Improving computing efficiency and accuracy is the key problem in this technique.
The work in this dissertation is as follows:
(1) The filtering model based on partial differential equation is an effective toolin ESPI filtering. Six non-orientation and two orientation partial differentialequation filtering models are analyzed and compared, and the feature of eachpartial differential equation filtering model and their respective flexibility aresummarized.
(2) By use of the analyzing and comparing the eight PDE filtering model, theresult indicates that the second-order oriented PDE model is the mosteffective model. This PDE model is analyzed and compared with severalother representative and recent ESPI filtering methods, mainly including thewindowed Fourier transform method (WFF), the oriented, regularizedquadratic cost function (ORQCF) method, the oriented spatial filter masks(OSFM) and the localized Fourier transform filter (LFF). The summary ofthe performance for these filtering methods are presented.
(3) Introducing the Radial basis function(RBF) to ESPI information extraction, mainly including: the new filtering method based on radial basis function forESPI fringe patterns with wide density; introducing the radial basis functionto interpolate the number of fringe in the fringe skeleton method; smoothingthe phase acquired by phase unwrapping algorithm by use of the radial basisfunction. By use of the information extraction method based on RBF, thethermal deformation of the Al2O3ceramic substrate at different moment ismeasured on the circumstance of laser radiation.
(4) A new method for displacement field analysis based on the combination ofDSCM with RBF interpolation is proposed. The ability to approximatescattered data make this method has the advantage with better accuracy andless computational time. Another advantage is that this method does notrequire any smoothing algorithm to process the discrete displacement fielddata obtained. Using this method, the displacement fields for rigid bodytranslation and three-point bending are analyzed, the accurate displacementfields are acquired.
引文
[1]冯其波,光学测量技术与应用,北京：清华大学出版社,2008:111~118.
[2]金观昌,计算机辅助光学测量,北京：清华大学出版社,2007:105~126.
[3]陈家璧,苏显渝,光学信息技术原理及应用,北京:高等教育出版社,2002:384~387.
[4]佟景伟,李鸿琦,光力学原理及测试技术,北京：科学出版社，2009.
[5]王任达,全息和散斑检测,北京：机械工业出版社,2005:100~119.
[6] W. H. Peters,W. F. Ranson, Digital imaging techniques in experimental stressanalysis. Opt. Eng.1982,21:427~431.
[7] Michael E.Nixon. Experimental characterization and modeling of the mechanicalresponse of titanium for quasi-static and high strain rate loads. University of Florida,2008.
[8] Seon-ho Choi. A quantification of the plastic blunting process in one-phasemetallic materials. Arizona State University,2005.
[9] Ahmad Nazari. A hybrid evaluation of toughening and the crack growth resistanceof human dentin. University of Maryland Baltimore County,2008.
[10] Byungmin Ahn. Deformation behavior and microstructural evolution ofnanocrystalline aluminum alloys and composites. University of Southern California,2008.
[11] Ramji Dhakal. Failure mechanism of lead-free tin-silver-copper solder BGAinterconnects. Binghamton University,2005.
[12] Vikrant Tiwari. Image correlation with applications for shape and deformationmeasurements. University of South Carolina,2008.
[13] Pan B., Kemao Q., Huimin X., et al. Two-dimensional digital image correlationfor in-plane displacement and strain measurement:a review. Measurement science andtechnology,2009.20(6):1~19.
[14] MA Sutton, WJ Wolters, WH Peters, et. al., Determination of displacementsusing an improved digital correlation method. Image and Vision Computing,1983,1(3):133~139.
[15] TC Chu, WF Ranson, MA Sutton, Applications of digital-image-correlationtechniques to experimental mechanics. Experimental mechanics,1985,
[16]Sutton M A, Cheng M Q, Peters W H, et.al, Application of an optimized digitalcorrelation method to planar deformation analysis. Image and Vision Computing,1986,4(3):143~150.
[17] H. A. Bruck, S. R. McNeil, M. A. Sutton et. al, Digital image correlation usingNewton-Raphson method of partial differential correction. Exp. Mech,1989,29:261~267.
[18] Lu H. Statistical anslysis of the random error in measurements obtained usingdigital correlation of speckle patterns. Proceedings of1993SEM Spring Conferenceon Experimental Mechanics,1993,930~937.
[19] C. Q. Davis and D. M. Freeman, Statistics of subpixel registration algorithmsbased on spatiotemporal gradients or block matching. Opt. Eng,1998,37:1290~1298.
[20] G. Borgefors, G. Ramella, G.A.D.Baja. Shape and topology preservingmulti-valued image pyramids for multi-resolution skeletonization. PatternRecognition Letters,2001,22(6-7):741~751.
[21] Cheng P, MA Sutton, HW Schreier,et al, Full-field speckle pattern imagecorrelation with B-spline deformation function. Exp. Mech.2002,42:344~352.
[22] Min Wang, Yuwan Cen, Xiaofang Hu, et. al., A weighting window applied to thedigital image correlation method. Optics&Laser Technology,2009,41:154~158.
[23] Poissant J,Barthelat F. A novel “subset splitting” procedure for digital imagecorrelation on discontinuous displacement fields. Experimental Mechanics,2010,50(3):353-364.
[24] Long Luu, Zhaoyang Wang, Minh Vo, Accuracy enhancement of digital imagecorrelation with B-spline interpolation. Opt. lett.,2011,36(16):3070~3072.
[25]芮嘉白,金观昌,徐秉业.一种新的数字散斑相关方法及其应用.力学学报,1994,26(5):599~607.
[26]王志，数字图像相关技术的研究及其在断裂力学中的应用：[硕士学位论文]，天津：天津大学，2001.
[27]林碧森,金观昌,姚学峰，正交小波变换在散斑图像相关计算中的应用，光子学报，2002，31(2)：235~240.
[28]唐晨,闫海青,佟景伟，小波变换用于数字图像相关法位移场的平滑处理，天津大学学报，2002，第35卷，第5期，577~580.
[29]邢冬梅，数字散斑相关方法研究及其在细观力学中的应用：[博士学位论文]，天津：天津大学，2002.
[30] Shaopeng Ma, Guanchang Jin. Digital speckle correlation method improved bygenetic algorithm. Acta Mechanica Solida Sinica,2003,16(4):366~373.
[31] S.Yoneyama, Y.Morimoto. Accurate displacement measurement by correlation ofcolored random patterns. JSME INT J A-SOLID M,2003,46(2):178~184.
[32] Chen Tang, Ming Liu, Haiqing Yan. The improved genetic algorithms for digitalimage correlation method. Chinese Optics Letters,2004,2(10):574~577.
[33] B Pan, A Asundi, H Xie, et.al., Digital image correlation using iterative leastsquares and pointwise least squares for displacement field and strain fieldmeasurements. Optics and Lasers in Engineering,2009,47(7/8):865~874.
[34] Bing Pan, Zhaoyang Wang, Zixing Lu, Genuine full-field deformationmeasurement of an object with complex shape using reliability-guided digital imagecorrelation. OPTICS EXPRESS,2010,18(2):1011~1023.
[35] Bing Pan, Dafang Wu, Zhaoyang Wang, et.al., High-temperature digital imagecorrelation method for full-field deformation measurement at1200℃. Meas. Sci.Technol.,2011,22(1):015701.
