Notes on: Currents for curve and surface matching

There is a need for registration algorithms to compare functional data, to compute distances between healthy and disease anatomies, and to build probabilistic atlases between the healthy and disease groups. To do this, medical images can be directly processed via 2d or 3d image matching, or after segmentation: extraction of some features points, curves or surfaces of interest. In this case, the most usual tool for registration is landmark (labelled points) matching, and one has to specify assignments of source/target pairs, which may not be relevant when these points sample curves or surfaces. Hence one needs to find models and algorithms for dealing with submanifolds.