How The Brain Estimates Distances, Heights And Velocities, With Computer Vision Applications

This article started arsenic a funny question: really overmuch taller a skyscraper needs to beryllium successful bid to beryllium perceived arsenic doubly its existent height? I assumed that nan perceiver was astatine crushed level astatine a horizontal region d from nan building, and that nan existent tallness is H.  We each cognize that nan building must beryllium much than doubly arsenic gangly owed to perspective, successful bid to springiness nan illusion that its tallness has doubled.

I utilized AI devices to find an reply but could not get anywhere. Then, looking astatine articles connected nan taxable – immoderate referenced successful my insubstantial – nan attraction was ever connected computing nan nonstop tallness by correcting nan position effect. All were alternatively trivial, involving elemental trigonometry. Eventually I came up pinch a method to accurately quantify nan induced illusion and correct it.

Highlights

I came up pinch an elegant mathematical solution, much precocious than what you will find successful textbooks, including nan hyperbolic sine usability and its inverse, integration successful polar coordinates, a 4th bid linear recursion, and moreover a spot of non-trivial number theory.

Magically, each measurement and equation lead to beautiful closed-form mathematical formulas, without nan request for approximations. This would make for an absorbing mathematics aliases physics problem for students acquainted pinch precocious calculus. A problem that you cannot lick – astatine slightest for now – utilizing OpenAI aliases akin tools. Or a occupation question and reply mobility for a intelligence role, wherever nan campaigner is allowed to usage AI to get an answer.

The 3-page paper, besides featuring related machine imagination problems specified arsenic assessing nan velocity and acceleration of a rocket based connected ocular perception, is disposable arsenic PDF #49, here.

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About nan Author

Vincent Granville is simply a pioneering GenAI intelligence and instrumentality learning expert, co-founder of Data Science Central (acquired by a publically traded institution successful 2020), Chief AI Scientist at MLTechniques.com and GenAItechLab.com, erstwhile VC-funded executive, writer (Elsevier) and patent proprietor — 1 related to LLM. Vincent’s past firm acquisition includes Visa, Wells Fargo, eBay, NBC, Microsoft, and CNET. Follow Vincent connected LinkedIn.