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Automated Fast Initial Guess in Digital Image Correlation

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Automated Fast Initial Guess in Digital Image Correlation An International Journal for Experimental Mechanics Automated Fast Initial Guess in Digital Image Correlation † ‡ Z. Wang*,M.Vo, H. Kieu* and T. Pan *Department of Mechanical Engineering, The Catholic University of America, Washington, DC 20064, USA † Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA ‡ Department of Civil Engineering, The Catholic University of America, Washington, DC 20064, USA ABSTRACT: A challenging task that has hampered the fully automatic processing of the digital image correlation (DIC) technique is the initial guess when large deformation and rotation are present. In this paper, a robust scheme combining the concepts of a scale-invariant feature transform (SIFT) algorithm and an improved random sample consensus (iRANSAC) algorithm is employed to conduct an automated fast initial guess for the DIC technique. The scale-invariant feature transform algorithm can detect a certain number of matching points from two images even though the corresponding deformation and rotation are large or the images have periodic and identical patterns. After removing the wrong matches with the improved random sample consensus algorithm, the three pairs of closest and non-collinear matching points serve for the purpose of initial guess calculation. The validity of the technique is demonstrated by both computer simulation and real experiment. KEY WORDS: digital image correlation, improved random sample consensus, initial guess, scale-invariant feature transform Introduction analysis is to minimise the coefficient C in Equation (1) to find the best matching. For a representative Digital image correlation (DIC) technique is one of the pixel (x ,y ) to be analysed in the reference image, a most widely used methods for shape, motion and 0 0 square pattern of N =(2M +1)×(2M +1)pixelswithits deformation measurements [1]. The DIC technique centre located at (x ,y )isusuallychosenasthe typically works by comparing and matching the grayscale 0 0 reference subset. The corresponding subset in the target images of an object captured from different views, at image, i.e., the target subset, is often of irregular shape. different time, or at different stages of deformation. Denoting the shift amount between the centres of the Through tracking every few pixels of interest in the two matching subset patterns as (ξ,η), the shape reference and target images, followed by carrying out data mapping function for the entire reference and target interpolation, the DIC technique can determine the subsets can be expressed as whole-field two-dimensional (2D) and three-dimensional fi ÀÁ (3D) shape, deformation and motion vector elds as well ′ ¼ þ ξ þ ξ ðÞþÀ ξ À x i xi x xi x0 y yi y as their gradient maps. Because of its primary advantages ÀÁ0 (2) ′ ¼ þ η þ η ðÞþÀ η À of easy implementation and wide range of measurement y i yi x xi x0 y yi y0 sensitivity and resolution, the DIC technique has found ξ ξ η η fi numerous applications in many fields [2]. where x, y, x and y are the coef cients of the shape The DIC technique generally employs a correlation function. To determine all the six unknowns of shape ξ η ξ ξ η η criterion to detect the best image matching for a group of function ( , , x, y, x, y)aswellasthescaleandoffset pixels (named subset) centred at each interrogated pixel. parameters (a,b)involvedinEquation(1),theDIC There exist a variety of correlation criteria for the DIC technique often employs an iterative algorithm such as analysis. For instance, a simple yet robust criterion named the Newton–Raphson or the Levenberg–Marquardt the parametric sum of squared difference criterion can be method to carry out the correlation optimization. The written as [3] iterative algorithm is capable of providing very fast and highly accurate correlation analysis [4]. The downside, N ÂÃÀÁ ÀÁ however, is that a reasonably good initial guess for the six ¼ ∑ ; þ À ′ ; ′ 2 C af xi yi b gxi y i (1) i¼1 unknowns of the shape function on the starting or seed point is required. where a is a scale factor, b is an offset of intensity and f(xi, When the shape change and the rotation of the target yi)andg(x′i,y′i) indicate the intensity values at the ith image with respect to the reference image are relatively pixel in the reference subset and the matching pixel in small, the initial values of ξx, ξy, ηx and ηy can be set to zeros. the target subset, respectively. The task of the correlation In this case, the initial values of ξ and η can be automatically © 2013 Wiley Publishing Ltd | Strain (2014) 50,28–36 28 doi: 10.1111/str.12063 Z. Wang et al. : Automated Fast Initial Guess in Digital Image Correlation detected by a full-field subset scanning process [5, 6]. On the Scale-invariant feature transform feature points contrary, when the shape change and/or the rotation are relatively large, the initial guess normally has to be Keypoints detector conducted by manually selecting three pairs of matching To achieve scale invariance, the interest points are obtained pixels in the reference and