The Liquid Resize, base on this article.
It was partially implemented in Graff px. Here are the first results:

More results:
The x resolution decreased only.

And some bad expierence of cource:

I think, it is possible to use face detection routines for detcting faces at the photos and mark the pixels which belong to the facial areas at photos. After that, we can increase the energy of these pixels to some efficient big constant number. That will preserve this pixels from deleting and therefore, the faces will be preserved during the liquid resizing.

We have completed implementing Liquid Resize.
Here we have enlargement results: