Maybe you've heard about that new kind of camera that adjusts people's faces so that they look more attractive. If you haven't, then: there's this new kind of camera that adjusts people's faces so that they look more attractive. This camera, even in prototype, raises all sorts of interesting questions like ``what is attractive?'' and ``shouldn't cameras reflect reality?'' and before you know it you've got into wondering if dried paint is actually just dripping very slowly off the ceiling and how long it would take the room go un-paint itself again. You probably don't have long enough to wait for that.
The tricky part of making this work is figuring when someone's taking a picture of a face, of course. You don't want to apply the attractiveness-enhancing thing on a non-person or a non-face or the camera can get into all kinds of mildly comic mischief, transforming an amusingly-named root vegetable into a representation of one of the many indistinct Presidents the United States had in the 19th century or something like that. And it would never do to have a landscape, manipulated into something more attractive: you'd have no way of proving you were ever in an unpleasant place. And think of the trouble in photographing the aftermath of a small car accident. You could end up with the dented fender-like structure not just smoothed out, but repainted, and turned into the end of a much more exciting car.
But let's assume you've got a face in place, which should be somewhere around the head and on the outside, for extroverts. Introverts can keep a face inside and they'd be happier if you did. But they'll be out of frame anyway, maybe working the camera so they don't have to bother with being seen in the presence of other people.
Now though there's the simple problem of having a face phase space made by taking a bunch of characteristic faces, which we'll call eigenfaces because everything sounds much more fun and gets this glaze of 19th century German linear algebraists when it has an eigen- in front of it. In fact, there was a whole set of work into eigenface eigenphase spaces, leading into work on eigeneigenface eigenphase eigenspaces before an eigenteam of (to be blunt) inadequately trained experts broke in and eigenstopped them. Eigen.
But once you have this set of standard reference attractive faces selected carefully and not at all from the loved ones of the camera inventors applying passive-aggressive forms of pressure about the whole selection process. Then since you've got this attractive face phase space of attractiveness it's a simple matter of applying an orthonormal finite-element projection to a linear face approximation. It's amazing people haven't been doing this all along, isn't it? Of course we can't be sure this isn't a convex face phase attractive space, so there might be a cluster of approximate face phase faces to face, offering the possibility of an attractor set of attractive face phase space places. I don't even know how much of this I'm making up anymore, but I am amusing myself. I just know how I'd do it, if I were going to, which I won't because it's a lot easier not taking pictures of any actual people. It's hard, particularly when I'm supposed to be the one photographing the family get-together, but it's easier than risking somebody noticing I'm taking a picture of them.
But once the camera does get out of the stage where it inspires articles upset about how photographs and reality are supposed to someday intersect that somehow aren't quite exciting enough to read all the way through, then we can start looking at more useful applications. For example, if we can have a filter to make faces more attractive then it follows we can have a filter to make faces look more green, or more like classic comic-strip figures, or more like they're in central Vermont. Before we know it we could end up with photographs that don't reflect anything that anyone has ever done ever, and won't that take the pressure off of making sure nobody's blinking?
Trivia: The second Spanish governor to arrive in Colombia, in 1543, brought the first cows seen in the area, and sold them for a thousand gold pesos each. Source: Food In History, Reay Tannahill.
Currently Reading: Four Colors Suffice: How The Map Problem Was Solved, Robin Wilson. I actually know the proof for the five-color theorem, or at least I knew it back when I was really studying graph theory. The four-color, of course, I never had time for.