Global digital image correlation (DIC) applied to infrared images is considered for a test where very significant and localized laser heating is applied. Because of temperature changes and high gradients, digital levels are to be corrected in addition to the displacement registration. Digital level corrections and kinematics are decomposed over an unstructured mesh to account for steep gradients. A regularization strategy is used to mend ill-posedness penalizing rapid variation of corrections and displacements. High gradients motivate further softening of the regularization (i.e., reduction of the regularization length scale) based on prior estimates. The methodology is tested on different experimental cases in which DIC residuals are drastically reduced and systematic displacement errors are cut down to 10^-2 pixel after gray level corrections (performed on numerical cases). Additionally, the regularization improves the convergence speed as well as the quality of the sought fields. The capability of the code to account for blur corrections is illustrated on a practical case.