A new methodology is proposed to estimate displacement fields from pairs of images (reference and strained) that evaluates continuous displacement fields. This approach is specialized to a finite-element decomposition, therefore providing a natural interface with a numerical modeling of the mechanical behavior used for identification purposes. The method is illustrated with the analysis of Portevin-Le Châtelier bands in an aluminum alloy sample subjected to a tensile test. A significant progress with respect to classical digital image correlation techniques is observed in terms of spatial resolution and uncertainty.