We describe a new method for computing a dense displacement field from a time-sequence of $2D$ or $3D$ images. It consists in minimizing an energy defined on the space of correspondence functions. This energy is divided into two terms, one term which matches contour points and particularly high curvature points, and one regularization term which constrains the continuity of the field. We introduce an adaptive mesh the resolution of which depends on the presence of edges and/or points of high curvature and we show how to use it to reduce the computational time of the method. We present experimental results on medical images which prove the validity of the approach and the accuracy of the computed displacement fields.