The problem is that the meshes are in 3D. So I first have to establish CORRESPONDENCES between the meshes; this vertex maps to that, this face maps to that and so on....and then I can interpolate.

I need a correspondence algorithm that does not need any user input. I have seen many correspondence algorithms that do the job, but they all need the user to input a few corresponding vertices on both the meshes, so that the alignment of the models against each other becomes fixed. Once the correspondence is done, the interpolation shouldn't be much of a problem.