Agree with sibling comments. There's something very slippery and tricky going on with "perceptual area," it's not simple geometry. This is actually an area where I think machine learning has something to offer.
Mrs. Scyzoryk is a typographer, confirms that it’s not just math, but can’t imagine using ML for what is an integral part of developing an „eye” and going through the process.
Well, I have some qualifications in typography, a reasonable familiarity with ML techniques, and am fairly good at math (though I can't claim to have won the Putnam), and I can imagine how to apply ML for this task.