Experimental assessment of noise robustness of the forward-additive, symmetric-additive and the inverse-compositional Gauss-Newton algorithm in digital image correlation

Digital Image Correlation (DIC) is a well-known optical experimental method based on the assumption that pixel intensity does not change with motion. This assumption is never exactly satisfied because various sources of noise exist (read-, shot-, dark-noise of the Charge Coupled Device (CCD), thermal dilatation of lens, non-constant illumination,...); moreover, to accurately track displacements, pixel intensity has to be interpolated at non-integer locations, thus introducing both phase and intensity errors due to the use of theoretically incorrect interpolating kernels. DIC can be implemented using various formulations, the most used being the Forward-Additive Gauss-Newton (FA-GN) and the Inverse-Compositional Gauss-Newton formulation (IC-GN). Even though both formulations give the same results at the first order, their speed, converging characteristics, and noise robustness differ considerably in particular with regard to the noise bias. Indeed, Shao et al. [1], using a theoretical analysis of a monodimensional signal and a numerical simulation on FFT-shifted images, recently showed that the latter formulation is not affected by noise bias, providing the correct differential operator is used. In this work, a fully experimental assessment of the noise-bias sensitivity of both algorithms is performed, confirming the theoretical findings and the numerical simulations available in the literature.