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# Lower and upper level sets

From Mathematics Is A Science

Jump to navigationJump to searchSuppose we have a real valued function f.

Given a number (level, threshold, etc) T, the T-th lower/upper level set is the set of all inputs with the value of f lower/higher than or equal to T.

Or, these two sets for each T:

{x: f(x) ≥ T} and {x: f(x) ≤ T}.

A relevant result here is the Implicit Function Theorem.

They are also called "excursion sets" (why?).

Via thresholding we use these sets in analysis of gray scale images.