A space-time approach in digital image correlation: Movie-DIC

A new method is proposed to estimate arbitrary velocity fields from a time series of images acquired by a single camera. This approach, here focused on a single spatial plus a time dimension, is specialized to the decomposition of the velocity field over rectangular shaped (finite-element) bilinear shape functions. It is therefore assumed that the velocity field is essentially aligned along one direction. The use of a time sequence over which the velocity is assumed to have a smooth temporal change allows one to use elements whose spatial extension is much smaller than in traditional digital image correlation based on successive image pairs. This method is first qualified by using synthetic numerical test cases, and then applied to a dynamic tensile test performed on a tantalum specimen. Improvements with respect to classical digital image correlation techniques are observed in terms of spatial resolution.     

The effect of out-of-plane motion on 2D and 3D digital image correlation measurements

The effect of out-of-plane motion (including out-of-plane translation and rotation) on two-dimensional (2D) and three-dimensional (3D) digital image correlation measurements is demonstrated using basic theoretical pinhole image equations and experimentally through synchronized, multi-system measurements. Full-field results obtained during rigid body, out-of-plane motion using a single-camera vision system with (a-1) a standard f55mm Nikon lens and (a-2) a single Schneider–Kreuznach Xenoplan telecentric lens are compared with data obtained using a two-camera stereovision system with standard f55mm Nikon lenses.Results confirm that the theoretical equations are in excellent agreement with experimental measurements. Specifically, results show that (a) a single-camera, 2D imaging system is sensitive to out-of-plane motion, with in-plane strain errors (a-1) due to out-of-plane translation being proportional to ΔZ/Z, where Z is the distance from the object to the pin hole and ΔZ the out-of-plane translation displacement, and (a-2) due to out-of-plane rotation are shown to be a function of both rotation angle and the image distance Z; (b) the telecentric lens has an effective object distance, Z_eff, that is 50× larger than the 55 mm standard lens, with a corresponding reduction in strain errors from 1250 μs/mm of out-of-plane motion to 25 μs/mm; and (c) a stereovision system measures all components of displacement without introducing measurable, full-field, strain errors, even though an object may undergo appreciable out-of-plane translation and rotation.     

Strain field estimation based on digital image correlation and radial basis function

Two methods based on digital image correlation (DIC) and radial basis function (RBF) were proposed to obtain the accurate strain field in this paper. One is a combined method. RBF was applied to remove the noisy discrete displacement data first. After that, the strain was computed by a local least-squares algorithm. The other is a partial derivative of RBF (PD-RBF) based strain estimation method which integrated denoising with differential process. The effectiveness and accuracy of the proposed methods were verified through two numerical simulation experiments. A practical application on the normal strain measurement of an aluminum alloy beam under symmetric four-point bending via an outer loading frame was also presented. The measurement results are in good accordance with the data obtained by strain gauges. Furthermore, a shape parameter selection method based on rate of convergence was suggested. The new method simplifies the choice of the good shape parameter.     

A fast digital image correlation method for deformation measurement

Fast and high-accuracy deformation analysis using digital image correlation (DIC) has been increasingly important and highly demanded in recent years. In literature, the DIC method using the Newton-Rapshon (NR) algorithm has been considered as a gold standard for accurate sub-pixel displacement tracking, as it is insensitive to the relative deformation and rotation of the target subset and thus provides highest sub-pixel registration accuracy and widest applicability. A significant drawback of conventional NR-algorithm-based DIC method, however, is its extremely huge computational expense. In this paper, a fast DIC method is proposed deformation measurement by effectively eliminating the repeating redundant calculations involved in the conventional NR-algorithm-based DIC method. Specifically, a reliability-guided displacement scanning strategy is employed to avoid time-consuming integer-pixel displacement searching for each calculation point, and a pre-computed global interpolation coefficient look-up table is utilized to entirely eliminate repetitive interpolation calculation at sub-pixel locations. With these two approaches, the proposed fast DIC method substantially increases the calculation efficiency of the traditional NR-algorithm-based DIC method. The performance of proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. Results reveal that the computational speed of the present fast DIC is about 120-200 times faster than that of the traditional method, without any loss of its measurement accuracy     

