SUMMARYA 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.