Most iconic methods for rigid matching consist in finding and minimizing a registration criterion specifically chosen to solve a given problem. For non-rigid matching, attention has rather focussed on the type of smoothing or physical model of deformation to be used. In this report, we propose to place the non-rigid matching problem into a minimization framework. We have developped our theoretical idea in the case of the least squares criterion, corresponding to the assumption that the intensities of points do not change over time, and we have implemented a first order gradient descent which, along with a multiresolution approach, minimizes this criterion- . We also prove that the «demons» algorithm, thought of until now as an as hoc matching technique, can be seen as an approximation of a second order gradient descent on this criterion. Analysis of the mechanisms of this gradient descent incites us to introduce two different weightings into the filters used to smooth the solution, which we called an a priori weighting improves the solution found for the minimization problem, which is shown by comparing results in a distance-roughness space, while the a posteriori weighting helps tackle the appearance or disappearance of matter and occlusions, both sensitive issues for non-rigid iconic methods.