数字图像相关中亚像素位移测量算法的研究

为提高位移测量精度而提出的各种亚像素位移测量算法被认为是数字图像相关方法 中的关键技术之一，详细了解已有各算法的性能无疑具有实际意义. 总结文献中3种 最常用的亚像素位移测量算法，首先用无噪声的计算机仿真散斑图对各算法的性能从计算精 度和计算效率两个方面进行了比较研究，并用实际实验图片对其性能做进一步的研究，结果 显示在图像子区大小相同的情况下，基于空域相关函数迭代的牛顿-拉普森方法计算结果最 为精确、稳定.     

数字图像相关分析法增量位移场测试技术

利用位移场的连续性,对亚像素位移场的算法进行了一些改进,设计了一套分步计算位移场、应变场的测量计算方法,较好地解决了数字图像相关分析法计算精度和效率.采用增量位移场叠加的方法计算大应变位移场,采用局部平面拟合的方法计算应变场.通过对高分子材料拉伸试验位移场的测量和结果标定,说明该方法具有较强的实用性和计算精度.同时,由于避免了对亚像素点的搜索,大大提高了计算效率.     

基于拟合求解数字图像相关亚像素位移算法

数字图像相关方法是一种非接触式的变形场测量方法。虽然目前该算法能取得较高的计算精度,但是通常存在计算量较大、计算时间较长的问题。为了提高算法的计算效率,本文提出了一种基于移动最小二乘算法拟合整像素位移求解亚像素位移的数字图像相关方法。因为采用移动最小二乘算法有效利用了局部特征,所以可以采用相对简单的多项式拟合求解复杂的周期型余弦变形,同时计算结果具有较高的精度。计算结果的平均误差为0.0238pixel,标准误差为0.0791pixel,与常用的空间相关亚像素位移计算结果精度相当。实验结果验证了本文算法的正确性和有效性。通过与等计算精度的NR算法对比分析,结果表明本文算法在亚像素位移计算阶段具有更高的计算效率。计算效率至少提升了58.1倍,最多提升了437.8倍。     

非连续数字图像相关方法在裂纹重构中的应用

数字图像相关方法作为一种新的非接触式位移测量方法,在力学工程中有广泛的应用前景,然而受限于标准方法对图像变形的连续性要求,这种高效的测量方法在断裂力学领域的推广受到了限制. 为解决这一问题,提出采用引入子区分离数学模型,代替标准方法的连续模型,来对非连续区域进行精确识别和匹配的非连续数字图像相关方法. 研究子区被裂纹等非连续分割后原始像素点的位移情况,并引入裂纹张开向量用以表征被分割子区的主区和副区的位移关系;从而建立子区分离模型的数学表达式,并且为所提出的模型设计相应的图像相关算法;然后将所提出的非连续数字图像相关方法应用于重构平板拉伸试验开裂过程中图像的位移. 研究结果表明,相比于标准的数字图像相关方法,所提出的非连续数字图像相关方法解决了图像相关法在非连续区域失效的问题,提高了数字图像相关方法对位移测量的正确率,特别是能够准确重构裂纹面及附近的位移场,其测量精度能够达到亚像素级别.      

非连续数字图像相关方法在裂纹重构中的应用

数字图像相关方法作为一种新的非接触式位移测量方法,在力学工程中有广泛的应用前景,然而受限于标准方法对图像变形的连续性要求,这种高效的测量方法在断裂力学领域的推广受到了限制.为解决这一问题,提出采用引入子区分离数学模型,代替标准方法的连续模型,来对非连续区域进行精确识别和匹配的非连续数字图像相关方法.研究子区被裂纹等非连续分割后原始像素点的位移情况,并引入裂纹张开向量用以表征被分割子区的主区和副区的位移关系;从而建立子区分离模型的数学表达式,并且为所提出的模型设计相应的图像相关算法;然后将所提出的非连续数字图像相关方法应用于重构平板拉伸试验开裂过程中图像的位移.研究结果表明,相比于标准的数字图像相关方法,所提出的非连续数字图像相关方法解决了图像相关法在非连续区域失效的问题,提高了数字图像相关方法对位移测量的正确率,特别是能够准确重构裂纹面及附近的位移场,其测量精度能够达到亚像素级别.     

关于数字图像相关中曲面拟合法的几点讨论

曲面拟合法求解亚像素位移是数字图像相关亚像素位移定位中的一种重要方法,它具有抗噪声能力较强、精度高、计算效率高等优点,在实际应用中多被采用.本文就该算法中影响亚像素位移定位精度的各要素进行了详细讨论,并用计算机生成的模拟散斑图和金属试件的刚体平移实验进行了验证,结果表明,整像素搜索时选取不同的计算窗口对计算结果的影响最大,而文中所列的几种相关函数的选取对计算结果的影响则可以忽略.     

