A fast digital image correlation method for deformation measurement

https://doi.org/10.1016/j.optlaseng.2011.02.023Get rights and content

Abstract

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

Highlights

► A fast digital image correlation method based high-accuracy Newton-Raphson algorithm is proposed in this paper.► Two simple but effective approaches were proposed to remove the redundant calculations involved in the classic Newton-Rapshon algorithm.► Experimental results reveal that the proposed fast DIC is approximately 120–200 times faster than traditional Newton-Raphson-algorithm-based DIC method, and its computational speed is comparable with existing commercial DIC software, but the principle behind the latter one is unclear to us.► It is expected that the proposed fast and high-accuracy DIC will find more potential applications in many situations where computational time is critical.

Introduction

Development in digital image correlation (DIC) [1], [2] in the last thirty years has made it a popular and powerful technique for full-field motion, deformation and shape measurement. As a typical non-interferometric optical metrology with distinct advantages of simple experimental set-up, low-requirement on experimental environment and wide range of applicability, the DIC technique has been widely used for deformation and shape measurement, mechanical parameters characterization as well as numerical–experimental and theoretical–experimental cross validations.

The basic principle of the standard and most widely used subset-based DIC method is rather simple, namely matching (or tracking) the same subsets (or subimages) located in the reference image and deformed image to retrieve the full-field displacements. Although the DIC technique is simple in principle and implementation, two main challenges are always presented in its practical applications. One is the sub-pixel registration accuracy, and the other is the computational efficiency. Naturally, the ultimate objective of DIC technique is to achieve high-accuracy and real-time deformation and/or shape measurements.

As for the first challenge (i.e., the accuracy and precision of DIC measurements), various factors, such as speckle pattern [3], [4], subset size [5], correlation criterion [6], shape function [7], [8], [9], [10], sub-pixel interpolation scheme [9], [10], [11], [12] as well as sub-pixel registration algorithm [13], [14], which have important influences on the registration accuracy of DIC, have been thoroughly investigated by various researchers. Currently, an iterative spatial domain cross-correlation algorithm (e.g., a Newton–Raphson (NR) algorithm), combined with a robust matching criterion (e.g., a zero-mean normalized cross-correlation criterion, ZNCC) and a high-accuracy sub-pixel interpolation algorithm (e.g., a bicubic interpolation scheme), has been considered as a gold standard for accurate sub-pixel motion detection. By taking the relative deformation and rotation of the target subset into consideration, the NR algorithm is capable of providing highest sub-pixel registration accuracy and widest applicability. In the past years, the original NR algorithm [15] has been improved by various researchers [16], [17], [18], [19], [20], [21] for reducing its complexity, improving its robustness and extending its applicability. Despite being the most widely used as well as the most accurate algorithm for sub-pixel motion estimation, one significant drawback of NR algorithm, however, remains to be its extremely huge computational cost. As various time-critical applications of DIC have been increasingly important in recent years, a fast DIC method using the high-accuracy NR algorithm is therefore highly desirable.

This reason why the NR-algorithm-based DIC method is computational expensive can be attributed to the following two aspects. First, the NR algorithm is a non-linear numerical optimization algorithm, which requires an accurate initial guess to converge accurately and rapidly [16]. Conventionally, the initial guess of each calculation point is separately estimated by performing a simple but time-consuming exhaustive integer displacement searching scheme within the pre-specified search range of the deformed image [15], [16], [17]. Various techniques [22], [23], [24], [25], [26], such as a frequency domain correlation based on FFT [22], a nested searching scheme [23] and a sum-table approach [24], [25], [26], have been proposed to speed the calculation of the integer displacement searching; however, these techniques at least have two shortcomings: (1) they are hard or unable to deal with a specimen subject to large rotation and/or deformation; (2) they more or less consume certain amount of calculation time, despite being relatively computational efficient. Second, during each step of iterative optimization using NR algorithm, certain sub-pixel interpolation algorithm must be used repeatedly to reconstruct the intensity as well as intensity gradients at each sub-pixel location for the displaced pixel points of target subset. The sub-pixel interpolation calculation of a pixel point of certain reference subset is not only performed in each round of iteration, but also needs to be carried out for the same pixel point appeared in adjacent reference subsets, as the interrogated subsets defined in the reference image are normally highly overlapping. The repeated interpolation calculation performed at sub-pixel locations, in particular, consumes most redundant calculations of the existing NR-algorithm-based DIC method.

In this paper, we will demonstrate that the above two calculations are either unnecessary or redundant. A fast DIC method is proposed to achieve fast yet accurate deformation analysis by effectively eliminating the aforementioned redundant calculations involved in the conventional NR-algorithm-based DIC method. The proposed fast DIC method includes the following two simple but effective approaches. First, a reliability-guided displacement scanning strategy is employed to completely avoid the time-consuming integer-displacement searching calculation by ensuring reliable and accurate initial guess transfer between adjacent points. Second, a pre-computed global interpolation coefficient look-up table is employed to eliminate repetitive interpolation calculation at sub-pixel locations. These two approaches effectively eliminate the repeating redundant calculations of existing NR-algorithm-based DIC method and substantially increase its calculation efficiency. To validate its performance, the proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. The results show that the proposed fast DIC method is able to process more than 5400 points per second using a subset of 21×21 pixels and a grid step of 5 pixels. It is approximately 120–200 times faster than the existing NR-algorithm-based DIC method, depending on the specific calculation parameters used, on the condition of maintaining its measurement accuracy. Therefore, high-accuracy deformation measurement using DIC can be achieved at very low computational cost.

Section snippets

Fundamental principles of DIC method

In practical implementation of DIC, a region of interest (ROI) must be specified in the reference image first and is further divided into evenly spaced virtual grids. The displacements are computed at each point of the virtual grids to obtain full-field deformation. The basic principle of the standard subset-based DIC is schematically illustrated in Fig. 1. To accurately track motion of each point of interest, a square reference subset of (2 M+1)×(2 M+1) pixels centered at the interrogated point P

Reliability-guided displacement scanning scheme to avoid integer displacement searching calculation

It is necessary to mention that, as a non-linear optimization algorithm, the NR algorithm requires an accurate initial guess to converge rapidly and accurately. The convergence radius was estimated to be smaller than a few pixels by Vendroux and Knauss [16]. Conventionally, the initial guess of each point of interest is estimated separately by a simple but time-consuming integer displacement searching scheme either performed in spatial domain or in frequency domain based on FFT. Several

Experimental verification

The proposed fast DIC method is tested using real experimental images shown in Fig. 3. The two images, with a resolution of 768×576 pixels at 256 gray levels, were recorded from a three-point bending experiment. A rectangular area in the middle of the reference image is chosen to be the region of interest. In following, C++ language was used to realize the proposed fast DIC method, the RG-DIC method and the traditional NR-algorithm-based DIC method, and all the calculations were performed on a

Concluding remarks

A time-efficient fast DIC method based on high-accuracy Newton–Raphson algorithm is proposed in this paper for fast and accurate deformation measurement. By use of a reliability-guided displacement tracking scheme, reliable and accurate initial guess transfer between consecutive points of interest can be achieved. As a result, time-consuming integer displacement required in conventional DIC method is therefore entirely avoided in the proposed fast DIC method. Also, by building a look-up table

Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) under grants 11002012 and 10902066, the Science Fund of State Key Laboratory of Automotive Safety and Energy under grant KF10041, the Specialized Research Fund for the Doctoral Program of Higher Education under grant 20101102120015 and the Fundamental Research Funds for the Central Universities.

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