Place an equation in two-column paper style

I am using an equation in IEEE style confrence paper. The pages are two column and I cannot place the following equation in the page. How I can make the equation be placed in one column ?

\begin{equation}
\label{eq:3}
min \left| \sum_{\substack{x,y\in b_{ij}}} I(x,y,t) - \sum_{\substack{x,y\in b^{'}_ {ij}}} I(x,y, t+\Delta t) \right|
\end{equation}

I think I have posted the wrong formula. The equation I cannot place in two-column is the following but I enjoyed your useful comments on the equation I posted earlier:

\begin{equation}
\label{eq:2}
\[ b(i,j,t+\Delta t) = \left\{
\begin{array}{ll}
1 & \quad \text{if} ~\left| \sum_{\substack{x,y\in b_{ij}}}  \left[I(x,y,t+\Delta  t) - I(x,y,t)\right]\right| >  $T_2$ \\
0 & \quad \text{otherwise}
\end{array}
\end{equation}
• Please provide a minimal working example (MWE). As such, the equation fits in one column. – user11232 Nov 28 '14 at 12:23
• Welcome to TeX.SX! You can have a look at our starter guide to familiarize yourself further with our format. – user11232 Nov 28 '14 at 12:24

min should be \min (never use math italic for multi-letter identifiers) and b^{'} should be b' and no need for \substack if you only have one line in the subscript.

but other than that, the equation fits in a two column IEEE document: \documentclass{IEEEtran}
\usepackage{amsmath}
\begin{document}

\noindent X\dotfill X
\begin{equation}
\label{eq:3}
\min \left| \sum_{x,y\in b_{ij}} I(x,y,t) -
\sum_{x,y\in b'_ {ij}} I(x,y, t+\Delta t) \right|
\end{equation}
\end{document}

Please always post complete documents that demonstrate any issue, noy just fragments.

For the revised question: \documentclass{IEEEtran}
\usepackage{amsmath}
\begin{document}

\noindent X\dotfill X
\begin{equation}
\label{eq:3}
\min \left| \sum_{x,y\in b_{ij}} I(x,y,t) -
\sum_{x,y\in b'_ {ij}} I(x,y, t+\Delta t) \right|
\end{equation}

\noindent X\dotfill X
\begin{multline}
\label{eq:2}
b(i,j,t+\Delta t)\\
= \begin{cases}
1 & \text{if} ~\left| \sum_{x,y\in b_{ij}}
\left[I(x,y,t+\Delta  t) - I(x,y,t)\right]\right| >  T_2 \\
0 & \text{otherwise}
\end{cases}
\end{multline}

\end{document}
• Thank you very much. I am sorry for duplicated question. Your solution worked very well. May I know what is the role of begin{cases} -- end{cases} in this case? – Yas Nov 28 '14 at 13:48
• @Yas cases is for making the layout you want with vertical cases and a { on the left. You did it by hand with \left\{ and array but that takes more markup and produces poorer spacing – David Carlisle Nov 28 '14 at 13:53
• \biggl| and \biggr| instead of \left| and \right|, please! ;-) – egreg Nov 28 '14 at 16:21

I've noticed that the subscript material below the summation symbols is wide enough to extend to the left and right of the summation symbols. TeX inserts extra whitespace so as to avoid any overlap with the surrounding. If you're really pressed for space, you could use the macro \smashoperator (or its relative, \smathoperator[r]) to suppress this whitespace. In the code below, there are two instances of \smathoperator[r] (to suppress the whitespace to the right of the summation symbol) and one instance of \smashoperator (to suppress whitespace on both sides). \documentclass{IEEEtran}
\usepackage{mathtools} % for \DeclarePairedDelimiter and \smashoperatr macros
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}  % macro to set "absolute value" bars

\begin{document}
\hrule %% just to illustrate width of column
\medskip
\begin{equation}
\label{eq:3}
\min \abs[\bigg]{\, \smashoperator[r]{\sum_{x,y\in b_{ij}}} I(x,y,t) -
\smashoperator{\sum_{x,y\in b'_{ij}}} I(x,y, t+\Delta t) }
\end{equation}

\begin{multline}
\label{eq:2}
b(i,j,t+\Delta t)\\
= \begin{dcases}  % "cases" environment in displaymath style
1 & \text{if } \abs[\bigg]{\, \smashoperator[r]{\sum_{x,y\in b_{ij}}}
\bigl[I(x,y,t+\Delta  t) - I(x,y,t)\bigr]} >  T_2 \\
0 & \text{otherwise}
\end{dcases}
\end{multline}
\end{document}