数字图像相关法中的优化插值滤波器
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摘要
针对数字图像相关方法中的亚像素插值误差,在复频域内利用滤波器的传递函数分析了亚像素位置和图像频率对插值误差的影响,在此基础上设计了一种基于B样条插值核的优化插值滤波器。为使该滤波器能自适应于不同散斑图像,提出了一种利用图像的频谱分析获取滤波器中权值函数的方法,以B样条滤波器系数为非线性优化插值滤波器的迭代初值,解算出图像的最优滤波系数。在不考虑数字图像相关法中其他位移测量误差影响的情况下,通过平移和单向拉伸两个数值实验,证实所提滤波器可以明显减小亚像素插值误差,更好地满足了实验力学中对利用数字图像相关法进行高精度位移测量的需求。
An optimized interpolation filter based on B-spline interpolation kernel is presented to solve the problem that there exists sub-pixel interpolation error in digital image correlation methods.The transfer function of the filter is used to analyze the influences of sub-pixel location and image frequency on interpolation error in the Fourier domain.A method is proposed to get a weight function of the filter by using the image spectrum analysis,so that the filter is adaptive to different speckle patterns.The filter coefficients of B-spline are used as initial value,and nonlinear iterations are performed for the interpolation filter to calculate optimal filter coefficients of the image.Numerical simulations with both the translation and the uniaxial tension test show that the proposed filter can well reduce the sub-pixel interpolation error and meet the requirements of experimental mechanics for using digital image correlation methods to achieve high precision in displacement measurement.
An optimized interpolation filter based on B-spline interpolation kernel is presented to solve the problem that there exists sub-pixel interpolation error in digital image correlation methods.The transfer function of the filter is used to analyze the influences of sub-pixel location and image frequency on interpolation error in the Fourier domain.A method is proposed to get a weight function of the filter by using the image spectrum analysis,so that the filter is adaptive to different speckle patterns.The filter coefficients of B-spline are used as initial value,and nonlinear iterations are performed for the interpolation filter to calculate optimal filter coefficients of the image.Numerical simulations with both the translation and the uniaxial tension test show that the proposed filter can well reduce the sub-pixel interpolation error and meet the requirements of experimental mechanics for using digital image correlation methods to achieve high precision in displacement measurement.
引文
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[2]潘兵,俞立平,吴大方.使用双远心镜头的高精度二维数字图像相关测量系统[J].光学学报,2013,33(4):105-115.PAN Bing,YU Liping,WU Dafang.High-accuracy two-dimensional digital image correlation measurement system using a bilateral telecentric lens[J].Acta Optica Sinica,2013,33(4):105-115.
[3]史红健,计宏伟,何小元.一种三维变形光学测量系统及微结构力学性能测试应用[J].光学学报,2011,31(3):135-140.SHI Hongjian,JI Hongwei,HE Xiaoyuan.Optical 3D deformation measurement system and its application to investigation of mechanical behaviors of microstructure[J].Acta Optica Sinica,2011,31(3):135-140.
[4]SCHREIE H W,BRAASCH J R,SUTTON M A.Systematic errors in digital image correlation caused by intensity interpolation[J].Optical Engineering,2000,39(11):2915-2921.
[5]PAN Bing,XIE Huimin,XU Boqin,et al.Performance of sub-pixel registration algorithms in digital image correlation[J].Measurement Science and Technology,2006,17(6):1615-1621.
[6]PAN Bing,QIAN Kemao,XIE Huimin,et al.On errors of digital image correlation due to speckle patterns[C]∥International Conference on Experimental Mechanics 2008.Bellingham,WA,USA:SPIE,2008:73754-73757.
[7]BALDI A,BERTOLINO F.Systematic errors due to polynomial interpolation in digital image correlation:analysis of some interpolating kernels and experimental validation[C]∥International Conference on Speckle Metrology.Bellingham,WA,USA:SPIE,2012:841306-841308.
[8]UNSER M,ALDROUBI A,EDEN M.Fast B-spline transforms for continuous image representation and interpolation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1991,13(3):277-285.
[9]THEVENAZ P T,UNSER M.Interpolation revisited[J].IEEE Transactions on Medical Imaging,2000,19(7):739-758.
[10]UNSER M,ALDROUBI A,EDEN M.B-spline signal processing:part II efficient design and applications[J].IEEE Transactions on Signal Processing,1993,41(2):834-848.
[11]TANG Zhengzong,LIANG Jin,GUO Cheng.Slantaxis digital image correlation method based on photogrammetry correction[J].Acta Optica Sinica,2011,31(11):157-165.
[2]潘兵,俞立平,吴大方.使用双远心镜头的高精度二维数字图像相关测量系统[J].光学学报,2013,33(4):105-115.PAN Bing,YU Liping,WU Dafang.High-accuracy two-dimensional digital image correlation measurement system using a bilateral telecentric lens[J].Acta Optica Sinica,2013,33(4):105-115.
[3]史红健,计宏伟,何小元.一种三维变形光学测量系统及微结构力学性能测试应用[J].光学学报,2011,31(3):135-140.SHI Hongjian,JI Hongwei,HE Xiaoyuan.Optical 3D deformation measurement system and its application to investigation of mechanical behaviors of microstructure[J].Acta Optica Sinica,2011,31(3):135-140.
[4]SCHREIE H W,BRAASCH J R,SUTTON M A.Systematic errors in digital image correlation caused by intensity interpolation[J].Optical Engineering,2000,39(11):2915-2921.
[5]PAN Bing,XIE Huimin,XU Boqin,et al.Performance of sub-pixel registration algorithms in digital image correlation[J].Measurement Science and Technology,2006,17(6):1615-1621.
[6]PAN Bing,QIAN Kemao,XIE Huimin,et al.On errors of digital image correlation due to speckle patterns[C]∥International Conference on Experimental Mechanics 2008.Bellingham,WA,USA:SPIE,2008:73754-73757.
[7]BALDI A,BERTOLINO F.Systematic errors due to polynomial interpolation in digital image correlation:analysis of some interpolating kernels and experimental validation[C]∥International Conference on Speckle Metrology.Bellingham,WA,USA:SPIE,2012:841306-841308.
[8]UNSER M,ALDROUBI A,EDEN M.Fast B-spline transforms for continuous image representation and interpolation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1991,13(3):277-285.
[9]THEVENAZ P T,UNSER M.Interpolation revisited[J].IEEE Transactions on Medical Imaging,2000,19(7):739-758.
[10]UNSER M,ALDROUBI A,EDEN M.B-spline signal processing:part II efficient design and applications[J].IEEE Transactions on Signal Processing,1993,41(2):834-848.
[11]TANG Zhengzong,LIANG Jin,GUO Cheng.Slantaxis digital image correlation method based on photogrammetry correction[J].Acta Optica Sinica,2011,31(11):157-165.