I have to write some equations in latex, but I'm having trouble finishing them.
My Latex equation for image 1:
\widehat{f}(x,y)=median \left\{g(s,t)\right\} 
My Latex equation for image 2:
A\oplus B = U A_{b} How can I make a subscript below the formulas?
You want
\hat{f}(x,y) = \underset{(s,t)\in S_{xy}}{\mathrm{median}} \{g(s,t)\} And
A \oplus B = \underset{b\in B}{\cup} A_b The important things being:
\underset which takes two arguments, the first is put under the second.\mathrm to make median appear upright and differentiate it from a multiplication of 6 variables named m, e, d, i, a, and n.\{ and \} need backslashes because { and } are part of the LaTeX base language.\cup which is a nicer symbol for a union.
g(x,y)=\begin{cases}1 & \text{If $s$ hits $f$}\\ 0 & \text{otherwise}\end{cases} and requires the package amsmath at least the first example is a case where limits are applied to an operator. using amsmath, put this in the preamble:
\DeclareMathOperator*{\median}{median} and enter the math expression as
\[ \hat{f}(x,y)= \median_{(s,t)\in S_{xy}} \left\{g(s,t)\right\} \] with this result:
\DeclareMathOperator will set the specified string as roman, although other alphabet styles can be specified; the starred version causes strings designated as sub- or superscripts to the operator to be set as limits.
for the second example, it's reasonable to treat this the same way, but specifying italic:
\DeclareMathOperator{\Uoperator}{\mathit{U}} then ... \Uoperator_{b\in B} ... would yield the requested result.
\DeclareMathOperator* is designed to support limits on its argument -- but only in display mode. (Limits would appear to the side in text mode.) This does require amsmath. Since this doesn't work for you, please ask a separate question, providing a complete compilable example showing what you are doing, and cite this question and answer in yours, describing exactly what is different in what you are doing. \documentclass{article} \usepackage{amsmath} \DeclareMathOperator*{\median}{median} \begin{document} \[ \hat{f}(x,y)= \median_{(s,t)\in S_{xy}} \left\{g(s,t)\right\} \] \end{document} works beautifully on my machine.
Uin the second example? I'd say it's\bigcup_{b\in B}