In this paper we propose a new approach of the two-image alignment problem based on a functional representation of images. This allows us to derive a one-to-several correspondence, multi-scale algorithm. At the same time, it also formalizes the problem as a robust estimation problem between possible matches. We then derive an accurate, robust and faster version for the alignment of edge images. The proposed algorithm is developed and tested in the context of offline longitudinal road profile reconstruction from stereo images.