\setheader{{\it CHAPTER \thechapter}}{}{}{\ctsimheadtitle}{}{{\it CHAPTER \thechapter}}
\ctsimfooter
-\section{Overview}\index{Conceptual overview}
+\section{Conceptual Overview}\index{Conceptual overview}
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
\helprefn{scanner}{conceptscanner}.
\section{Phantoms}\label{conceptphantom}
-\subsection{Overview}\label{phantomoverview}\index{Phantom!Overview}%
\ctsim\ uses geometrical objects to describe the object being
scanned. A phantom is composed of one or more phantom elements.
Shepp and Logan\cite{SHEPP74} uses only ellipses.
\subsubsection{rectangle}
-Rectangles use \texttt{cx} and \texttt{cy} to define the position of
+Rectangles use \texttt{(cx,cy)} to define the position of
the center of the rectangle with respect to the origin. \texttt{dx}
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)
+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.
0.101 in each direction.
\section{Scanner}\label{conceptscanner}\index{Scanner!Concepts}%
-\subsection{Dimensions}
Understanding the scanning geometry is the most complicated aspect of
using \ctsim. For real-world CT simulators, this is actually quite
simple. The geometry is fixed by the manufacturer during the
being a very flexible simulator, gives tremendous options in
setting up the geometry for a scan.
+\subsection{Dimensions}
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
\subsection{Divergent Geometries}\label{geometrydivergent}\index{Equilinear geometry}\index{Equiangular geometry}
\index{Scanner!Equilinear}\index{Scanner!Equiangular}
-\subsubsection{Overview}
For both equilinear (second generation) and equiangular
(third, fourth, and fifth generation) geometries,
the x-ray beams diverge from a single source to a detector array.
Herman\cite{HERMAN80}. They are:
\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}
+\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{itemize}
These measurements are defined in equations \ref{dequation} through \ref{bigrequation}.
In these equations, $p$ denotes the phantom image, $r$ denotes the reconstruction