A recent survey and course of techniques that people have used in this area are here: http://old.siggraph.org/publications/2006cn/course30.pdf
TL: DR. There is no โrightโ way to do this in any absolute sense. You must define your goal in such a way as to calculate it. Then find out what additional (preliminary) information you need to get, in addition to the image data itself. Collapsing with โtexture warpโ or other interpolation schemes before you decide what you need to do is a waste of time.
You mention โan expression like an open mouth,โ and I interpret it as meaning that you want to create an image similar to what a real face would look like if the subject were photographed with an open mouth. The selected markers clearly do not provide enough information about this - in particular, they do not express any concept of โmouthโ. In fact, this concept is not found anywhere in the image. So, strictly speaking, your task is insoluble unless you add more information to it.
I suggest you take a look at the paper above and reconsider your problem again.
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