This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Lower and upper level sets

### From Mathematics Is A Science

Suppose 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.