Two-step digital image correlation for micro-region measurement

A method of two-step digital image correlation is well developed with more stable and reliable calculating technology, which consists of a simple searching method and an iterative correlation method. This new method can not only improve the calculating speed and the measuring accuracy, but also simplify the process of the experiment. In order to further increase the sensitivity of the technique, the sub-pixel reconstruction is performed in sub-image by utilizing the higher precision calculation of bicubic spline interpolation value method, and the accuracy of displacement is extended to better than 0.01 pixel; the strain resolution is limited to less than 0.0002 in micro-region. The above method is applied to quantify the micro-deformation of bimaterial sample and coating sample. The experimental results show that the method of two-step digital image correlation is a potential boon to investigations at extremely small-size scales.     

Quality assessment of speckle patterns for digital image correlation

Digital image correlation (DIC) is an optical–numerical full-field displacement measuring technique, which is nowadays widely used in the domain of experimental mechanics. The technique is based on a comparison between pictures taken during loading of an object. For an optimal use of the method, the object of interest has to be covered with painted speckles. In the present paper, a comparison is made between three different speckle patterns originated by the same reference speckle pattern. A method is presented for the determination of the speckle size distribution of the speckle patterns, using image morphology. The images of the speckle patterns are numerically deformed based on a finite element simulation. Subsequently, the displacements are measured with DIC-software and compared to the imposed ones. It is shown that the size of the speckles combined with the size of the used pixel subset clearly influences the accuracy of the measured displacements.     

Kalman filter based initial guess estimation for digital image correlation

In applications digital image correlation based algorithms often present a basis for analysis of movement/deformation of bodies. The sequence of the obtained images is analyzed for this purpose. Especially, in cases when the body׳s movement/deformation between two successive images is significant, the initial guess can have a major influence on the execution speed of the algorithm. In the worst case it can even cause the divergence of the algorithm. This was the inspiration to develop a new and unique approach for an accurate and reliable determination of an initial guess for each image pixel. Kalman filter has been used for this purpose. It uses past measurements of observed variable(s) for calculations. Beside that it also incorporates state space model of the actual system. This is one of the most important advantages provided by Kalman filter. The determined initial guess by the proposed method is actually close to the true one and it enables fast convergence. Even more important property of this approach is the fact that it is not path-dependant because each image pixel, which is defined in ROI, is tracked through the sequence of images based on its own past measurements and general state space model. Consequently, the proposed method can be used to analyze tasks where discontinuities between image pixels are present. The applied method can be used to predict an initial guess where reference and deformed subsets are related by translational and rotational motion. The advantages mentioned above are verified with numerical and real experiments. The experimental validations are performed by NR (Newton–Raphson) approach which is the most widely used. Beside NR method the presented algorithm is applicable for other registration methods as well. It is used as an addition for calculation of initial guesses in a sequence of deformed images.     

A subpixel motion estimation algorithm based on digital correlation for illumination variant and noise image sequences

One of the challenges in practical subpixel motion estimation is how to obtain high accuracy with sufficient robustness to both illumination variations and additive noise. Motivated by the fact that the normalized spatial cross-correlation is invariant to illumination, we introduce a gradient-based subpixel registration method by maximizing the digital correlation (DC) function between the reference and target frames. Such DC function is remodeled with the presence of image noise, yielding that the correlation coefficient is only sensitive to noise standard variance. To fairly suppress the noise corruption, not only the target frame but also the reference one is reformulated into Taylor gradient expression with half but opposite motion vector. The final solution to motion estimates can be approximated into a closed form by reserving first-order coefficient terms of unregistered motion variables. The error trend of approximated solution is discussed. Computer simulations and actual experiments’ results demonstrate the superiority of the proposed method to the LMSE-based method and ordinary DC method when illumination variations and noise exist. Among the experiments, the influences of real subpixel translation value and noise variance degree on accuracy are studied; correspondingly, an optimized iterative idea for big translations and the recommended noise level adaptive to our method are introduced.     

