Statistical Error Analysis of the Inverse Compositional Gauss-Newton Algorithm in Digital Image Correlation

Abstract

In this paper, a theoretical model of the inverse compositional Gauss-Newton (IC-GN) algorithm was derived based on the sum of squared differences correlation criterion and linear interpolation. The model indicates that the IC-GN algorithm has better noise robustness than the forward additive Newton-Raphson (FA-NR) algorithm, and shows no noise-induced bias if the gray gradient operator is chosen properly. Both numerical simulations and experiments show good agreements with the theoretical predictions. Based on the proposed theoretical model, a new statistical error formulation of digital image correlation is presented.