Image Matching Error Assessment in Digital Image Correlation

Using concepts from statistics and probability theory and a least squares matching metric, the effects of various parameters on image plane motion measurements are demonstrated. Specifically, theoretical formulae defining the effect of noise in the intensity pattern, image contrast and interpolation method on both bias and variability in one-dimensional motion measurements are presented. Image correlation simulations (through subset matching) confirm the theoretical results for the case of linear intensity pattern interpolation. I. Background Reconstruction of object motions from image-based measurements remains an area of active interest in both the vision community as well as among experimental mechanicians. Since image plane errors during pattern matching will affect both single camera and stereovision reconstruction accuracy, there is a long-standing need to develop an understanding of the key parameters affecting motion measurements. In this regard, there is some existing literature regarding aspects of image based error analysis. Assuming isotropy in image-based matching, investigators [1, 2,.3] have developed estimates for positional errors, suggesting that variability in the intensity pattern is directly related to the accuracy of the image motions. Schreier et al [4] showed that sub-pixel matching errors are a function of the interpolation process used to reconstruct the deformed intensity pattern, even when intensity noise is not considered. Assuming Gaussian intensity pattern noise and a least squares pattern matching metric, the authors provide theoretical equations that clearly demonstrate the importance of various parameters (e.g., interpolation method, intensity noise) when reconstructing one-dimensional motions. Both numerical simulations and theoretical results are presented to demonstrate the effect of specific parameters. II. Basic Formulation and Definitions A least squares matching metric for subset-based intensity-pattern comparisons is used to define the optimal image-plane motion. Letting I(xi , yj) be the noiseless intensity pattern in the reference image at pixel location (i,j), we initially assume that digitization error (quantization) are small and do not affect the optimally estimated motions. Additive intensity pattern noise is defined to be a Gaussian distribution that is uncorrelated from pixel to pixel. Here, we let ε1 and ε2 denote the additive noise term at each pixel location in the reference and translated images, respectively, with zero mean and standard deviation of σ (gray levels). The least squares intensity matching metric can be written in the following form; Proceedings of the SEM Annual Conference June 1-4, 2009 Albuquerque New Mexico USA ©2009 Society for Experimental Mechanics Inc.