Summary: The purpose of this article is twofold: First to overview the recently proposed 3D image registration algorithm presented in the Ph.D. dissertation of the first author and secondly to apply the results to the registration of images which have a certain level of noise. Our method is developed by adjusting the divergence and curl of the image displacement field by means of which we can control translation, rotation, and deformations of image pixels. Our method incorporates sum of squared differences as the similarity metric and uses the Lagrange multipliers method to solve the existing optimization problem from which we obtain an optimality system that consists of four Poisson equations. In the 2D case a finite-difference multigrid strategy is used to solve these Poisson equations. Multi-level coarse-to-fine iterations allow us efficient, accurate and robust registration even if one or both of the images to be registered have a significant level of noise.