Self-adaptive B-spline approximation for smoothing and differentiating noisy displacement data in DIC
Abstract The discrete displacement data obtained by digital image correlation (DIC), even by the recently developed Smart-DIC with self-adaptive optimal parameter selection (i.e., subset size and shape function), is unavoidably contaminated by random noise. Differentiating such noisy displacement data to calculate strain is challenging due to noise amplification and physical inconsistency. To address this challenge, a self-adaptive B-spline approximation (SA-BSA) method with automatically determined knot distributions is proposed for displacement smoothing and strain computation. The method performs an initial B-spline approximation with uniform knots and iteratively refines the knot distribution based on full-field curvature and residuals, enabling accurate capture of localized deformations while maintaining smoothness in uniform regions. The inherent global consistency of B-spline approximation further ensures continuous displacement and strain fields, effectively suppressing local noise. The performance of SA-BSA is validated through both numerical and real-world experiments, with comparisons to several representative smoothing methods. The results demonstrate that SA-BSA consistently achieves superior strain accuracy and robustness, particularly under high-noise levels and complex deformations, by effectively balancing noise suppression and deformation adaptivity. Furthermore, the proposed SA-BSA method can be implemented as an add-on module to existing DIC software, providing a practical and powerful solution for robust displacement smoothing and accurate strain computation.