[36]刘小勇,数字图像相关方法及其在材料力学性能测试中的应用:[博士学位论文],长春:吉林大学,2012.
[37]YK Zhu, GY Tian, RS Lu. A review of optical NDT technologies. Sensors,2011,11:7773~7798.
[38]戴蓉,激光技术在无损检测领域的应用与发展,激光与光电子学进展,2000,1~4.
[39]Katia Genovese, Luciano Lamberti, Carmine Pappalettere. A comprehensiveESPI based system for combined measurement of shape and deformation of electroniccomponents. Optics and Lasers in Engineering,2004,42:543~562.
[40] Wei-Chung Wang, Chi-Hung Hwang, and Shu-Yu Lin, Vibration measurementby the time-averaged electronic speckle pattern interferometry methods. AppliedOptics,1996,4502~4509.
[41] M. C. Shellabear and J. R. Tyrer,“Application of ESPI to three-dimensionalvibration measurements,” Opt. Lasers Eng.1991,15:43~56.
[42] Hong Tao. Plastic deformation and fracture behaviors of resistance spot-weldeddual-phase steel and laser-welded aluminum sheet metals. Yale University,2006.
[43] Michael Wade. Weld parameter and post weld heat treatment effects on6xxxseries friction stir weld properties. Miami University,2007.
[44] David Robert Hufner. Progressive failure of woven polymer-based compositesunder dynamic loading; Theory and analytical simulation. University ofConnecticut,2008.
[45] Henry Allen Padilla. Multiscale experimental study on the effect of texture andanisotropy on the thermomechanical response of zirconium. University of lllinois atUrbana-Champaign,2008.
[46] Antonia Maki Antoniou. Experimental observations of shear band nucleation andpropagation in a bulk metallic glass using wedge-like cylindrical indentation. IowaState University,2006.
[47] Madhusudhana S. Kirugulige. A study of mixed-mode dynamic fracture inadvanced particulate composites by optical interferometry, digital image correlationand finite element methods. Auburn University,2007.
[48] Sung Woo Cho. Nanoscale deformation and fracture mechanics ofpolycrystalline silicon and diamond-like carbon for MEMS by the AFM/DIC method.University of Virginia,2008.
[49] Krishna Nagasai Jonnalagadda. Failure and fracture of thin film materials forMEMS. University of Illinois,2008.
[50] Waleed Mekky. Fracture toughness of the nickel-alumina laminates by digitalimage-correlation technique. McMaster University,2005.
[51] Hang Yao. Mechanical testing of bone and bone-like materials using imagecorrelation strain measurement technique. Southern Methodist University,2007.
[52] Zhan Gao. Modeling and simulation of the coupled mechanical-electricalresponse of dielectric elastomers. The State University of New Jersey,2007.
[53] Tao Cheng. Mechanical properties of human middle ear tissues. University ofOklahoma,2007.
[54] Xiaodan Ke. Development and application of advanced vision systems forbiomechanics measurements. University of South Carolina,2008.
[55] Santaneel Ghosh. A non-contact measurement technique at the micro scale. TheUniversity of Arizona,2005.
[56] Dhananjay R. Panchagade. Damage prediction of lead free ball grid arraypackages under shock and drop environment. Auburn University,2007.
[57] Ta-hsuan Lin. Assembly process development, reliability and numericalassessment of copper column flexible flip chip technology. BinghamtonUniversity,2008
[58] Da Yu. Dynamic responses of PCB under product level free drop impact.Binghamton University,2008
[59] Jae B. Kwak. DIC methods for small scale measurements. BinghamtonUniversity,2005.
[60] Dong Gun Lee. Strain measurement of flip-chip solder bumps using digital imagecorrelation with optical microscopy. Binghamton University,2009.
[61] Michael J.McGinnis. Experimental and numerical development of thecore-drilling method for the nondestructive evaluation of in-situ stresses in concretestructures. Lehigh University,2006.
[62] Jason Peter Thorpe. Ground movements during tunnelling in sand. Queen sUniversity,2007.
[63] Michael J.Genduso, E.I. Permanent strain accumulation in a granular materialdue to cyclic loading. Florida Atlantic University,2005.
[64] Elena Romeo. Measurement and prediction of fundamental tensile failure limitsof hot mix asphalt (HMA). University of Florida,2008.
[65] Kamalesh Yegneswaran. Deviation between the sliding direction of the chip overthe tool and the direction of the friction force in oblique cutting. Madras University,2001.
[66] M. Aslan, Toward the development of high-speed microscopic ESPI system formonitoring laser heating/drilling of alumina Al2O3substrates, Ph.D. dissertation(Pennsylvania State University)2000.
[67] X. Su and W. Chen, Fourier transform profilometry: a review. Opt. Lasers Eng.2001,35:263~284.
[68] Zhong J, Weng J. Spatial carrier-fringe pattern analysis by means of wavelettransform: wavelet transform profilometry. Appl Opt.,2004,43:4993~4998.
[69] K. H. Womack, Interferometric phase measurement using spatial synchronousdetection. Opt. Eng.，1984,23:391~395.
[70]李新忠,宋文武,王希军,激光散斑计量技术及其应用.光机电信息,2005,3:16~20.
[71] M. Servin, J. A. Quiroga, F. J. Cuevas, Demodulation of carrier fringe patterns bythe use of non-recursive digital phase locked loop, Opt. Commun.,2001,200:87~97.
[72]M. Servin, D. Malacara, R. Rodriguez-Vera, Phase-locked loop interferometryapplied to aspheric testing with a computer-stored compensator. App. Opt.,1994,33:2589~2595.
[73] M. Servin, J. L. Marroquin, F. J. Cuevas, Fringe-follower regularized phasetracker for demodulation of closed-fringe interferograms, J. Opt. Soc. Am. A,2001,18(3):689~695.
[74] J. L. Marroquin, Rivera M., Botello S.,et al., Regularization methods for process-ing fringe-pattern images, Appl. Opt.,1999,38(5):788~794.
[75] Julio C. Estrada, M. Servin, Javier Vargas,2D simultaneous phase unwrappingand filtering: A review and comparison. Optics and Lasers in Engineering,2012,50:1026~1029.
[76] Y. Surrel, Design of algorithms for phase measurements by the use of phasestepping. Appl. Opt.1996,35(1):51~60.
[77] S. Nakadate, H. Saito, Fringe scanning speckle-pattern interferometry. Appl. Opt.1985,24:2172~2180.
[78] C.C. Kao, G.B. Yeh, S.S. Lee, C.K. Lee, C.S. Yang and K.C. Wu, Phase-shiftingalgorithms for electronic speckle pattern interferometry. Appl. Opt.2002,41:46~54.
[79] T.I. Voronyak, A.B. Kmet', O.V. Lychak. Single-step phase-shifting speckleinterferometry. Mater Sci.2007,43:554~567.
[80] D. Kerr, F. M. Santoyo, J. R. Tyrer, Extraction of phase data from electronicspeckle pattern interferometric fringes using a single-phase-step method: a novelapproach. J. Opt. Soc. Am. A.1990,7:820~826.
[81] Lei Ying. A study of2-D phase unwrapping. University of Illinois atUrbana-Champaign,2003.