数字图像相关曲面拟合法相关系数修正算法的实验研究

为了提高数字图像相关曲面拟合法亚像素定位精度,经研究发现,在实际应用中,曲面拟合法在亚像素位移为0.5像素左右时会发生较大的波动,与实际亚像素位移发生一定偏离,导致此位置位移的不连续。本文通过分析曲面拟合法亚像素位移偏离真实位移的原因,给出了具体修正方法,用模拟平移实验讨论了修正系数k和子区大小对修正结果的影响,用三点弯曲实验验证了修正方法在复杂变形情况下的有效性,提高了曲面拟合法在实际应用中的测量精度。     

网格数字图像相关方法测量位移场的研究

本文将数字图像相关方法与古老的网格法相结合,给出了一种测量面内位移场的新方法——网格数字图像相关方法,实现了高精度的测量,精度可达0.02亚像素．在该方法中网格点采用圆标记点,使该方法特别适用于小线应变位移场的研测．本文运用Windows下的新的图像采集方法测量物体位移场,突破了Dos系统下对内存操作的限制,并使每一帧图像的像素数由512×512增至768×576,提高了图形的分辨率．     

一种考虑旋转位移分量的数字图像相关法及其精度分析

提出了一种新的考虑旋转位移分量的数字图像相关法[CD2]旋转相关匹配法,其特点是先对图像子区进行预旋转,再进行相关匹配、相关系数、整像素和亚像素位移的计算。在物体产生旋转位移分量时,该方法可有效提高变形前后图像子区间的相关系数和位移计算精度。通过斜拉伸、剪切和悬臂梁弯曲实验,对旋转相关匹配法和直接相关匹配法进行了对比研究,并用灰度梯度法计算旋转后新图像子区和变形后图像子区间的亚像素位移。结果表明,在旋转位移分量小于10°的情况下,相比于直接相关匹配法,旋转相关匹配法可以得到更高的相关系数;在用灰度梯度法计算亚像素位移条件下,位移精度与试件位移不产生旋转时的直接相关匹配相当。     

后验概率算法用于位移场的确定

提出了一种基于贝叶斯最大后验估计算法确定固体表面位移场的方法。在图像处理过程中，把位移看作随机变量，首先建立贝叶斯模型，对变形前数字图像中的一个像素点，选定变形前后两幅数字图像中对应的圆形子区，将两子区所对应的所有可能位移逐一代入贝叶斯后验概率公式进行计算，使后验概率最大的位移值就是所求该点的位移。在得到整像素位移之后，引入亚像素重建技术，确定图像的精确位移场。本文通过计算机数字模拟实验和实物标准位移实验，验证了该方法的可行性，并得到了0．02pixel的位移测量精度。     

Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations

High-efficiency and high-accuracy deformation analysis using digital image correlation (DIC) has become increasingly important in recent years, considering the ongoing trend of using higher resolution digital cameras and common requirement of processing a large sequence of images recorded in a dynamic testing. In this work, to eliminate the redundant computations involved in conventional DIC method using forward additive matching strategy and classic Newton–Raphson (FA-NR) algorithm without sacrificing its sub-pixel registration accuracy, we proposed an equivalent but more efficient DIC method by combining inverse compositional matching strategy and Gauss-Newton (IC-GN) algorithm for fast, robust and accurate full-field displacement measurement. To this purpose, first, an efficient IC-GN algorithm, without the need of re-evaluating and inverting Hessian matrix in each iteration, is introduced to optimize the robust zero-mean normalized sum of squared difference (ZNSSD) criterion to determine the desired deformation parameters of each interrogated subset. Then, an improved reliability-guided displacement tracking strategy is employed to achieve further speed advantage by automatically providing accurate and complete initial guess of deformation for the IC-GN algorithm implemented on each calculation point. Finally, an easy-to-implement interpolation coefficient look-up table approach is employed to avoid the repeated calculation of bicubic interpolation at sub-pixel locations. With the above improvements, redundant calculations involved in various procedures (i.e. initial guess of deformation, sub-pixel displacement registration and sub-pixel intensity interpolation) of conventional DIC method are entirely eliminated. The registration accuracy and computational efficiency of the proposed DIC method are carefully tested using numerical experiments and real experimental images. Experimental results verify that the proposed DIC method using IC-GN algorithm and the existing DIC method using classic FA-NR algorithm generate similar results, but the former is about three to five times faster. The proposed reliability-guided IC-GN algorithm is expected to be a new standard full-field displacement tracking algorithm in DIC.     

