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> The FAST feature detector is an algorithm for finding regions of an image that are visually distinctive, …

Is that related to ‘Energy Function’ in any way?

(I ask because a long time ago I was involved in an Automated Numberplate Reading startup that was using an FPGA to quickly find the vehicle numberplate in an image)

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What you are thinking of operates at a different level of abstraction. Energy functions are a general way of structuring a problem, used (sometimes abused) to apply an optimization algorithm to find a reasonable solution for it.

FAST is an algorithm for efficiently looking for "interesting" parts (basically, corners) of an image, so you can safely (in theory) ignore the rest of it. The output from a feature detector may end up contributing to an energy function later, directly or indirectly.

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