> One could learn the vector field at fixed points (just take some fixed points from the training set to use as anchors) and interpolate in some manner. One su

> One could learn the vector field at fixed points (just take some fixed points from the training set to use as anchors) and interpolate in some manner. One such interpolation that has nice properties (smooth everywhere, invertible, can be constructed for any set of pointwise correspondences) are diffeomorphisms. Unfortunately, the mathematical objects are infinite-dimensional, which makes computation with them somewhat involved, even if they are derived from a small-dimensional set of point correspondences. See, e.g., <http://www.cs.unc.edu/Research/MIDAG/pubs/papers/Joshi_TIP_2000.pdf> http://www.cs.unc.edu/Research/MIDAG/pubs/papers/Joshi_TIP_2... for one method of constructing them.