The operation of \ctsim\ begins with the phantom object. A
phantom object consists of geometric elements. A scanner is
specified and the collection of x-ray data, or projections, is
-simulated. That projection data can be reconstructed using various
+simulated. This projection data can be reconstructed using various
user-controlled algorithms producing an image of the phantom
object. These reconstructions can be visually and statistically
compared to the original phantom object.
\subsubsection{ellipse}
Ellipses use \texttt{dx} and \texttt{dy} to define the semi-major and
-semi-minor axis lengths, with the center of the ellipse at \texttt{(cx,cy)}.
+semi-minor axis lengths with the center of the ellipse at \texttt{(cx,cy)}.
Of note, the commonly used phantom described by
Shepp and Logan\cite{SHEPP74} uses only ellipses.
and \texttt{dy} are the half-width and half-height of the rectangle.
\subsubsection{triangle}
-Triangles are drawn with the center of the base at \texttt{(cx,cy)},
-with a base half-width of \texttt{dx} and a height of \texttt{dy}.
+Triangles are drawn with the center of the base at \texttt{(cx,cy)
+and a base half-width of \texttt{dx} and a height of \texttt{dy}.
Rotations are then applied about the center of the base.
\subsubsection{segment}
being a very flexible simulator, gives tremendous options in
setting up the geometry for a scan.
-In general, the geometry for a scan all starts with the size of
+The geometry for a scan starts with the size of
the phantom being scanned. This is because \ctsim\ allows for
statistical comparisons between the original phantom image and
it's reconstructions. Since CT scanners scan a circular area, the
by \ctsim. They are taken from the standard measurements used by
Herman\cite{HERMAN80}. They are:
-\begin{twocollist}
-\twocolitem{\textbf{$d$}}{The normalized root mean squared distance measure.}
-\twocolitem{\textbf{$r$}}{The normalized mean absolute distance measure.}
-\twocolitem{\textbf{$e$}}{The worst case distance measure over a \latexonly{$2\times2$}\latexignore{\emph{2 x 2}} pixel area.}
+\begin{itemize}\itemsep=0pt
+\item[-]\textbf{$d$}\quad The normalized root mean squared distance measure.
+\item[-]\textbf{$r$}\quad The normalized mean absolute distance measure.
+\item[-]\textbf{$e$}\quad The worst case distance measure over a \latexonly{$2\times2$}\latexignore{\emph{2 x 2}} pixel area.
\end{twocollist}
These measurements are defined in equations \ref{dequation} through \ref{bigrequation}.