A new method is proposed to measure the finite element (FE) displacement field from a deformed image in comparison to a reference one. In opposition to standard FE approaches, the unknown displacement is sought as a sum of products of separated dimensions functions. The problems in each dimension being uncoupled, the method involves only 1D meshes and 1D problems. An algorithm that builds successive best rank-one approximations is proposed and integrated into the nonlinear iterations of the correlation problem. Although the method can be applied to spaces of any dimension, this paper focuses on 2D images. Many synthetic examples are provided to evaluate the performance of the method. In addition, it is shown that, even with this separated representation, the introduction of a regularization operator is convenient. The latter makes it possible to perform a pixel-wise measure with huge computational savings.