Random Error in Strain Calculation using Regularized Polynomial Smoothing (RPS) and Point-wise Least Squares (PLS) in Digital Image Correlation

•The estimations of random error and under-matched error caused by two strain calculation methods (point-wise least squares (PLS) and regularized polynomial smoothing method (RPS)) are proposed, based on two assumptions on the noise error of calculated displacement.•For the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters.•The self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and obtain a more accurate result if the provided displacement field conforms strictly to assumptions.