combining arbitrarily transformed images

Schölkopf and I worked over coffee to come up with a method for the Lang–Schölkopf idea of combining Web-scraped images using pixel rank information. The idea is that human-viewable images can be very strangely transformed, but if they have been transformed in a way that doesn't re-order pixel brightnesses (at least locally), there ought to be ways to combine them. We came up with several simple methods. It was an interesting conversation, because I like to think about problems as having a causal, generative, probabilistic model underlying them and justify all procedures as being approximations to the Right Thing To Do (tm) within that model framework. Schölkopf likes to think about fast, tractable, scalable procedures with good properties, and only then see if there is an understanding of that procedure in terms of inference. Fortunately, I think we have it all; more soon after we try it out. My job (as usual) is to start the document. While we were talking, Lang was scraping the Web and calibrating images with Astrometry.net.