Digital Image Correlation with Enhanced Accuracy and Efficiency: A Comparison of Two Subpixel Registration Algorithms

The two major subpixel registration algorithms, currently being used in subset-based digital image correlation, are the classic Newton-Raphson (FA-NR) algorithm with forward additive mapping strategy and the recently introduced inverse compositional Gauss-Newton (IC-GN) algorithm. Although the equivalence of these two algorithms has been proved in existing studies, practical implementations of the two subpixel registration algorithms do involve differences, and therefore lead to different performance. In the present work, detailed theoretical error analyses of the two algorithms are performed. Based on the simple sum of squared difference criterion and the practical first-order shape function, analytic formulae that can quantify both the bias error (systematic error) and the variability (random error) in the displacements measured by IC-GN and FA-NR algorithms with various interpolation methods (i.e., cubic convolution interpolation, cubic polynomial interpolation, cubic B-spline interpolation and quintic B-spline interpolation) are derived. It is shown that, compared with FA-NR algorithm, IC-GN algorithm leads to reduced bias error in displacement estimation by eliminating noise-induced bias error, and gives rise on the average to smaller random errors in displacement estimation in the cases of high noise levels or using small subsets. Numerical tests with precisely controlled subpixel displacements confirm the correctness of the theoretical derivations. The results reveal that IC-GN algorithm outperforms the classic FA-NR algorithm not only in terms of computational efficiency, but also in respect of subpixel registration accuracy and noise-proof performance, and is strongly recommended as a standard subpixel registration algorithm for practical DIC applications instead of FA-NR algorithm.