数字图像相关法测量局域变形场中形函数和模板尺寸的影响

数字图像相关法测量均匀变形场已被普遍接受, 其测量结果可与应变片测量结果比较. 然而, 在工程测量中, 针对局域变形场(应变高度集中, 如波特文-勒夏特利埃带、试件缺口附近和裂纹尖端等), 应变片受限于其尺寸, 其测量结果是接触面内的平均应变值. 此时, 采用数字图像相关法能够测量这些局域变形场. 但形函数和模板尺寸等计算参数对计算结果影响很大, 这也导致使用者很难判断计算结果的可靠性. 论文通过对合金拉伸实验获得的不同应变梯度的波特文-勒夏特利埃带和模拟生成的带的计算分析, 发掘了形函数和模板尺寸作用于计算结果的深层机制, 证明了二阶形函数比一阶形函数更适用于高度非均匀的局域变形场. 提出了在局域应变场测量中, 当一阶和二阶形函数计算结果的相对误差小于10% 时, 二阶形函数的结果是可靠的判据.      

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.     

基于单层荧光颗粒的三维细胞牵引力的研究

细胞与细胞外微环境的力学相互作用对于细胞迁移、增殖和分化起着至关重要的作用。近年来,基于数字图像相关和数字体积相关方法的细胞牵引力研究得到了广泛的开展。然而,传统的基于数字图像相关的方法只能测量面内的变形;传统的基于数字体积相关的方法将荧光标记颗粒置于水凝胶基底内部,扫描层数过多导致图像采集时间长、光毒性增大。本文中,我们结合激光扫描共聚焦技术和数字体积相关方法,将单层荧光颗粒平铺在水凝胶表面,通过共聚焦显微镜采集细胞迁移过程中不同时刻的图像,采用二阶形函数的数字体积相关方法得到细胞-基底界面处的三维位移场和三维牵引力场。该方法采用单层荧光颗粒,不仅有效地降低了多层激光扫描产生的光毒性,还极大地减少了图像采集时间,从而在扫描同一序列图像时,细胞形态变化相对较小,提高了原始图像的准确性。并且,采用二阶形函数可以描述细胞迁移过程中基底产生的弯曲等更复杂形式的一阶形函数无法描述的变形。     

基于Haar小波变换的位移场测量方法

本文提出了一种应用小波变换对固体表面位移场进行测量的新方法，在图像分析时，用各点属于不同尺度的小波变换系数来表征该点周围的子区。将试件表面位移前后的两幅数字图像进行小波变换，通过变形前后两幅图像小波变换系数之间的相互匹配，使位移前后两幅图中的子区对应起来，从而确定图像的位移场。本文应用Haar小波变换进行了计算机模拟实验和实物位移实验。引入亚像素技术，获得了0．02的位移测量精度。     

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。     

数字图像相关的噪声导致系统误差及散斑质量评价标准

数字图像相关中散斑质量评价标准应该综合考虑系统误差和随机误差的作用。之前的工作考虑了无图像噪声情况下插值引起的系统误差,本文则进一步研究了有图像噪声情况的系统误差,并与随机误差综合考虑提出了完善的散斑质量评价参数。本文推导了有噪声情况下系统误差的解析形式,揭示了噪声引入系统误差产生的内在本质在于插值引起噪声不确定性对亚像素位置的依赖。依据理论分析,插值噪声耦合函数的概念被引入,它由插值基函数平移平方和的斜率决定,表征了噪声引入系统误差随亚像素位置的变化。插值耦合函数将之前的研究成果纳入统一的理论体系,并从本质上解释了高阶B-样条插值对应的噪声引起系统误差较小的现象。数值模拟与本文的理论分析显示一致,在真实的亚像素平移实验验证中,本文将公式推广到非均匀噪声情况,并与实验结果获得了较好的吻合。基于对系统误差的理论分析,综合考虑系统误差和随机误差影响,提出了两种计算误差评估参数:总误差的最大值和平方平均值,并提出了快速估计算法且通过数值模拟进行了验证。计算误差评估参数实际也是一种散斑质量评价参数,提出的评估参数弥补了现存散斑质量评价参数未足够考虑插值影响的缺陷,是更完善的散斑质量评价标准。本文应用新提出的散斑评价参数对一些常见散斑图进行了评价,并将其用于对模拟散斑图的优化。     