target images through human– from scale-space extrema of the difference of Gaussian computer interaction, which yields six equations to solve (DoG). This can be conducted efficiently by constructing for the six unknowns in Equation (2) as an initial guess. an image pyramid in a procedure as follows. First, the Another notable case where a manual initial guess is Gaussian pyramid is formed from the original image by usually demanded is when each of the reference and successive smoothing and subsampling. Second, the DoG target images has multiple identical or nearly identical pyramid is built from the differences of the subsampled regions; the reason is that the existing automatic images and its Gaussian smoothing version at that pyramid initial guess methods may not be able to detect the correct level, as illustrated in Figure 1. Third, the extrema of the matches in those regions. It is also noted that the shape scale-space function are detected by comparing each pixel mapping function in Equation 2 may have more than six in the pyramid image with its 26 neighbour pixels. Last, a parameters to include higher-order terms; nevertheless, quadratic polynomial is fitted to the local sample points of thehigher-ordertermsarenegligiblefortheinitial each detected extremum to localise it with a higher guess purpose. accuracy. This refinement is particularly important to Manual selection of points for the initial guess in the estimate more accurately the scale information that is used DIC analysis has hampered the fully automatic analysis for scale normalisation to achieve a scale invariant feature. feature of the technique. The situation can become worse The interpolation fitting function is also useful in when there are multiple regions of interest, each requiring determining the stability of the local extremum. a reliable initial guess. In this paper, a robust scheme combining the concepts of a scale-invariant feature Keypoints descriptor transform (SIFT) algorithm and an improved random The SIFT descriptor exploits the local gradient information sample consensus (iRANSAC) algorithm is employed to of image intensities to summarise the image appearance in achieve an automated fast initial guess for the DIC a local neighbourhood around each interest point. To technique. The SIFT algorithm is widely used in computer obtain rotational invariance, each interest point is assigned vision to detect and describe local features in images, and an orientation corresponding to the dominant direction it has been recently applied to deformation measurements computed from a local histogram of gradient directions [7, 8]. Despite that, the advantages of the SIFT algorithm accumulated over a neighbourhood of the point. It is noted for the DIC measurements have not been fully utilised. that before being added to the histogram, each sample’s The novel approach to be presented has the ability to gradient magnitude is weighted by a Gaussian window accurately and automatically detect a number of centred at the interrogated point with the size proportional matching points from two images even though the deformation and rotation are large or the images have periodic and identical patterns. Principle Finding correct correspondences between images captured from different directions is traditionally a difficult problem. Recently, important advances have been made to tackle this problem. Among a few of them, the SIFT featureisoneofthemostimportant[9].Theessenceof the SIFT method is twofold: (i) identify feature locations intheimagespacethatareinvariantwithrespecttothe image translation, scaling and rotation; (ii) compute local descriptor around each feature point in the image that captures saliency of the point. The SIFT feature allows the correspondences of feature points between two images to be easily detected. The best matching pairs can be further identified, and the wrong matches can be eliminated by Figure 1: Scale-space pyramid. The image is subsampled by two in the iRANSAC algorithm. every octave © 2013 Wiley Publishing Ltd | Strain (2014) 50,28–36 doi: 10.1111/str.12063 29 Automated Fast Initial Guess in Digital Image Correlation : Z. Wang et al. to its detection scale. Next, a 4 × 4 square grid of size proportional to the detection scale of the interest point centred at the interest point with its orientation determined by the dominant orientation is laid out in the image, as demonstrated in Figure 2. An eight-bin accumulated histogram is then generated from the image gradientdirectionswithineachgrid. As a whole, these local histograms give rises to an image descriptorof4×4×8=128dimensionsforeachinterestpoint. This resulting image descriptor is referred to as the SIFT descriptor. In order to improve the robustness of the descriptor to illumination invariance, the 128-dimensional histogram is Figure 3: Illustration of line fitting using random sample consensus normalised to unit sum. to select reliable matchings Feature point matching With a set of image descriptors, the correspondences algorithm [12] and group sample consensus (GroupSAC) between images can be found by mutually matching their algorithm [13], which are briefly described below.
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