Digital Image Correlation (DIC) denotes in the field of experimental solid mechanics what is also referred to as image registration in computer vision. This problem can be summarized as follows: given a set of images taken over time that follow the deformation of the structure, the goal is to match the images; that is, to find a displacement field over the structure which enables to move from one image to another. With the advent of imaging technologies, accompanied by the high increase of the sensor definition, DIC and in particular Finite-Element DIC (FE-DIC) that uses the same FE meshes as in simulations, now appears as the ideal solution to generate data in the current context of data assimilation and digital twins in solid mechanics. More than a 2D technique, it also efficiently extends in 3D with the stereo-DIC that makes use of several cameras to access the three components of the displacement at the non-planar surface of a specimen. However, the drawback is that the measured FE displacement field generally contains too many Degrees Of Freedom (DOF) compared to the image data, so it is requested to regularize FE-DIC. In this work, Truncated Hierarchical B-Splines (THBS) are considered in a Free-Form-Deformation DIC approach to regularize FE-DIC in a strong, non-invasive, and adaptive manner. The idea is to embed the fine FE mesh in a THBS box whose unstructured refinement along with possible coarsening are automatically performed during the process to arrive at an optimal number of Degrees Of Freedom (DOF) for the solution. The nodal FE DOF of the measured field are related to a more regular field described by the box. The self-adaptive refinement algorithm is based on the greylevel residual; the THBS functions that have an important impact are refined while the ones with minimal impact are coarsened. The refinement process is also stopped when the noise level is reached and an additional criterion is formulated to ensure that the inverse DIC problem remains well conditioned. In the end, we obtain a regularized but conventional FE measured field which can be computed from a standard FE-DIC code. The method covers the cases of DIC and stereo-DIC.