Incremental calculation for large deformation measurement using reliability-guided digital image correlation

Conventional digital image correlation (DIC) technique using a fixed reference image provides high-accuracy measurements but normally fails when serious decorrelation effect occurs in the deformed images due to large deformation, serious illumination fluctuations or other reasons. In this paper, an incremental reliability-guided digital image correlation (RG-DIC) technique, by combining the recently developed RG-DIC technique and an automatic reference image updating scheme, is proposed for large deformation measurement. In the incremental RG-DIC technique, a seed point is defined in the original reference image and searched in the deformed images, if the estimated correlation coefficient is larger than a preset threshold, which means no serious decorrelation effect exists in the deformed image, the RG-DIC technique is used to continue correlation analysis to obtain full-field displacements. Otherwise, the image recorded just before the current deformed image is chosen as an updated reference image to proceed with correlation analysis. Afterwards, the incremental displacements extracted by comparing the current deformed image and the updated reference image can be cumulated to determine the overall deformation. The effectiveness of the proposed technique is demonstrated by retrieving the full-field deformation of a foam sample subjected to large compressive deformation.     

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.     

Strain measurement of SU-8 photoresist by a digital image correlation method with a hybrid genetic algorithm

Digital image correlation (DIC) is a whole-field and non-contact strain measuring method. It could provide deformation information of a specimen by processing two digital images that are captured before and after the deformation. To search the deformed images, a hybrid genetic algorithm, in which a simulated annealing mutation process and adaptive mechanisms are added to the real-parameter genetic algorithm, is proposed in this work. To increase the accuracy and reliability of this method, some key parameters of this method are suggested. Then, this method is used to measure the strain during the micro tensile testing of SU-8 photoresist. In addition to the conventional single region, a double region is proposed to calculate the strain by DIC. The results indicate that while the strains obtained by single region are reasonable, those obtained by double region are accurate. Also the mechanical properties of SU-8 could be accurately obtained.     

Image pre-filtering for measurement error reduction in digital image correlation

In digital image correlation, the sub-pixel intensity interpolation causes a systematic error in the measured displacements. The error increases toward high-frequency component of the speckle pattern. In practice, a captured image is usually corrupted by additive white noise. The noise introduces additional energy in the high frequencies and therefore raises the systematic error. Meanwhile, the noise also elevates the random error which increases with the noise power. In order to reduce the systematic error and the random error of the measurements, we apply a pre-filtering to the images prior to the correlation so that the high-frequency contents are suppressed. Two spatial-domain filters (binomial and Gaussian) and two frequency-domain filters (Butterworth and Wiener) are tested on speckle images undergoing both simulated and real-world translations. By evaluating the errors of the various combinations of speckle patterns, interpolators, noise levels, and filter configurations, we come to the following conclusions. All the four filters are able to reduce the systematic error. Meanwhile, the random error can also be reduced if the signal power is mainly distributed around DC. For high-frequency speckle patterns, the low-pass filters (binomial, Gaussian and Butterworth) slightly increase the random error and Butterworth filter produces the lowest random error among them. By using Wiener filter with over-estimated noise power, the random error can be reduced but the resultant systematic error is higher than that of low-pass filters. In general, Butterworth filter is recommended for error reduction due to its flexibility of passband selection and maximal preservation of the allowed frequencies. Binomial filter enables efficient implementation and thus becomes a good option if computational cost is a critical issue. While used together with pre-filtering, B-spline interpolator produces lower systematic error than bicubic interpolator and similar level of the random error. Cubic B-spline interpolator can achieve comparable efficiency as bicubic interpolator, while quintic B-spline interpolator requires about 1.5 times the running time.     

