I was looking for a good photo of Ronald Reagan to caricature (he's so wrinkly...), and I came across this amazing article. It's about topology and how continuous deformations of objects can yield recognizable, though drasitcally different mirror-objects. The question asked (and never answered by the article) is: why is it that we recognize a cartoon of a certain person as that person. How is it that all the cartoons about George W. Bush are clearly about him, even when the White House and other context-driven clues are removed? It also asks why people can recognize someone with only a tiny piece of the face--the eyes, the hair, the nose, the mouth, etc.
Most caricatures are not done by mathematic means but by emphasizing already prominent features (while maintaining space relationships between different facial planes). What does that mean? Cartoonists are effectively using biological topology every day. Why do pictures that emphasize George Bush's hair not look like him while those that emphasize Rod Blagojevich's do? Why are Jimmy Carter's lips always big, while Richard Nixon's nose is always long? These are the identifying characteristics, and, I would posit, they are the planes that most strongly depart from the ideal face of beauty, be they bigger, smaller, wider, thinner, or whatever.