Many image analysis and computer vision problems have been expressed as the minimization of global energy functions describing the interactions between the observed data and the image representations to be extracted in a given task. In this note, we investigate a new comprehensive approach to minimize global energy functions using a multiscale relaxation algorithm. The energy function is minimized over nested subspaces of the original space of possible solutions. These subspaces consist of solutions which are constrained at different scales. The constrained relaxation is implemented via a coarse-to-fine multiresolution algorithm that yields fast convergence towards high quality estimates when compared to standard monoresolution or multigrid relaxation schemes. It also appears to be far less sensitive to local minima than standard relaxation algorithms. The efficiency of the approach is demonstrated on a highly nonlinear combinatorial problem which consists of estimating long-range motion in an image sequence on a discrete label space. The method is compared to standard relaxation algorithms on real world and synthetic image sequences. 1994 Academic Press, Inc.