Large deformation measurement scheme for 3D digital image correlation method

Difficulties often arise for digital image correlation (DIC) technique when serious de-correlation occurs between the reference image and the deformed image due to large deformation. An updating reference image scheme could be employed to deal with large deformation situation, however that will introduce accumulated errors. A large deformation measurement scheme, combining improved coarse search method and updating reference image scheme, is proposed in this paper. For a series of deformation images, the correlation calculation begins with a seed point and spreads out. An improved coarse search method is developed to calculate the initial correlation parameters for the seed point, which guarantees that the correlation calculation can be carried out successfully even in large deformation situation. Only for extremely large deformation, the reference image is updated. Using this method, not only extremely large deformation can be measured successfully but also the accumulated error could be controlled. A polymer material tensile test and a foam compression test are used to verify the proposed scheme. Experimental results show that up to 450% tensile deformation and 83% compression deformation can be measured successfully.     

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.     

A comparison of 2D and 3D digital image correlation for a membrane under inflation

Three-dimensional (3D) digital image correlation (DIC) is becoming widely used to characterize the behavior of structures undergoing 3D deformations. However, the use of 3D-DIC can be challenging under certain conditions, such as high magnification, and therefore small depth of field, or a highly controlled environment with limited access for two-angled cameras. The purpose of this study is to compare 2D-DIC and 3D-DIC for the same inflation experiment and evaluate whether 2D-DIC can be used when conditions discourage the use of a stereo-vision system. A latex membrane was inflated vertically to 5.41 kPa (reference pressure), then to 7.87 kPa (deformed pressure). A two-camera stereo-vision system acquired top-down images of the membrane, while a single camera system simultaneously recorded images of the membrane in profile. 2D-DIC and 3D-DIC were used to calculate horizontal (in the membrane plane) and vertical (out of the membrane plane) displacements, and meridional strain. Under static conditions, the baseline uncertainty in horizontal displacement and strain were smaller for 3D-DIC than 2D-DIC. However, the opposite was observed for the vertical displacement, for which 2D-DIC had a smaller baseline uncertainty. The baseline absolute error in vertical displacement and strain were similar for both DIC methods, but it was larger for 2D-DIC than 3D-DIC for the horizontal displacement. Under inflation, the variability in the measurements were larger than under static conditions for both DIC methods. 2D-DIC showed a smaller variability in displacements than 3D-DIC, especially for the vertical displacement, but a similar strain uncertainty. The absolute difference in the average displacements and strain between 3D-DIC and 2D-DIC were in the range of the 3D-DIC variability. Those findings suggest that 2D-DIC might be used as an alternative to 3D-DIC to study the inflation response of materials under certain conditions.     

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.     

An improved method for shape measurement using two-dimensional digital image correlation

Shape measurement is a significant application of digital image correlation (DIC). An improved method that combines a rotatable plane mirror is proposed to measure the shape of an immovable object. In this method, two images, one before and the other after rotating the plane mirror, are obtained and then in-plane translation which related to the shape of the detected object can be calculated by the use of two-dimensional digital image correlation (2D DIC). The relationship between the in-plane translation and the shape of the object is described. Experimental results show that the proposed method is feasible for shape and distance measurement with high accuracy.     

Digital speckle correlation method with compensation technique for strain field measurements

In the strain field measurements, especially in large strain field measurements, the correlation coefficient values obtained by the digital speckle correlation method are usually very low due to the relative pixel movement of the subset. The measuring error, therefore, is increased. A primary method, that is called compensation algorithm, is introduced for improving the correlation coefficient. A flow scheme with the compensation algorithm of our software is developed and some improved techniques for reducing the calculation time and error are discussed in the paper. After obtaining a set of displacement data with high correlation coefficient, a de-noise wavelet processing is adopted. It is obvious that the measuring accuracy of the strain field is better then before. A strain field of testing experiment is performed with this compensation technique. The correlation coefficients can increase from 0.70 to 0.99, which will be of much benefit for the improvements of the measuring accuracy.