What examples are there on research related to human perception and mathematical objects?
There is also a lot of research done on how people choose numerical passwords, or what people consider as "random numbers" and random sequences of numbers, but I am not looking for examples on how people handles randomness, or deal with strategies in a game.
What I am looking for is where math appears in relation to peoples' perception, such as in this example: there is a an interesting article on a mathematical model for "generating annoying, scratching sounds". The conclusion (conjecture) is that the boundary between order (sine wave) and chaos (white noise) is what make nails on a chalkboard so distinctively unpleasant. The researchers found that listening to the graph of the logistic map is highly unpleasant, while other more random, and more ordered functions did not have this property. The authors try to explain this experience by properties of the function they examine.
Another example is the mathematical model of the Droste effect. This model (based on complex analysis) was used to complete one of M.C Escher's famous paintings. I believe this is related to Escher's map.
Yet another example is the following 20-page paper, titled A mathematical theory of illusions and figural aftereffects, published in a Springer journal.
Also, a while back, a physicist posted The proof of innocence on arXiv, giving a mathematical model on why he (erroneously) got a traffic ticket, due to an optical illusion explainable by mathematics. From the abstract: The paper was awarded a special prize of $400 that the author did not have to pay to the state of California.