Normalized gradient-based inverse compositional Gauss-Newton (NG-IC-GN) algorithm for digital image correlation under non-uniform illumination variations

The introduction of digital image correlation (DIC) techniques has opened the way for studying full-field kinematics (either displacement or strain) of complex structures using low-cost optical measurements [1]. By choosing a subset in the reference image, DIC searches for the most similar subset in the deformed image according to certain correlation criterion [2]. These techniques result in a non-linear criterion to be minimized with respect to the parameters (local displacement or homogenous strain over the subset). The minimization is usually performed by a Newton-Raphson algorithm. One inherent limitation of the Newton-Raphson method is that the Hessian matrix and its inverse are updated in each iteration. Baker and Matthews proposed the efficient IC-GN algorithm in the field of compute vision [3]. The most interesting property of the IC-GN algorithm is that the Hessian matrix needs only to be calculated once during the iterations for each subset. Pan et al. applied the IC-GN to optimize a ZNSSD criterion and obtained remarkable results for DIC application [4] in the case of scale and offset of lights. The real environment light is complex and non-uniform. We propose a different DIC algorithm, the normalized gradient-based inverse composition Gauss-Newton (NG-IC-GN) algorithm, to overcome a non-uniform change of the image intensities by minimizing the SSD of gradients criterion. The NG-IC-GN is insensitive to the image intensity changes due to the insensitivity of the image gradient to the illumination variation. The present algorithm inherits the advantages of the original IC-GN and optimizes the simple SSD, instead of ZNSSD criterion, to obtain the deformation parameters.