The 3-d modeling and rotation is building on the work Yaniv did as part of Face.com (face recognition startup), which was acquired by Facebook.com. Studied here: http://vis-www.cs.umass.edu/lfw/results.html
Also Marc'Aurelio was just hired away from Google and is a deep learning expert.
See my other comment for my guess on what's actually providing the boost: https://news.ycombinator.com/item?id=7393378
It looks like the main contribution to me :-)
If you'd rather have orientation identification (ie. rotation angle) and scale in that mix but don't care about position, the radon transform is nice and easy to work with.
But beyond inverting 1-2 key transformations, one usually has to pay a pretty hefty computational cost which often precludes online (near real-time) use.