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。     

数字图像相关计算中的识别函数构造

本文通过建立数字图像相关检测的数学模型和构造新的识别函数。解决了在确定图像位移时图像之间伴随有较大刚体转动情况下的相关检测问题。为利用数字图像相关计算。进行微细观层次上的位移和变形测量提供了一种途径。     

基于双线性位移模式数字图像相关方法的误差分析及应用

探讨数字图像相关方法测试结果的误差分布规律对提高该方法的测试精度具有重要意义。本文从理论上分析了基于双线性位移模式数字图像相关方法的子区变形场测试误差分布规律,结果表明,当试件的真实变形可由双线性位移模式描述时,变形场最大测试误差通常出现在子区的边界或节点处。因此,若试件发生均匀拉伸等常应变变形,可利用相关系数选取一个最优子区,认为测得最优子区中心应变为试件真实应变。零变形实验验证了该测试方法的可靠性。最后对手机导光板试件在单轴拉伸载荷下的数字图像进行分析,并利用本文方法测试了其弹性常数。     

Systematic errors in digital image correlation due to undermatched subset shape functions

Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains. In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.     

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.     

Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

     

Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.     

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Improved Models of Systematic and Random Errors

The literature contains many studies on assessment of DIC uncertainties, particularly in the ultimate error regime, when the shape function used to describe the material transformation perfectly matches the actual transformation. For pure sub-pixel translations, bias and random errors obtained for experimental or synthetic images show more complex evolution versus the fractional part of displacement than those predicted by the existing theoretical models. Indeed, small deviations arise, mainly around integer values of imposed displacements for noisy images, and they are interpreted as the unrepresentativeness of the underlying hypotheses of the theoretical models. In a first step, differences between imposed and measured displacements are analysed: random error is independent of fractional displacement, and systematic error does not decrease for values close to integer displacements whatever the noise level. Therefore, new prediction models are proposed based on the analysis of identified phenomena from synthetic speckle-pattern 8-bit images. The statistical approach used in this paper generalizes the methods proposed in the literature and mimics the experimental methodology usually used for displacement measurements performed in different subsets in the same image. Two closed-form expressions for the systematic and random errors and a linear interpolation scheme are developed. These models, depending only on image properties and the imposed displacement, are built with a very limited number of parameters. It is then possible to predict the evolution of bias and random errors from one to four images.     

数字图像相关方法在桥梁裂缝变形监测中的应用

本文结合工程实际背景分析了数字图像相关方法应用在桥梁裂缝变形监测中的可行性及优越性。根据桥梁裂缝变形的特点采用数字图像处理技术中的位移梯度法进行所选区域的相关匹配搜索并对相关系数的计算公式加以改进。使实验过程得以简化。计算结果全场化、直观化。本文对数字图像处理软件的测量精度和在实际测量中的测试误差进行了分析和研究。证明该软件能够更加精确地测定裂缝在各种荷载作用下的变形量值．实际的桥梁测试也验证了该方法的可行性和优越性。若图像记录设备的分辨率是12．47pixel／mm(0．0802ram／pixel)。本文所涉及到的桥梁裂缝边缘的位移测试精度为0．000802mm。     

On the Use of NURBS Functions for Displacement Derivatives Measurement by Digital Image Correlation

In this paper, we propose to investigate the potential improvement of using Non-Uniform Rational B-Spline (NURBS) functions for displacement measurements by digital image correlation (DIC). The aim is at improving the performance of DIC to capture with low uncertainty and low noise levels not only the displacement field but also its derivatives. Indeed, when the displacement field is used to feed constitutive law identification procedures, displacement derivatives are required and thus may be measured with robustness. Two examples illustrate the potential of NURBS for DIC: a compressive test on a wood sample and a bending test on a steel beam. For the latter, beam kinematics are adopted and NURBS are used in order to capture the variation of the curvature (second derivative of the displacement) along the beam axis. For these two examples, an error study based on a decomposition of the error into the correlation error and the interpolation error, is carried out and shows the great potential of NURBS functions for DIC.     

Assessment of Digital Image Correlation Measurement Errors: Methodology and Results

Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519)”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed.