Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements

Digital image correlation (DIC) method using iterative least squares algorithm (ILS) for displacement field measurement and pointwise least squares algorithm (PLS) for strain field measurement is proposed in this paper. A more general and practical intensity change model is employed with consideration of the linear intensity change of the deformed image, followed by an iterative least squares algorithm for calculating displacement field with sub-pixel accuracy. The concept of correlation function is not used in the ILS method, even though we prove that the algorithm is actually equivalent to the optimization of the sum of squared difference correlation function using improved Newton–Raphson method. Besides, different from the conventional strain estimation approaches based on smoothing the displacement fields first and followed by differentiation of the smoothed displacement fields, a simple yet effective PLS algorithm is proposed for extracting strain fields from the computed displacement fields. The effectiveness and accuracy of the proposed techniques is verified through numerical simulation experiments. A practical application of the algorithms to residual plastic deformation field measurement of GH4169 alloy subjected to tensile fatigue is also presented.     

激光散斑的亚像素位移法计算及比较

根据激光散斑相关测量中采用的插值法、梯度算法和牛顿一拉夫森迭代法3种亚像素位移算法的特点,逐一在亚像素尺度计算出磁流体干燥过程中的同一激光散斑图的偏均值和标准差变化曲线。基于得到的偏差均值和标准差讨论了3种算法处理激光散斑图的特点,比较了3种算法处理散斑图的计算精度、稳定性和计算用时。结果显示,在小变形的亚像素位移测量时,梯度算法的精度较高,且较为稳定,计算效率也较牛顿一拉夫森算法快约9倍。因此,在进行小变形亚像素位移测量时,采用梯度算法计算激光散斑是有效的。     

Noise robustness and parallel computation of the inverse compositional Gauss–Newton algorithm in digital image correlation

The inverse compositional Gauss–Newton (IC-GN) algorithm is one of the most popular sub-pixel registration algorithms in digital image correlation (DIC). The IC-GN algorithm, compared with the traditional forward additive Newton–Raphson (FA-NR) algorithm, can achieve the same accuracy in less time. However, there are no clear results regarding the noise robustness of IC-GN algorithm and the computational efficiency is still in need of further improvements. In this paper, a theoretical model of the IC-GN algorithm was derived based on the sum of squared differences correlation criterion and linear interpolation. The model indicates that the IC-GN algorithm has better noise robustness than the FA-NR algorithm, and shows no noise-induced bias if the gray gradient operator is chosen properly. Both numerical simulations and experiments show good agreements with the theoretical predictions. Furthermore, a seed point-based parallel method is proposed to improve the calculation speed. Compared with the recently proposed path-independent method, our model is feasible and practical, and it can maximize the computing speed using an improved initial guess. Moreover, we compared the computational efficiency of our method with that of the reliability-guided method using a four-point bending experiment, and the results show that the computational efficiency is greatly improved. This proposed parallel IC-GN algorithm has good noise robustness and is expected to be a practical option for real-time DIC.     

Performance of iterative gradient-based algorithms with different intensity change models in digital image correlation

Digital image correlation (DIC) is a non-contact and powerful tool for whole-field displacement and strain measurement in modern optical metrology. In the DIC technique, the gradient-based algorithm is one of the most commonly used sub-pixel registration algorithms due to its effectiveness and accuracy. Thus, this algorithm has been further investigated and improved by many researchers to increase its accuracy. In the existing gradient-based algorithms, there are three relation models for the gray level intensity of a point in the undeformed and deformed images: namely the constant intensity model, the linear intensity change model and the non-linear intensity change model. However, little quantitative investigation has been conducted to compare their performance. In this paper, three iterative gradient-based algorithms are given using the corresponding intensity change model and the iterative least squares (ILS) solving method. The accuracy, robustness and computational efficiency of the three algorithms for intensity variation are investigated through numerical simulation experiments. The experimental results reveal that the algorithm generated using the non-linear intensity change model is the most accurate, robust and efficient of the three algorithms and the algorithms generated using the linear and non-linear intensity change models have approximately the same accuracy when the intensity variation is small between undeformed and deformed images.     

High accuracy digital image correlation powered by GPU-based parallel computing

A sub-pixel digital image correlation (DIC) method with a path-independent displacement tracking strategy has been implemented on NVIDIA compute unified device architecture (CUDA) for graphics processing unit (GPU) devices. Powered by parallel computing technology, this parallel DIC (paDIC) method, combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm for integer-pixel initial guess estimation, achieves a superior computation efficiency over the DIC method purely running on CPU. In the experiments using simulated and real speckle images, the paDIC reaches a computation speed of 1.66×10⁵ POI/s (points of interest per second) and 1.13×10⁵ POI/s respectively, 57–76 times faster than its sequential counterpart, without the sacrifice of accuracy and precision. To the best of our knowledge, it is the fastest computation speed of a sub-pixel DIC method reported heretofore.     

Path-independent digital image correlation with high accuracy,speed and robustness

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy.     

数字图像相关中基于位移场局部最小二乘拟合的全场应变测量

为了从含噪声的位移场中计算得到可靠的应变场,提出一种基于位移场局部最小二乘拟合的全场应变求解方法。介绍了数字图像相关方法的原理,阐述了基于位移场局部最小二乘拟合的全场应变求解方法,并讨论了计算区域边界、孔洞及裂纹附近区域等情况下的应变计算。对均匀变形和中心带圆孔的薄铝板拉伸实验的计算结果表明,该方法能有效地从原始位移场数据中提取全场应变信息。在均匀变形情况下应选择大的应变计算窗口,计算结果更逼近真值;在非均匀变形情况下,如果位移场中包含较强的噪声,则应选择较大的应变计算窗口,而位移场精度很高时可选择更小的应变计算窗口。     

On the use of the digital image correlation method for heterogeneous deformation measurement of porous solids

In this paper, several crucial issues arising from the application of the digital image correlation (DIC) method to the measurement of heterogeneous deformation of porous solids are discussed. To handle samples with complex geometry, the performance of the two commonly employed DIC methods, namely the subset-based DIC and the finite-element based DIC methods are first evaluated and compared. A combined DIC approach and an adaptive DIC approach suitable for samples with discontinuities/holes are then proposed. Aluminum plates with circular holes subject to compressive loading are employed to evaluate the accuracy of the proposed methods. It has been found that in addition to other factors such as the number of pixels and speckle size, the orientation of the camera lens also plays an important role on the measurement accuracy. A calibration method for the adjustment of camera orientation is proposed, which leads to a good agreement between the experimentally measured displacements and finite element simulation results. Another finding of the presented work is that for relatively stiff specimens, the deformation of the loading system itself must be considered in order to obtain an accurate displacement.     

Accuracy enhancement of digital image correlation with B-spline interpolation

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting version is employed to enhance the accuracy of DIC analysis. Theories are introduced, and simulation results are presented to illustrate the effectiveness of the method as compared with the common bicubic interpolation.     

A weighting window applied to the digital image correlation method

In the digital image correlation method, two steps are used to calculate the displacements of tested images. The first step is to locate the integer-pixel displacement, and the next one is to compute the sub-pixel displacement based on the first step. The benefit from the computation method for the integer-pixel displacement is that its results directly affect the displacement accuracy of each point in tested images. In this paper, a new method is developed to calculate the displacement fields between two images taken before and after deformation of an object. A new correlation function with a weighting factor related to the position of each point in the image is taken into account. The analysis and experimental results confirm the validity of the new method. In addition, the calculation results from our method have more accuracy than that of the traditional one.     

两种插值亚像素定位法在数字散斑测量中的应用

利用数字散斑相关测量法只能得到试件的整像素位移量,不能满足高精度的测量要求。探讨了两种插值法在数字散斑亚像素级测量中的应用,并对相关系数多项式插值法和对数插值法的测量结果进行了比较,为在不同亚像素级位移条件下选择较为恰当的测量方法提供了依据。     

High-efficiency and high-accuracy digital image correlation for three-dimensional measurement

The computational efficiency and measurement accuracy of the digital image correlation (DIC) have become more and more important in recent years. For the three-dimensional DIC (3D-DIC), these issues are much more serious. First, there are two cameras employed which increases the computational amount several times. Second, because of the differences in view angles, the must-do stereo correspondence between the left and right images is equivalently a non-uniform deformation, and cannot be weakened by increasing the sampling frequency of digital cameras. This work mainly focuses on the efficiency and accuracy of 3D-DIC. The inverse compositional Gauss–Newton algorithm (IC-GN²) with the second-order shape function is firstly proposed. Because it contains the second-order displacement gradient terms, the measurement accuracy for the non-uniform deformation thus can be improved significantly, which is typically one order higher than the first-order shape function combined with the IC-GN algorithm (IC-GN¹), and 2 times faster than the second-order shape function combined with the forward additive Gauss–Newton algorithm (FA-GN²). Then, based on the features of the IC-GN¹ and IC-GN² algorithms, a high-efficiency and high-accuracy measurement strategy for 3D-DIC is proposed in the end.     

预测搜索算法在图像相关中的应用

数字散斑相关方法在亚像素测量过程中运算量大,在对实时性要求较高的系统中该方法的应用受到了限制。提出了一种原理简单、搜索速度快、精度高的预测搜索算法,介绍了预测搜索算法的原理,并给出预测位移的公式。通过实验验证了对算法的精度、效率和鲁棒性,说明对数字散斑相关方法进行优化后,既不损失亚像素位移的计算精度又提高了图像处理的效率。     

数字散斑亚像素小角位移测量的曲面拟合法

与传统测量方法相比,数字散斑相关法由于其目标特征单元网格划分的灵活性,能够更好地满足不同场合小角位移的测量需求。针对该方法亚像素小角位移测量的曲面拟合参数选择问题,研究了亚像素测量图像小角旋转前后的九点二次曲面拟合法,并根据计算机生成模拟散斑进行模拟实验分析,得到最佳误差效率优化条件下的曲面拟合法求解亚像素小角位移的最佳散斑尺寸3.5 pixel、计算窗口尺寸41×41 pixel和拟合窗口尺寸3×3 pixel。实验验证了上述测量参数的有效性,为进一步的曲面拟合法数字散斑成像角位移测量提供参考。     

Quality assessment of speckle patterns for DIC by consideration of both systematic errors and random errors

The performance of digital image correlation (DIC) is influenced by the quality of speckle patterns significantly. Thus, it is crucial to present a valid and practical method to assess the quality of speckle patterns. However, existing assessment methods either lack a solid theoretical foundation or fail to consider the errors due to interpolation. In this work, it is proposed to assess the quality of speckle patterns by estimating the root mean square error (RMSE) of DIC, which is the square root of the sum of square of systematic error and random error. Two performance evaluation parameters, respectively the maximum and the quadratic mean of RMSE, are proposed to characterize the total error. An efficient algorithm is developed to estimate these parameters, and the correctness of this algorithm is verified by numerical experiments for both 1 dimensional signal and actual speckle images. The influences of correlation criterion, shape function order, and sub-pixel registration algorithm are briefly discussed. Compared to existing methods, method presented by this paper is more valid due to the consideration of both measurement accuracy and precision.     

CCD摄像头圆目标中心定位方法

在大型设备自动对接系统中,需要CCD摄像头对一设备截面的圆目标进行图像获取,并找出图像的中心点坐标,用于两设备的中心对准。为了满足实时性测量和高精度定位要求,提出一种CCD摄像头圆目标中心定位方法。先对图像使用中值滤波方法进行图像增强,利用广义数字形态学中的多结构抗噪膨胀腐蚀型算子提取单像素宽图像边缘,用多项式插值法对图像边缘进行亚像素定位,用半径约束最小二乘圆拟合法对圆中心进行精确定位。实验测量结果表明,该方法测量时间短、精度高、稳定性好,亚像素定位精度优于1/20像素,中心点总标准偏差小于0.01,可满足设备自动对接系统要求。     

Determination of displacement distributions in bolted steel tension elements using digital image techniques

Digital imaging methods have found a great interest in various engineering fields to study stress-deformation characteristics of materials. Recent enhancements in visual instrumentation with the availability of cost-effective hardware and software products make the digital imaging techniques a viable tool to replace direct strain or displacement measurement methods in engineering applications. In this study, deformation characteristics of bolted steel connections are investigated by calculating in-plane displacement distributions using digital image correlation method (DIC). Validation of the method is presented by comparing the strains measured in standard tension specimens using electrical resistance strain gages and the DIC method. Finite element analysis of the connection specimen is also performed to compare the in-plane displacement distributions calculated from both methods. Results from the validation process indicate that the strains obtained from the DIC method compare well with the results of strain gages. The findings also indicate that the displacement distributions calculated from the finite element method may differ from those of the DIC method in terms of distribution pattern, and the location and magnitude of the extreme values of displacements. It is suggested that the proposed method can be used to determine the in-plane displacement distributions for the bolted connections, hence to evaluate their deformation characteristics under loading.     

摄像测量在舰船变形测量中的应用研究

针对舰船不同安装基座间相对变形的高精度测量要求,提出了一种利用单摄像机三维姿态测量原理和亚像素定位法,通过若干台摄像机进行传递测量船体变形的方法,来解决对两个或多个不通视安装基座之间相对变形进行高精度测量的问题。分别对单摄像测量和多级摄像传递测量进行了测量精度分析,采用4台2K×2K分辨率的摄像机进行传递测量,测量精度优于23″。该方法在舰船上较易实施,且精度较高。     

三维大型任意阵列宽带波束指向性图的快速计算

为解决常规频域直接方法计算大型三维阵列宽带波束图(BP)速度较慢,无法满足大型三维宽带阵优化设计需求的问题,提出了一种适用于大型三维任意阵列的宽带BP图的快速算法.在利用二维非均匀快速傅里叶变换(NUFFT)伴随操作实现二维阵列BP频域快速计算方法的基础上,引入第三空间频率变量,将与阵元纵向坐标有关的相位因子转化为第三...     

Strain field denoising for digital image correlation using a regularized cost-function

In digital image correlation (DIC), the widely used forward-additive Newton–Raphson (FA-NR) algorithm and the recently introduced equivalent but more efficient inverse-compositional Gauss–Newton (IC-GN) algorithm are capable of providing both displacements and displacement gradients (strains) for each calculation point. However, the obtained displacement gradients are seriously corrupted by various noises, and for this reason these directly computed strains are usually considered as useless information and therefore discarded. To extract strain distributions more accurately, much research efforts have been dedicated to how to smooth and differentiate the noisy displacement fields using appropriate numerical approaches. In this contribution, contrary to these existing strain estimation approaches, a novel and alternative strain estimation approach, based on denoising the noisy strain fields obtained by FA-NR or IC-GN algorithm using a regularized cost-function, is proposed. The effectiveness and practicality of the proposed strain estimation technique is carefully examined using both computer-simulated images with imposed homogeneous and inhomogeneous deformation, and experimentally obtained images. Experimental results reveal that the strains obtained by the proposed method are comparable to those determined by post-processing of the displacement fields using conventional pointwise least squares strain estimation approach.