[82] M. Takeda, H. Ina, S. Kobayashi, Fourier-transform method of fringe-patternanalysis for computer-based topography and interferometry. JOSA,1982,72(1):156~160.
[83] Batuhan Osmano lu, Applications and development of new algorithms fordisplacement analysis using Insar time series. University of Miami,2011.
[84] D. C. Ghiglia, Louis A. Romero, Minimum Lp-norm two-dimensional phaseunwrapping. J. Opt. Soc. Am. A,1996,13(10):1999~2013.
[85] D.C.Ghiglia, Romero L A, Robust two-dimensional weighted and unweightedphase unwrapping that uses fast transforms and iterative methods, J.Opt.Soc. Am.A,1994,11(1):107~117.
[86] D.C.Ghiglia, Pritt M D, Two-Dimensional phase unwrapping-theory, algorithms,and software. Wiley New York,1998.
[87] Howard Y. H. Huang, L. Tian, et.al, Path-independent phase unwrapping usingphase derivative and total-variation (TV) denoising. Biomedical Optics and3DImaging OSA.2012,1~3.
[88] Q. Kemao, Windowed Fourier transform for fringe pattern analysis, Appl. Opt.2004,43:2695~2702.
[89] Q. Kemao, Two-dimensional windowed Fourier transform for fringe patternanalysis: principles, applications and implementations, Opt. Lasers Eng.,2007,45:304~317.
[90] C. Li, C. Tang, H. Yan, et. al, Localized Fourier transform filter for noiseremoval in electronic speckle pattern interferometry wrapped phase patterns, Appl.Opt.2011,50:4903~4911.
[91]冯象初,王卫卫,图像处理的变分和偏微分方程方法.北京:科学出版社,2009.
[92]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京:科学出版社,2008.
[93] J. Weikert, Anisotropic Diffusion in Image Processing.1998.
[94] Chan, T.F., J. Shen, L. Vese, Variational PDE models in image processing.Notices of AMS,2003,50(1):14~26.
[95] A. P. Witkin, Scale-space filtering, In Proceedings of International JointConference on Artificial Intelligence,1983, pp:1019~1021.
[96] P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion.IEEE Trans. Pattern Anal. Machine Intell,1990,12:629~639.
[97] F. Catté, P.-L. Lions, J.-M. Morel, et. al., Image selective smoothing and edgedetection by nonlinear diffusion. SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal,1992,29:182-193.
[98] Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, Smoothing and edge detection bytime-varying coupled nonlinear diffusion equations. Computer Vision and ImageUnderstanding,2001,82:85~100.
[99] L. Alvarez, P.-L. Lions, J.-M. Morel, Image selective smoothing and edgedetection by nonlinear diffusion. SIAM J. Numer. Anal,1992,29:845~866.
[100] M.D.Buhmann, Radial basis functions: theory and implementations. CambridgeUniversity Press,2003.
[101]吴宗敏,散乱数据拟合的模型、方法和理论,北京:科学出版社,2007.
[102] R. L. Hardy, Multiquadric equations of topography and other irregular surfaces.J.Geophys Res,1971,76:1905~1915.
[103] J. Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces.Laboratoire de Mathematiques Appliquees.(Springer Verlag,)1977, pp.85~100.
[104] DS Broomhead, D Lowe, Radial basis functions, multi-variable functionalinterpolation and adaptive networks.1988, DTIC Document
[105]王洪元,史国栋,人工神经网络技术及其应用.中国石化出版社,2002.
[106] C. A. Micchelli. Interpolation of scattered data: Distance matrices andconditionally positive definite functions. Constr. Approx.,1986,2:11~22.
[107] Z. Wu, R.Schaback, Local error estimates for radial basis function interpolationof scattered data[J]. IMA.J.Numer.Anal,1993,13(7):13~27.
[108] Z. Wu. Multivariate compactly supported positive definite radial functions.Advances in Computational Mathematics,1995,4:283~292.
[109] Wendland H. Piecewise polynomial, positive definite and compactly supportedradial basis functions of minimal degree. Adv Comput Math,1995,4:389~396.
[110] Wendland H, Error estimates for interpolation by compactly supported radialbasis functions of minimal degree. J Approx Theeory,998,93:258~272.
[111] Kansa,E.J. Multiquadrics–a scattered data approximation scheme withapplications to computational fluid dynamics-I. Computers Math. Applic.,1990,19(8/9):127~145.
[112] Kansa,E.J. Multiquadrics–a scattered data approximation scheme withapplications to computational fluid dynamics-II. Computers Math.Applic.,1990,19(8/9):147~161.
[113]黄锋,基于径向基函数神经网络的图像识别研究.太原理工大学,2007.
[114] M. Balasubramanian, S. Palanivel, V. Ramalingam, Real time face and mouthrecognition using radial basis function neural networks. Expert Systems withApplications,2009,36:6879~6888.
[115]张少迪,王延杰,孙宏海,三角剖分以及径向基函数神经网络在星图识别中的应用.光学精密工程,2012,20(2):395~402.
[116] GG Slabaugh, G Unal, Method and system for image segmentation by evolvingradial basis functions. US Patent7925087,2011.
[117] Yingxuan Zhu, Image Segmentation Structural Similarity, Belief Propagationand Radial Basis Functions for Level Set Based Methods. Syracuse University,2010.
[118]胡晓飞,边界模糊图像的径向基函数神经网络分割方法研究.现代电子技术,2007,7(246):166~168.
[119] J.C. Carr, RK. Beatson,JB. Cherrie, et.al, Reconstruction and representation of3D objects with radial basis functions. In Proceedings of ACM SIGGRAPH,2001,67~76.
[120]Savchenko V., Kojekine N., Unno H., A practical image retouching method.InCW02: Proceedings of the First International Symposium on CyberWorlds(Washington, DC, USA)2002, pp:480-487.
[121]周廷方,基于径向基函数的图像修复技术.中国图象图形学报,2004,9(10):1190~1196.
[122] Adil Masood Siddiqui, Asif Masood, Muhammad Saleem, A locally constrainedradial basis function for registration and warping of images. Pattern RecognitionLetters,2009,30:377~390.
[123] Shusharina, N. Sharp G., Image registration using radial basis functions withadaptive radius. Medical Physics,2012,39:6542~6549.
[124]RJ Lapeer, SK Shah, RS Rowland, An optimised radial basis function algorithmfor fast non-rigid registration of medical images. Computers in Biology and Medicine,2010,40(1):1~7.
[125] C. Tang, F. Zhang, and Z. Chen, Contrast enhancement for electronic specklepattern interferometry fringes by the differential equation enhancement method. App.Opt.,2006,45:2287~2294.
[126] Wei Lv, Chen Tang and Wenping Wang, Noise reduction in electronic specklepattern interferometry fringes by fourth-order Partial Differential Equations.Proceedings of SPIE,2007,62790T.1~62790T.6.
[127] Y. You, M. Kaveh, Fourth-order partial differential equations for noise removal.IEEE Trans. Image Process,2000,9:1723~1730.
[128] Leonid I. Rudin, Stanley Osher, Emad Fatemi, Nonlinear total variation basednoise removal algorithms. Physica,1992,60:259~268.
