On the Compositional Step of the IC-GN Digital Image Correlation Algorithm

Digital Image Correlation (DIC) is a well-known experimental optical technique for measuring the displacement field based on the assumption that pixel intensity does not change with motion. DIC can be implemented using various alternative approaches. The most used in the Experimental Mechanics field are the Forward-Additive Gauss-Newton (FA-GN) and the Inverse-Compositional Gauss-Newton (IC-GN) formulations. The former corresponds to the original formulation proposed by Lucas and Kanade, while the latter was proposed by Baker and Matthews twenty years later. Although both formulations give the same results at the first order, their speed, convergency characteristic and noise robustness differ considerably. Nowadays, the IC-GN method is usually preferred because of its lower computational load and the significantly better noise sensitivity. However, the Inverse Compositional approach, as its name states, requires the inversion and composition of the displacement field, thus enforcing the use of invertible displacement fields. This can be a significant limitation because it may introduce an under-matching error in the solution. This work shows that a simple modification of the viewpoint makes the compositional step simpler, thus giving a DIC formulation as fast as that of the IC-GN, with the same noise-bias characteristic and without requiring an invertible displacement field.