I found the title somewhat misleading. I was expecting some clever application of the nearest-neighbor interpolation. But this seems to involve neural nets and appears far from "simple" to me (I'm not in the image processing field though).
It seems that this could be used in theory with any feature descriptors, such as local color histograms, although the results wouldn't probably be as good.
Edit: Being a nearest neighbor probably also carries the usual computational complexity problems of the method. If I understand it correctly, they ease this by actually first finding just subset of best matching full images using the CNN features and then do a local nearest neighbor search just in those images.