[129] M. Lysaker, A. Lundervold, and X.-C. Tai, Noise removal using fourth-orderpartial differential equation with applications to medical magnetic resonance imagesin space and time. IEEE Trans. Image Process,2003,12:1579~1590.
[130] L. Cheng, C. Tang, S. Yan, et.al, New fourth-order partial differential equationsfor filtering in electronic speckle pattern interferometry fringes. Opt. Commun.,2011,284:5549~5555.
[131] G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images withapplications to color filtering. IEEE Transactions on Image Processing,1996,5:1582~1586.
[132] Wikipedia, Euler-Lagrange equation. http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation.
[133] G. Sapiro, Geometric Partial Differential Equations and Image Analysis.Cambridge University Press,2001.
[134] C. Tang, F. Zhang, H. Yan, et. al., Denoising in electronic speckle patterninterferometry fringes by the filtering method based on partial differential equations.Opt. Commun.,2006,260:91~96.
[135] C. Tang, W. Lu, S. Chen, et. al., Denoising by coupled partial differentialequations and extracting phase by backpropagation neural networks for electronicspeckle pattern interferometry. Appl. Opt.,2007,46:7475~7484.
[136] S. K. Weeratunga, C. Kamath, A comparison of PDE based non-linearanisotropic diffusion techniques for image denoising. Proc. SPIE, Image Processing:Algorithms and Systems II, UCRL-JC-151493,2003.
[137] H. M. Salinas, D. C. Fernández, Comparison of PDE-based nonlinear diffusionapproaches for image enhancement and denoising in optical coherence tomography.IEEE Trans. Med. Imag.,2007,26:761~771.
[138] C. Tang, L. Han, H. Ren, et. al., Second-order oriented partial-differentialequations for denoising in electronic-speckle-pattern interferometry fringes. Opt. Lett.,2008,33:2179~2181.
[139] C. Tang, L. Han, H. Ren, et. al., The oriented-couple partial differentialequations for filtering in wrapped phase patterns. Opt. Express.,2009,17:5606~5617.
[140] H.A.Aebischery, S.Waldner, A simple and effective method for filteringspeckle-interferometric phase fringe patterns. Opt. Commun.,1999:162:205~210.
[141] Y. Qin, J. Chen, H. Fan, The study and application of a new filtering method onelectronic speckle pattern interferometric fringe. Opt. Laser Eng.2003,39:449~456.
[142] Q. Yu, X. Liu, and K. Andresen, New spin filters for interferometric fringepatterns and grating patterns. Appl. Opt.1994,33:3705~3711.
[143] G.H. Kaufmann and G.E. Galizzi, Speckle noise reduction in televisionholography fringes using wavelet thresholding. Opt. Eng.1996,35:9~14.
[144] A. Federico and G.H. Kaufmann, Comparative study of wavelet thresholdingtechniques for denoising electronic speckle pattern interferometry fringes. Opt. Eng.2001,40:2598~2604.
[145] Q.Yu, X. Sun and X. Liu, Spin filtering with curve windows for interferometricfringes. Appl. Opt.2002,41:2650~2654.
[146] C. Tang, W. Wang, H. Yan, et. al, Tangent Least-squares fitting filteringmethod for electrical speckle pattern interferometry phase fringe. Appl. Opt.2007,46:2907~2913.
[147] C. Quan, C. J. Tay, F. Yang, et. al, Phase extraction from a single fringe patternbased on guidance of an extreme map. Appl. Opt.2005,44:4814~4821.
[148] Jesús. V, Juan A. Q. and Ismael D. R., Regularized quadratic cost function fororiented fringe-pattern filtering. Opt. Lett.2009,34:1741~1743.
[149] C.Tang, T. Gao, S.Yan, et. al., The oriented spatial filter masks for electronicspeckle pattern interferometry phase patterns. Opt. Express.2010,18:8942-8947.
[150]Anna N, Investigating Filtering Methods for the Denoising and ContrastEnhancement, and Eventual Skeletonization, of ESPI Images, pp.1–22,(2009)/http://mesoscopic.mines.edu/mediawiki/images/d/de/Project_Report_Neimark.pdfS.
[151] K. Qian, L. T. H. Nam, L. Feng, et. al, Comparative analysis on some filters forwrapped phase maps. Appl. Opt.2007,46:7412~7418.
[152] M. Servin, F. J. Cuevas, D. Malacara, et. al, Phase unwrapping throughdemodulation by use of the regularized phase-tracking technique. Appl. Opt.1999,38:1934~1941.
[153] M. Servin, M. Kujawinska, Modern fringe pattern analysis in interferometry,Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds.(Dekker),2001,12:373~426.
[154] H. Y. Yun, C. K. Hong, S. W. Chang, Least-square phase estimation withmultiple parameters in phase-shifting electronic speckle pattern interferometry. J. Opt.Soc. Am. A,2003,20:240~247.
[155] R. Kramer, O. Loffeld, Presentation of an improved phase unwrappingalgorithm based on Kalman filters combined with local slope estimation. InProceedings of Fringe96ESA Workshop Applications of ERS SAR Interferometry(ESA),1996.
[156] E. Trouve, M. Caramma, H. Maitre, Fringe detection in noisy complexinterferograms. Appl. Opt.,1996,35:3799~3806.
[157] E. Trouve, J. Nicolas, and H. Maitre, Improving phase unwrapping unwrappingtechniques by the use of local frequency estimates. IEEE Trans. Geosci. Remote Sens.1998,36:1963~1972.
[158] J. M. Huntley, Random phase measurement errors in digital speckle patterninterferometry. Opt. Lasers Eng.1997,26:131~150.
[159] H. Wang and Q. Kemao, Comparative analysis on some spatial-domain filtersfor fringe pattern denoising. Appl. Opt.2007,50:1687~1696.
[160] H. Wang, Q. Kemao, W. Gao, et. al, Fringe pattern denoising using coherenceenhancing diffusion. Opt. Lett.2009,34:1141~1143.
[161] M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, Performance evaluation oftexture measures for ground cover iden-tification in satellite images by means of aneural network classifier. IEEE Trans. Geosci. Remote Sensing,1995,33:616~626.
[162] C. Tang, Z. Wang, L. Wang, et. al, Estimation of fringe orientation for opticalfringe patterns with poor quality based on Fourier transform. Appl. Opt.2010,49:554~561.
[163]Otsu, N., A Threshold Selection Method from Gray-Level Histograms. IEEETransactions on Systems, Man, and Cybernetics,1979,9:62~66.
[164] G. Wahba. Spline Models for Observational Data. Number59in CBMS-NSFRegional Conference Series in Applied Math. SIAM,1990.
[165] C. Tang, F. Zhang, B. Li, et. al, Performance evaluation of partial differentialequation models in electronic speckle pattern interferometry and δ-mollificationmethod of phase map. Appl. Opt.2006,45:7392~7400.
[166] B. Wattrisse, A. Chrysochoos, J. M. Muracciole and M. Némoz-Gaillard,Analysis of strain localization during tensile tests by digital image correlation. Exp.Mech,2001,41:29~39.
[167] P. Zhou and K. E. Goodson, Subpixel displacement and deformation gradientmeasurement using digital image/speckle correlation. Opt. Eng.,2001,40:1613~1620.
[168] D. J. Chen, F. P. Chiang, Y.S. Tan and H.S. Don, Digital speckle-displacementmeasurement using a complex spectrum method. Appl. Opt.,1993,32:1839~1849.
[169] H. Jin and H. Bruck, Pointwise digital image correlation using geneticalgorithms. Exp. Tech.,2005,29:36~39.
[170] M. C. Pitter, C. W. See and M. G. Somekh, Subpixel microscopic deformationanalysis using correlation and artificial neural networks. Opt. Exp.,2001,8:322~327.
[171] B. Pan, H. M. Xie, B. Q. Xu and F. L. Dai, Performance of sub-pixelregistration algorithms in digital image correlation. Meas. Sci. Technol.,2006,17:1615~1621.
[172] J. Zhang, G. Jin, S. Ma, et.al., Application of an improved subpixel registrationalgorithm on digital speckle correlation measurement, Opt. Laser Technol.,2003,35:533~542.
[2]金观昌,计算机辅助光学测量,北京：清华大学出版社,2007:105~126.
[3]陈家璧,苏显渝,光学信息技术原理及应用,北京:高等教育出版社,2002:384~387.
[4]佟景伟,李鸿琦,光力学原理及测试技术,北京：科学出版社，2009.
[5]王任达,全息和散斑检测,北京：机械工业出版社,2005:100~119.
[6] W. H. Peters,W. F. Ranson, Digital imaging techniques in experimental stressanalysis. Opt. Eng.1982,21:427~431.
[7] Michael E.Nixon. Experimental characterization and modeling of the mechanicalresponse of titanium for quasi-static and high strain rate loads. University of Florida,2008.
[8] Seon-ho Choi. A quantification of the plastic blunting process in one-phasemetallic materials. Arizona State University,2005.
[9] Ahmad Nazari. A hybrid evaluation of toughening and the crack growth resistanceof human dentin. University of Maryland Baltimore County,2008.
[10] Byungmin Ahn. Deformation behavior and microstructural evolution ofnanocrystalline aluminum alloys and composites. University of Southern California,2008.
[11] Ramji Dhakal. Failure mechanism of lead-free tin-silver-copper solder BGAinterconnects. Binghamton University,2005.
[12] Vikrant Tiwari. Image correlation with applications for shape and deformationmeasurements. University of South Carolina,2008.
[13] Pan B., Kemao Q., Huimin X., et al. Two-dimensional digital image correlationfor in-plane displacement and strain measurement:a review. Measurement science andtechnology,2009.20(6):1~19.
[14] MA Sutton, WJ Wolters, WH Peters, et. al., Determination of displacementsusing an improved digital correlation method. Image and Vision Computing,1983,1(3):133~139.
[15] TC Chu, WF Ranson, MA Sutton, Applications of digital-image-correlationtechniques to experimental mechanics. Experimental mechanics,1985,
[16]Sutton M A, Cheng M Q, Peters W H, et.al, Application of an optimized digitalcorrelation method to planar deformation analysis. Image and Vision Computing,1986,4(3):143~150.
[17] H. A. Bruck, S. R. McNeil, M. A. Sutton et. al, Digital image correlation usingNewton-Raphson method of partial differential correction. Exp. Mech,1989,29:261~267.
[18] Lu H. Statistical anslysis of the random error in measurements obtained usingdigital correlation of speckle patterns. Proceedings of1993SEM Spring Conferenceon Experimental Mechanics,1993,930~937.
[19] C. Q. Davis and D. M. Freeman, Statistics of subpixel registration algorithmsbased on spatiotemporal gradients or block matching. Opt. Eng,1998,37:1290~1298.
[20] G. Borgefors, G. Ramella, G.A.D.Baja. Shape and topology preservingmulti-valued image pyramids for multi-resolution skeletonization. PatternRecognition Letters,2001,22(6-7):741~751.
[21] Cheng P, MA Sutton, HW Schreier,et al, Full-field speckle pattern imagecorrelation with B-spline deformation function. Exp. Mech.2002,42:344~352.
[22] Min Wang, Yuwan Cen, Xiaofang Hu, et. al., A weighting window applied to thedigital image correlation method. Optics&Laser Technology,2009,41:154~158.
[23] Poissant J,Barthelat F. A novel “subset splitting” procedure for digital imagecorrelation on discontinuous displacement fields. Experimental Mechanics,2010,50(3):353-364.
[24] Long Luu, Zhaoyang Wang, Minh Vo, Accuracy enhancement of digital imagecorrelation with B-spline interpolation. Opt. lett.,2011,36(16):3070~3072.
[25]芮嘉白,金观昌,徐秉业.一种新的数字散斑相关方法及其应用.力学学报,1994,26(5):599~607.
[26]王志，数字图像相关技术的研究及其在断裂力学中的应用：[硕士学位论文]，天津：天津大学，2001.
[27]林碧森,金观昌,姚学峰，正交小波变换在散斑图像相关计算中的应用，光子学报，2002，31(2)：235~240.
[28]唐晨,闫海青,佟景伟，小波变换用于数字图像相关法位移场的平滑处理，天津大学学报，2002，第35卷，第5期，577~580.
[29]邢冬梅，数字散斑相关方法研究及其在细观力学中的应用：[博士学位论文]，天津：天津大学，2002.
[30] Shaopeng Ma, Guanchang Jin. Digital speckle correlation method improved bygenetic algorithm. Acta Mechanica Solida Sinica,2003,16(4):366~373.
[31] S.Yoneyama, Y.Morimoto. Accurate displacement measurement by correlation ofcolored random patterns. JSME INT J A-SOLID M,2003,46(2):178~184.
[32] Chen Tang, Ming Liu, Haiqing Yan. The improved genetic algorithms for digitalimage correlation method. Chinese Optics Letters,2004,2(10):574~577.
[33] B Pan, A Asundi, H Xie, et.al., Digital image correlation using iterative leastsquares and pointwise least squares for displacement field and strain fieldmeasurements. Optics and Lasers in Engineering,2009,47(7/8):865~874.
[34] Bing Pan, Zhaoyang Wang, Zixing Lu, Genuine full-field deformationmeasurement of an object with complex shape using reliability-guided digital imagecorrelation. OPTICS EXPRESS,2010,18(2):1011~1023.
[35] Bing Pan, Dafang Wu, Zhaoyang Wang, et.al., High-temperature digital imagecorrelation method for full-field deformation measurement at1200℃. Meas. Sci.Technol.,2011,22(1):015701.
[36]刘小勇,数字图像相关方法及其在材料力学性能测试中的应用:[博士学位论文],长春:吉林大学,2012.
[37]YK Zhu, GY Tian, RS Lu. A review of optical NDT technologies. Sensors,2011,11:7773~7798.
[38]戴蓉,激光技术在无损检测领域的应用与发展,激光与光电子学进展,2000,1~4.
[39]Katia Genovese, Luciano Lamberti, Carmine Pappalettere. A comprehensiveESPI based system for combined measurement of shape and deformation of electroniccomponents. Optics and Lasers in Engineering,2004,42:543~562.
[40] Wei-Chung Wang, Chi-Hung Hwang, and Shu-Yu Lin, Vibration measurementby the time-averaged electronic speckle pattern interferometry methods. AppliedOptics,1996,4502~4509.
[41] M. C. Shellabear and J. R. Tyrer,“Application of ESPI to three-dimensionalvibration measurements,” Opt. Lasers Eng.1991,15:43~56.
[42] Hong Tao. Plastic deformation and fracture behaviors of resistance spot-weldeddual-phase steel and laser-welded aluminum sheet metals. Yale University,2006.
[43] Michael Wade. Weld parameter and post weld heat treatment effects on6xxxseries friction stir weld properties. Miami University,2007.
[44] David Robert Hufner. Progressive failure of woven polymer-based compositesunder dynamic loading; Theory and analytical simulation. University ofConnecticut,2008.
[45] Henry Allen Padilla. Multiscale experimental study on the effect of texture andanisotropy on the thermomechanical response of zirconium. University of lllinois atUrbana-Champaign,2008.
[46] Antonia Maki Antoniou. Experimental observations of shear band nucleation andpropagation in a bulk metallic glass using wedge-like cylindrical indentation. IowaState University,2006.
[47] Madhusudhana S. Kirugulige. A study of mixed-mode dynamic fracture inadvanced particulate composites by optical interferometry, digital image correlationand finite element methods. Auburn University,2007.
[48] Sung Woo Cho. Nanoscale deformation and fracture mechanics ofpolycrystalline silicon and diamond-like carbon for MEMS by the AFM/DIC method.University of Virginia,2008.
[49] Krishna Nagasai Jonnalagadda. Failure and fracture of thin film materials forMEMS. University of Illinois,2008.
[50] Waleed Mekky. Fracture toughness of the nickel-alumina laminates by digitalimage-correlation technique. McMaster University,2005.
[51] Hang Yao. Mechanical testing of bone and bone-like materials using imagecorrelation strain measurement technique. Southern Methodist University,2007.
[52] Zhan Gao. Modeling and simulation of the coupled mechanical-electricalresponse of dielectric elastomers. The State University of New Jersey,2007.
[53] Tao Cheng. Mechanical properties of human middle ear tissues. University ofOklahoma,2007.
[54] Xiaodan Ke. Development and application of advanced vision systems forbiomechanics measurements. University of South Carolina,2008.
[55] Santaneel Ghosh. A non-contact measurement technique at the micro scale. TheUniversity of Arizona,2005.
[56] Dhananjay R. Panchagade. Damage prediction of lead free ball grid arraypackages under shock and drop environment. Auburn University,2007.
[57] Ta-hsuan Lin. Assembly process development, reliability and numericalassessment of copper column flexible flip chip technology. BinghamtonUniversity,2008
[58] Da Yu. Dynamic responses of PCB under product level free drop impact.Binghamton University,2008
[59] Jae B. Kwak. DIC methods for small scale measurements. BinghamtonUniversity,2005.
[60] Dong Gun Lee. Strain measurement of flip-chip solder bumps using digital imagecorrelation with optical microscopy. Binghamton University,2009.
[61] Michael J.McGinnis. Experimental and numerical development of thecore-drilling method for the nondestructive evaluation of in-situ stresses in concretestructures. Lehigh University,2006.
[62] Jason Peter Thorpe. Ground movements during tunnelling in sand. Queen sUniversity,2007.
[63] Michael J.Genduso, E.I. Permanent strain accumulation in a granular materialdue to cyclic loading. Florida Atlantic University,2005.
[64] Elena Romeo. Measurement and prediction of fundamental tensile failure limitsof hot mix asphalt (HMA). University of Florida,2008.
[65] Kamalesh Yegneswaran. Deviation between the sliding direction of the chip overthe tool and the direction of the friction force in oblique cutting. Madras University,2001.
[66] M. Aslan, Toward the development of high-speed microscopic ESPI system formonitoring laser heating/drilling of alumina Al2O3substrates, Ph.D. dissertation(Pennsylvania State University)2000.
[67] X. Su and W. Chen, Fourier transform profilometry: a review. Opt. Lasers Eng.2001,35:263~284.
[68] Zhong J, Weng J. Spatial carrier-fringe pattern analysis by means of wavelettransform: wavelet transform profilometry. Appl Opt.,2004,43:4993~4998.
[69] K. H. Womack, Interferometric phase measurement using spatial synchronousdetection. Opt. Eng.，1984,23:391~395.
[70]李新忠,宋文武,王希军,激光散斑计量技术及其应用.光机电信息,2005,3:16~20.
[71] M. Servin, J. A. Quiroga, F. J. Cuevas, Demodulation of carrier fringe patterns bythe use of non-recursive digital phase locked loop, Opt. Commun.,2001,200:87~97.
[72]M. Servin, D. Malacara, R. Rodriguez-Vera, Phase-locked loop interferometryapplied to aspheric testing with a computer-stored compensator. App. Opt.,1994,33:2589~2595.
[73] M. Servin, J. L. Marroquin, F. J. Cuevas, Fringe-follower regularized phasetracker for demodulation of closed-fringe interferograms, J. Opt. Soc. Am. A,2001,18(3):689~695.
[74] J. L. Marroquin, Rivera M., Botello S.,et al., Regularization methods for process-ing fringe-pattern images, Appl. Opt.,1999,38(5):788~794.
[75] Julio C. Estrada, M. Servin, Javier Vargas,2D simultaneous phase unwrappingand filtering: A review and comparison. Optics and Lasers in Engineering,2012,50:1026~1029.
[76] Y. Surrel, Design of algorithms for phase measurements by the use of phasestepping. Appl. Opt.1996,35(1):51~60.
[77] S. Nakadate, H. Saito, Fringe scanning speckle-pattern interferometry. Appl. Opt.1985,24:2172~2180.
[78] C.C. Kao, G.B. Yeh, S.S. Lee, C.K. Lee, C.S. Yang and K.C. Wu, Phase-shiftingalgorithms for electronic speckle pattern interferometry. Appl. Opt.2002,41:46~54.
[79] T.I. Voronyak, A.B. Kmet', O.V. Lychak. Single-step phase-shifting speckleinterferometry. Mater Sci.2007,43:554~567.
[80] D. Kerr, F. M. Santoyo, J. R. Tyrer, Extraction of phase data from electronicspeckle pattern interferometric fringes using a single-phase-step method: a novelapproach. J. Opt. Soc. Am. A.1990,7:820~826.
[81] Lei Ying. A study of2-D phase unwrapping. University of Illinois atUrbana-Champaign,2003.
[82] M. Takeda, H. Ina, S. Kobayashi, Fourier-transform method of fringe-patternanalysis for computer-based topography and interferometry. JOSA,1982,72(1):156~160.
[83] Batuhan Osmano lu, Applications and development of new algorithms fordisplacement analysis using Insar time series. University of Miami,2011.
[84] D. C. Ghiglia, Louis A. Romero, Minimum Lp-norm two-dimensional phaseunwrapping. J. Opt. Soc. Am. A,1996,13(10):1999~2013.
[85] D.C.Ghiglia, Romero L A, Robust two-dimensional weighted and unweightedphase unwrapping that uses fast transforms and iterative methods, J.Opt.Soc. Am.A,1994,11(1):107~117.
[86] D.C.Ghiglia, Pritt M D, Two-Dimensional phase unwrapping-theory, algorithms,and software. Wiley New York,1998.
