Remarks
When including an image using \includegraphics from the garphicx package (preloaded by beamer), then you can specify the options clip and trim, where trim takes additional parameters for the borders. In conjunction with clip the trimmed borders are cut off. When omitting clip only the borders are shift (i.e. the bounding box changes).
The trim parameters are
\includegraphics[clip,trim = left bottom right top]{...}
The units are bp (big point is 1/72 inch).
Implementation
Image111.png is the file from your link, placed in the same directory.
\documentclass{beamer}
\begin{document}
\begin{frame}{Upper left}
\centering
\includegraphics[clip,trim=0 90 120 0]{Image111}
\end{frame}
\begin{frame}{Lower left}
\centering
\includegraphics[clip,trim=0 0 125 90]{Image111}
\end{frame}
\begin{frame}{Upper right}
\centering
\includegraphics[clip,trim=125 90 0 0]{Image111}
\end{frame}
\begin{frame}{Lower right}
\centering
\includegraphics[clip,trim=125 0 0 90]{Image111}
\end{frame}
\end{document}
Output (First slide)

trimparameters are:trim = left bottom right top. The units arebp(big point is 1/72 inch). – Henri Menke Jun 21 '13 at 20:59