In the upcoming version of Photoshop there is a feature called Content-Aware fill.
This feature will fill a selection of an image based on the surrounding image - to the
As a guess (and that's all that it would be) I'd expect that it does some frequency analysis (some like a Fourier transform) of the image. By looking only at the image at the edge of the selection and ignoring the middle, it could then extrapolate back into the middle. If the designers choose the correct color plains and what not, they should be able to generate a texture that seamlessly blends into the image at the edges.
edit: looking at the last example in the video; if you look at the top of the original image on either edge you see that the selection line runs right down a "gap" in the clouds and that right in the middle there is a "bump". These are the kind of artifacts I'd expect to see if my guess is correct. (OTOH, I'd also expect to see them is it was using some kind of sudo-mirroring across the selection boundary.)
I'm guessing that for the smaller holes they are grabbing similarly textured patches surrounding the area to fill it in. This is described in a paper entitled "PatchMatch: A Randomized Correspondence Algorithm for Structural Image Editing" by Connelly Barnes and others in SIGGRAPH 2009. For larger holes they can exploit a large database of pictures with similar global statistics or texture, as describe in "Scene Completion Using Millions of Photographs". If they somehow could fused the two together I think it should work like in the video.
Well, they are not going to tell for the obvious reasons. The general name for the technique is "inpainting", you can look this up.
Specifically, if you look at what Criminisi did while in Microsoft http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.9407 and what Todor Georgiev does now at Adobe http://www.tgeorgiev.net/Inpainting.html, you'll be able to make a very good guess. A 90% guess, I'd say, which should be good enough.
The general approach is called seam-carving. Ariel Shamir's group is responsible for the seminal work here, which was presented in SIGGRAPH 2007. See: http://www.faculty.idc.ac.il/arik/site/subject-seam-carve.asp
I am a co-author of the PatchMatch paper previously mentioned here, and I led the development of the original Content-Aware Fill feature in Photoshop, along with Ivan Cavero Belaunde and Eli Shechtman in the Creative Technologies Lab, and Jeff Chien on the Photoshop team.
Photoshop's Content-Aware Fill uses a highly optimized, multithreaded variation of the algorithm described in the PatchMatch paper, and an older method called "SpaceTime Video Completion." Both papers are cited on the following technology page for this feature:
http://www.adobe.com/technology/projects/content-aware-fill.html
You can find out more about us on the Adobe Research web pages.
I work on a similar problem. From what i read they use "PatchMatch" or "non-parametric patch sampling" in general.
PatchMatch: A Randomized Correspondence Algorithm for Structural Image Editing