A new method is proposed to measure the finite element (FE) displacement field from a deformed image in comparison with a reference one. In opposition to standard FE approaches, the unknown displacement is sought as a sum of products of separated dimension functions. With the problems in each dimension being uncoupled, the method involves only one-dimensional meshes and one-dimensional 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 two-dimensional 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. Copyright © 2012 John Wiley & Sons, Ltd.