For example, here is an image of a cat:
And here is an edited image of that cat. The very small mouth part has been stretched out to be very big, and the whole image has warped and moved around the mouth to compensate for the stretch, so there are no discontinuities.
How can I achieve this effect a (preferably free) image editor? I primarily use Paint.NET but I'm happy to use whatever program has this capability. I've been searching for information but I haven't found anything useful because I don't know what keywords to search for. I don't know what the technical term for this operation is.
Would really appreciate any help here!