基于数字图像体相关的物体内部三维位移场分析

在二维数字图像相关算法的基础上,推导了三维数字图像体相关算法,并应用于物体内部的三维位移场分析。用计算机模拟方法对SR-CT重建的物体内部三维图像施加已知变形,对变形前后三维数字图像进行体相关运算,获得三维位移场。在计算亚像素位移时,本文提出了一种三维的基于灰度梯度的算法,给出了梯度函数,阐述了数字模拟三维体相关的计算过程,通过数字模拟实验证明了算法的正确性和可靠性。     

Planar fluorescence for round bubble imaging and its application for the study of an axisymmetric two-phase jet

A correlation-based processing algorithm for bubble identification by a planar fluorescence for bubble imaging (PFBI) technique is presented in this paper. The algorithm includes procedures to identify bubble positions and sizes, as well as to track bubbles and correct bubble displacement vectors. Moreover, several schemes for calculation time optimisation were realised to achieve a reliable calculation time. The developed algorithm identifies and tracks overlapping bubble images or images with non-uniform intensity distributions. The employed correlation and iterative passing approach provides sub-pixel accuracy of bubble displacement estimation. In addition, the presented algorithm for bubble ring detection can be easily applied to shadow photography images of bubbles, after the application of a derivative filter. The PFBI technique, combined with the particle image velocimetry and particle tracking velocimetry algorithms, was applied for the experimental study of bubbly free jet two-phase flows at Re = 12,000. Four cases of volumetric gas content in the jet core were studied: 0, 1.2, 2.4 and 4.2%, with the same mean bubble diameter—0.85 mm. The developed technique measures two-dimensional distributions of instantaneous void fractions, as well as both gaseous and liquid-phase velocities. Consequently, the mean void fraction and velocity fields and a set of second-order statistical moments were obtained, including correlations of void fraction and velocity pulsations. It was shown that the increase in volumetric gas content leads to the suppression of liquid-phase velocity fluctuations in the jet mixing layer.     

李级数算法和显式辛算法的相位分析

以线性可分Hamilton动力学系统为例,研究了李级数算法和显式辛算法的相位精度,研究了李级数算法的保辛精度及其保辛精度的提高方法;指出了显式辛算法相位精度与算法阶次的不协调性,印辛算法的阶次高并不意味着其相位精度也高,李级数算法不存在这种问题,指出了一个算法的相位可能超前也可能滞后.分析结果表明三阶显式辛算法具有比较高的相位精度.     

结构性软土弹塑性模型的隐式算法实现

对于考虑软土结构性的高度非线性弹塑性本构模型,在采用Newton-CPPM隐式算法对模型进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题。为此,本文提出了两种改进隐式算法。考虑到Newton-CPPM隐式算法是局部收敛性算法,因此引入大范围收敛的同伦延拓算法对Newton-CPPM算法的迭代初值进行改进,形成了同伦-Newton-CPPM算法。考虑到Newton-CPPM隐式算法单个迭代步的计算量过大,因此借鉴显式算法的思想提出一种两阶段迭代算法,第一阶段先求出一致性参数,第二阶段采用类似于显示算法的方法进行回代得出状态变量的值。然后,以考虑软土结构性的SANICLAY模型为例,从弹塑性本构模型的组成和算法的特点两个角度分析了引起Jacobian矩阵奇异和不收敛问题的原因,并且在单单元计算的基础上,对全显式算法、传统隐式算法和两种改进隐式算法在计算收敛性、计算精度和计算效率方面进行了对比。最后,将同伦-Newton-CPPM算法和传统隐式算法用于地基承载力多单元计算中,结果表明该算法能够有效地解决Jacobian矩阵奇异和不收敛问题。      

Digital Image Correlation with Self-Adaptive Gaussian Windows

A novel subpixel registration algorithm with Gaussian windows is put forward for accurate deformation measurement in digital image correlation technique. Based on speckle image quality and potential deformation states, this algorithm can automatically minimize the influence of subset sizes by self-adaptively tuning the Gaussian window shapes with the aid of a so-called weighted sum-of-squared difference correlation criterion. Numerical results of synthetic speckle images undergoing in-plane sinusoidal displacement fields demonstrate that the proposed algorithm can significantly improve displacement and strain measurement accuracy especially in the case with relatively large deformation.     

Bias and precision errors of digital particle image velocimetry

The bias and precision errors of digital particle image velocimetry are quantified. Uniform displacement images are used to evaluate the uncertainty attributed to various sub-pixel peak finding algorithms. Bias errors are found to exist for all algorithms, and the presence of bias error tends to affect the precision error. The ability to “calibrate” out the bias error is explored using a rectangular free jet experiment. The calibration was effective in removing the bias error in the potential core and less effective in the shear layer. The bias error is found to functionally depend on the displacement gradients present in the interrogation region. The study stresses the need for in situ quantification of DPIV uncertainty. Received: 3 November 1998 / Accepted: 26 June 1999