Digital image correlation involves an inverse problem: A regularization scheme based on subset size constraint

Digital image correlation (DIC) is essentially implicated in a class of inverse problem. Here, a regularization scheme is developed for the subset-based DIC technique to effectively inhibit potential ill-posedness that likely arises in actual deformation calculations and hence enhance numerical stability, accuracy and precision of correlation measurement. With the aid of a parameterized two-dimensional Butterworth window, a regularized subpixel registration strategy is established, in which the amount of speckle information introduced to correlation calculations may be weighted through equivalent subset size constraint. The optimal regularization parameter associated with each individual sampling point is determined in a self-adaptive way by numerically investigating the curve of 2-norm condition number of coefficient matrix versus the corresponding equivalent subset size, based on which the regularized solution can eventually be obtained. Numerical results deriving from both synthetic speckle images and actual experimental images demonstrate the feasibility and effectiveness of the set of newly-proposed regularized DIC algorithms.