One word, alone says it all "Holomorphic functions". Here, it's just simple polynomial "curve"-fitting of an image verses a sample of points. It's morphing without all the complicated machinery of Delaunay triangulation, meshes and so on. And it works quite well, if you don't ... er ... STRETCH it too far.

Here's a demo. (Both the skirt and the face were morphed).

https://twitter.com/Federation2005/status/545397224486604800/photo/1