In this paper, we develop data driven registration algorithms, relying on robust pixel similarity metrics, that enable an accurate (subpixel) rigid registration of dissimilar single and multimodal 2D/3D images. A "soft redescending" estimator is associated to a top down stochatic multigrid relaxation algorithm in order to obtain robust, data driven multimodal image registrations. With the stochastic multigrid strategy, the registration is not affected by local minima in the objective function and a manual initialization near the optimal solution is not necessary. The proposed robust similarity metrics are compared to the most popular standard similarity metrics, on synthetic as well as on real world image pairs showing gross dissimilarities. Two case-studies are considered: the registration of single and multimodal 3D medical images and the matching of multispectral remotely sensed images showing large overcast areas.