[87] Howard Y. H. Huang, L. Tian, et.al, Path-independent phase unwrapping usingphase derivative and total-variation (TV) denoising. Biomedical Optics and3DImaging OSA.2012,1~3.
[88] Q. Kemao, Windowed Fourier transform for fringe pattern analysis, Appl. Opt.2004,43:2695~2702.
[89] Q. Kemao, Two-dimensional windowed Fourier transform for fringe patternanalysis: principles, applications and implementations, Opt. Lasers Eng.,2007,45:304~317.
[90] C. Li, C. Tang, H. Yan, et. al, Localized Fourier transform filter for noiseremoval in electronic speckle pattern interferometry wrapped phase patterns, Appl.Opt.2011,50:4903~4911.
[91]冯象初,王卫卫,图像处理的变分和偏微分方程方法.北京:科学出版社,2009.
[92]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京:科学出版社,2008.
[93] J. Weikert, Anisotropic Diffusion in Image Processing.1998.
[94] Chan, T.F., J. Shen, L. Vese, Variational PDE models in image processing.Notices of AMS,2003,50(1):14~26.
[95] A. P. Witkin, Scale-space filtering, In Proceedings of International JointConference on Artificial Intelligence,1983, pp:1019~1021.
[96] P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion.IEEE Trans. Pattern Anal. Machine Intell,1990,12:629~639.
[97] F. Catté, P.-L. Lions, J.-M. Morel, et. al., Image selective smoothing and edgedetection by nonlinear diffusion. SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal,1992,29:182-193.
[98] Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, Smoothing and edge detection bytime-varying coupled nonlinear diffusion equations. Computer Vision and ImageUnderstanding,2001,82:85~100.
[99] L. Alvarez, P.-L. Lions, J.-M. Morel, Image selective smoothing and edgedetection by nonlinear diffusion. SIAM J. Numer. Anal,1992,29:845~866.
[100] M.D.Buhmann, Radial basis functions: theory and implementations. CambridgeUniversity Press,2003.
[101]吴宗敏,散乱数据拟合的模型、方法和理论,北京:科学出版社,2007.
[102] R. L. Hardy, Multiquadric equations of topography and other irregular surfaces.J.Geophys Res,1971,76:1905~1915.
[103] J. Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces.Laboratoire de Mathematiques Appliquees.(Springer Verlag,)1977, pp.85~100.
[104] DS Broomhead, D Lowe, Radial basis functions, multi-variable functionalinterpolation and adaptive networks.1988, DTIC Document
[105]王洪元,史国栋,人工神经网络技术及其应用.中国石化出版社,2002.
[106] C. A. Micchelli. Interpolation of scattered data: Distance matrices andconditionally positive definite functions. Constr. Approx.,1986,2:11~22.
[107] Z. Wu, R.Schaback, Local error estimates for radial basis function interpolationof scattered data[J]. IMA.J.Numer.Anal,1993,13(7):13~27.
[108] Z. Wu. Multivariate compactly supported positive definite radial functions.Advances in Computational Mathematics,1995,4:283~292.
[109] Wendland H. Piecewise polynomial, positive definite and compactly supportedradial basis functions of minimal degree. Adv Comput Math,1995,4:389~396.
[110] Wendland H, Error estimates for interpolation by compactly supported radialbasis functions of minimal degree. J Approx Theeory,998,93:258~272.
[111] Kansa,E.J. Multiquadrics–a scattered data approximation scheme withapplications to computational fluid dynamics-I. Computers Math. Applic.,1990,19(8/9):127~145.
[112] Kansa,E.J. Multiquadrics–a scattered data approximation scheme withapplications to computational fluid dynamics-II. Computers Math.Applic.,1990,19(8/9):147~161.
[113]黄锋,基于径向基函数神经网络的图像识别研究.太原理工大学,2007.
[114] M. Balasubramanian, S. Palanivel, V. Ramalingam, Real time face and mouthrecognition using radial basis function neural networks. Expert Systems withApplications,2009,36:6879~6888.
[115]张少迪,王延杰,孙宏海,三角剖分以及径向基函数神经网络在星图识别中的应用.光学精密工程,2012,20(2):395~402.
[116] GG Slabaugh, G Unal, Method and system for image segmentation by evolvingradial basis functions. US Patent7925087,2011.
[117] Yingxuan Zhu, Image Segmentation Structural Similarity, Belief Propagationand Radial Basis Functions for Level Set Based Methods. Syracuse University,2010.
[118]胡晓飞,边界模糊图像的径向基函数神经网络分割方法研究.现代电子技术,2007,7(246):166~168.
[119] J.C. Carr, RK. Beatson,JB. Cherrie, et.al, Reconstruction and representation of3D objects with radial basis functions. In Proceedings of ACM SIGGRAPH,2001,67~76.
[120]Savchenko V., Kojekine N., Unno H., A practical image retouching method.InCW02: Proceedings of the First International Symposium on CyberWorlds(Washington, DC, USA)2002, pp:480-487.
[121]周廷方,基于径向基函数的图像修复技术.中国图象图形学报,2004,9(10):1190~1196.
[122] Adil Masood Siddiqui, Asif Masood, Muhammad Saleem, A locally constrainedradial basis function for registration and warping of images. Pattern RecognitionLetters,2009,30:377~390.
[123] Shusharina, N. Sharp G., Image registration using radial basis functions withadaptive radius. Medical Physics,2012,39:6542~6549.
[124]RJ Lapeer, SK Shah, RS Rowland, An optimised radial basis function algorithmfor fast non-rigid registration of medical images. Computers in Biology and Medicine,2010,40(1):1~7.
[125] C. Tang, F. Zhang, and Z. Chen, Contrast enhancement for electronic specklepattern interferometry fringes by the differential equation enhancement method. App.Opt.,2006,45:2287~2294.
[126] Wei Lv, Chen Tang and Wenping Wang, Noise reduction in electronic specklepattern interferometry fringes by fourth-order Partial Differential Equations.Proceedings of SPIE,2007,62790T.1~62790T.6.
[127] Y. You, M. Kaveh, Fourth-order partial differential equations for noise removal.IEEE Trans. Image Process,2000,9:1723~1730.
[128] Leonid I. Rudin, Stanley Osher, Emad Fatemi, Nonlinear total variation basednoise removal algorithms. Physica,1992,60:259~268.
[129] M. Lysaker, A. Lundervold, and X.-C. Tai, Noise removal using fourth-orderpartial differential equation with applications to medical magnetic resonance imagesin space and time. IEEE Trans. Image Process,2003,12:1579~1590.
[130] L. Cheng, C. Tang, S. Yan, et.al, New fourth-order partial differential equationsfor filtering in electronic speckle pattern interferometry fringes. Opt. Commun.,2011,284:5549~5555.
[131] G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images withapplications to color filtering. IEEE Transactions on Image Processing,1996,5:1582~1586.
[132] Wikipedia, Euler-Lagrange equation. http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation.
[133] G. Sapiro, Geometric Partial Differential Equations and Image Analysis.Cambridge University Press,2001.
[134] C. Tang, F. Zhang, H. Yan, et. al., Denoising in electronic speckle patterninterferometry fringes by the filtering method based on partial differential equations.Opt. Commun.,2006,260:91~96.
