A novel adaptive isogeometric digital height correlation (DHC) technique has been developed in which the set of shape functions, needed for discretization of the ill-posed DHC problem, is autonomously optimized for each specific set of profilometric height images, without a priori knowledge of the kinematics of the experiment. To this end, an adaptive refinement scheme is implemented, which refines the shape functions in a hierarchical manner. This technique ensures local refinement, only in the areas where needed, which is beneficial for the noise robustness of the DHC problem. The main advantage of the method is that it can be applied in experiments where the deformation mechanisms are unknown in advance, thereby complicating the choice of suitable shape functions. The method is applied to a virtual experiment in order to provide a proof of concept. A second virtual experiment is executed with stretchable electronics interconnects, which entail localized buckles upon deformation with complex kinematics. In both cases, accurate results were obtained, demonstrating the beneficial aspects of the proposed method. Moreover, the technique performance on profilometric images of a real experiment with stretchable interconnects was demonstrated.