The following is off-topic, but it bears some resemblence to bitmap-to-vector transformation, in the sense that an algorithm needs to work out characteristics of a picture on its own. And the results are pretty damn spectacular. Point your browser to
this link, and then click on the 'Demonstration' link. The algorithm is capable of removing a helluvalot of noise from an image without distorting its global features. It can even selectively 'paint in' missing parts of a picture: take a look at the parrot behind bars, for example. And since the algorithm can 'fake' parts of an image, it is also incredibly good at upsizing images---well, not in an absolute sense perhaps, but certainly when compared to classical algorithms.
Exceedingly impressive work, and a beautiful application of an arcane topic in mathematics: tensor calculus. I skimmed it in advanced classes during my studies in chemical engineering, and make no mistake: those things are
not easy.
