This is the correct way to type in the equation.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\alpha_b =
\begin{cases}
1, & I_{i,r}^b \geq I_{thr} \\
0, & I_{i,r}^b < I_{thr}
\end{cases}
\end{equation}
\end{document}

Depending on its meaning, “thr” could be better as
I_{\mathrm{thr}}
Use this if it's a textual abbreviation.
About your code, it's hard to find something right, I'm afraid.
The command \large
is not allowed in math mode. Probably you wanted to use it for enlarging the result of \atop
. But \atop
is not to be used anywhere in LaTeX, if you load amsmath
(and you do, because you have \text
).
The command \text
is used to insert textual parts in an equation, but you're using it for math parts; finally \right}
is not allowed and it should be \right.
for a null delimiter.
However, using a fraction for doing a cases
environment is wrong to begin with. I'm quite surprised you know about \atop
and not about cases
. If \atop
has been suggested to you by a friend, this could be a good occasion for breaking this friendship. ;-)
_
is a math mode command. It must only appear in math mode. You have it within\text{ ... }
which puts you in text mode unsurprisingly. So_
is undefined and fails – Au101 Nov 9 '16 at 3:53\right}
at the end, where I assume you want\right\}
– Au101 Nov 9 '16 at 3:58