[135] C. Tang, W. Lu, S. Chen, et. al., Denoising by coupled partial differentialequations and extracting phase by backpropagation neural networks for electronicspeckle pattern interferometry. Appl. Opt.,2007,46:7475~7484.
[136] S. K. Weeratunga, C. Kamath, A comparison of PDE based non-linearanisotropic diffusion techniques for image denoising. Proc. SPIE, Image Processing:Algorithms and Systems II, UCRL-JC-151493,2003.
[137] H. M. Salinas, D. C. Fernández, Comparison of PDE-based nonlinear diffusionapproaches for image enhancement and denoising in optical coherence tomography.IEEE Trans. Med. Imag.,2007,26:761~771.
[138] C. Tang, L. Han, H. Ren, et. al., Second-order oriented partial-differentialequations for denoising in electronic-speckle-pattern interferometry fringes. Opt. Lett.,2008,33:2179~2181.
[139] C. Tang, L. Han, H. Ren, et. al., The oriented-couple partial differentialequations for filtering in wrapped phase patterns. Opt. Express.,2009,17:5606~5617.
[140] H.A.Aebischery, S.Waldner, A simple and effective method for filteringspeckle-interferometric phase fringe patterns. Opt. Commun.,1999:162:205~210.
[141] Y. Qin, J. Chen, H. Fan, The study and application of a new filtering method onelectronic speckle pattern interferometric fringe. Opt. Laser Eng.2003,39:449~456.
[142] Q. Yu, X. Liu, and K. Andresen, New spin filters for interferometric fringepatterns and grating patterns. Appl. Opt.1994,33:3705~3711.
[143] G.H. Kaufmann and G.E. Galizzi, Speckle noise reduction in televisionholography fringes using wavelet thresholding. Opt. Eng.1996,35:9~14.
[144] A. Federico and G.H. Kaufmann, Comparative study of wavelet thresholdingtechniques for denoising electronic speckle pattern interferometry fringes. Opt. Eng.2001,40:2598~2604.
[145] Q.Yu, X. Sun and X. Liu, Spin filtering with curve windows for interferometricfringes. Appl. Opt.2002,41:2650~2654.
[146] C. Tang, W. Wang, H. Yan, et. al, Tangent Least-squares fitting filteringmethod for electrical speckle pattern interferometry phase fringe. Appl. Opt.2007,46:2907~2913.
[147] C. Quan, C. J. Tay, F. Yang, et. al, Phase extraction from a single fringe patternbased on guidance of an extreme map. Appl. Opt.2005,44:4814~4821.
[148] Jesús. V, Juan A. Q. and Ismael D. R., Regularized quadratic cost function fororiented fringe-pattern filtering. Opt. Lett.2009,34:1741~1743.
[149] C.Tang, T. Gao, S.Yan, et. al., The oriented spatial filter masks for electronicspeckle pattern interferometry phase patterns. Opt. Express.2010,18:8942-8947.
[150]Anna N, Investigating Filtering Methods for the Denoising and ContrastEnhancement, and Eventual Skeletonization, of ESPI Images, pp.1–22,(2009)/http://mesoscopic.mines.edu/mediawiki/images/d/de/Project_Report_Neimark.pdfS.
[151] K. Qian, L. T. H. Nam, L. Feng, et. al, Comparative analysis on some filters forwrapped phase maps. Appl. Opt.2007,46:7412~7418.
[152] M. Servin, F. J. Cuevas, D. Malacara, et. al, Phase unwrapping throughdemodulation by use of the regularized phase-tracking technique. Appl. Opt.1999,38:1934~1941.
[153] M. Servin, M. Kujawinska, Modern fringe pattern analysis in interferometry,Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds.(Dekker),2001,12:373~426.
[154] H. Y. Yun, C. K. Hong, S. W. Chang, Least-square phase estimation withmultiple parameters in phase-shifting electronic speckle pattern interferometry. J. Opt.Soc. Am. A,2003,20:240~247.
[155] R. Kramer, O. Loffeld, Presentation of an improved phase unwrappingalgorithm based on Kalman filters combined with local slope estimation. InProceedings of Fringe96ESA Workshop Applications of ERS SAR Interferometry(ESA),1996.
[156] E. Trouve, M. Caramma, H. Maitre, Fringe detection in noisy complexinterferograms. Appl. Opt.,1996,35:3799~3806.
[157] E. Trouve, J. Nicolas, and H. Maitre, Improving phase unwrapping unwrappingtechniques by the use of local frequency estimates. IEEE Trans. Geosci. Remote Sens.1998,36:1963~1972.
[158] J. M. Huntley, Random phase measurement errors in digital speckle patterninterferometry. Opt. Lasers Eng.1997,26:131~150.
[159] H. Wang and Q. Kemao, Comparative analysis on some spatial-domain filtersfor fringe pattern denoising. Appl. Opt.2007,50:1687~1696.
[160] H. Wang, Q. Kemao, W. Gao, et. al, Fringe pattern denoising using coherenceenhancing diffusion. Opt. Lett.2009,34:1141~1143.
[161] M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, Performance evaluation oftexture measures for ground cover iden-tification in satellite images by means of aneural network classifier. IEEE Trans. Geosci. Remote Sensing,1995,33:616~626.
[162] C. Tang, Z. Wang, L. Wang, et. al, Estimation of fringe orientation for opticalfringe patterns with poor quality based on Fourier transform. Appl. Opt.2010,49:554~561.
[163]Otsu, N., A Threshold Selection Method from Gray-Level Histograms. IEEETransactions on Systems, Man, and Cybernetics,1979,9:62~66.
[164] G. Wahba. Spline Models for Observational Data. Number59in CBMS-NSFRegional Conference Series in Applied Math. SIAM,1990.
[165] C. Tang, F. Zhang, B. Li, et. al, Performance evaluation of partial differentialequation models in electronic speckle pattern interferometry and δ-mollificationmethod of phase map. Appl. Opt.2006,45:7392~7400.
[166] B. Wattrisse, A. Chrysochoos, J. M. Muracciole and M. Némoz-Gaillard,Analysis of strain localization during tensile tests by digital image correlation. Exp.Mech,2001,41:29~39.
[167] P. Zhou and K. E. Goodson, Subpixel displacement and deformation gradientmeasurement using digital image/speckle correlation. Opt. Eng.,2001,40:1613~1620.
[168] D. J. Chen, F. P. Chiang, Y.S. Tan and H.S. Don, Digital speckle-displacementmeasurement using a complex spectrum method. Appl. Opt.,1993,32:1839~1849.
[169] H. Jin and H. Bruck, Pointwise digital image correlation using geneticalgorithms. Exp. Tech.,2005,29:36~39.
[170] M. C. Pitter, C. W. See and M. G. Somekh, Subpixel microscopic deformationanalysis using correlation and artificial neural networks. Opt. Exp.,2001,8:322~327.
[171] B. Pan, H. M. Xie, B. Q. Xu and F. L. Dai, Performance of sub-pixelregistration algorithms in digital image correlation. Meas. Sci. Technol.,2006,17:1615~1621.
[172] J. Zhang, G. Jin, S. Ma, et.al., Application of an improved subpixel registrationalgorithm on digital speckle correlation measurement, Opt. Laser Technol.,2003,35:533~542.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |