\setfooter{\thepage}{}{}{}{}{\thepage}%
\section{Overview}\label{conceptoverview}\index{Concepts,Overview}%
-In CTSim, a phantom object, or a geometrical description of the object
+In \ctsim, a phantom object, or a geometrical description of the object
of a CT study is constructed and an image can be created. Then a
scanner geometry can be specified, and the projection data simulated.
Finally that projection data can be reconstructed using various user
controlled algorithms producing an image of the phantom or study object.
-In order to use CTSim effectively, some knowledge of how CTSim works
-and the approach taken is required. \ctsim deals with a variety of
-object, but the two we need to be concerned with are the 'phantom' and
+In order to use \ctsim\ effectively, some knowledge of how \ctsim\ works
+and the approach taken is required. \ctsim\ deals with a variety of
+object, but the two objects we need to be concerned with are the 'phantom' and
the 'scanner'.
\section{Phantoms}\label{conceptphantom}\index{Concepts,Phantoms}%
\subsection{Overview}\label{phantomoverview}\index{Concepts,Phantoms,Overview}%
-CTSim uses geometrical objects to
-describe the object being scanned: rectangles, triangles, ellipses,
-sectors and segments. With these the standard phantoms used in the CT
-literature (the Herman and the Shepp-Logan) can be constructed. In fact
-CTSim provides a shortcut to construct those phantoms for you. It also
+\ctsim\ uses geometrical objects to
+describe the object being scanned. A phantom is composed a one or more
+phantom elements. These elements are simple geometric shapes,
+specifically, rectangles, triangles, ellipses, sectors and segments.
+With these the standard phantoms used in the CT literature (the Herman
+and the Shepp-Logan) can be constructed. In fact
+\ctsim\ provides a shortcut to construct those phantoms for you. It also
allows you to write a file in which the composition of your own phantom is
described.
\subsubsection{ellipse}
Ellipses use dx and dy to define the semi-major and semi-minor axis lengths,
with the centre of the ellipse at cx and cy. Of note, the commonly used
-phantom described by Shepp and Logan\cite{SHEPP77} uses only ellipses.
+phantom described by Shepp and Logan\cite{SHEPP74} uses only ellipses.
\subsubsection{rectangle}
Rectangles use
than the bore! In this model, the scanner size or field of view would
be used as the standard length scale.
-However, CTSim takes another approach. I believe this approach arose
+However, \ctsim\ takes another approach. I believe this approach arose
because the "image" of the phantom produced from the phantom description
was being matched to the reconstruction image of the phantom. That is,
the dimensions of the 'before' and 'after' images were being matched.
which completely contains the phantom. Let $l_p$ be the width (or height)
of this square.
-\subsubsection{Focal Length & Field of View}
+\subsubsection{Focal Length \& Field of View}
The two other important variables are the field-of-view-ratio ($f_{vR}$)
and the focal-length-ratio ($f_{lR}$). These are used along with $l_p$ to
define the focal length and the field of view (not ratios) according to
-\begin{equation}
+\latexonly{\begin{equation}
f_l = \sqrt{2} (l_p/2)(f_{lR})= (l_p/\sqrt{2}) f_{lR}
\end{equation}
\begin{equation}
f_v = \sqrt{2}l_p f_{vR}
-\end{equation}
+\end{equation}}
So the field of view ratio is specified in units of the phantom diameter,
whereas the focal length is specified in units of the phantom radius. The
-factor of $\sqrt(2)$ can be understood if one refers to figure 1, where
+factor of
+\latexonly{$\sqrt(2)$}
+\latexignore{sqrt(2)}
+can be understood if one refers to figure 1, where
we consider the case of a first generation parallel beam CT scanner.
\subsubsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}
For these geometries, the following logic is executed: A variable dHalfSquare
$d_{hs}$ is defined as
-\begin{equation}
+\latexonly{\begin{equation}
d_{hs} = (f_v)/(2\sqrt{2}) = (l_p/2) f_{vR}
-\end{equation}
+\end{equation}}
This is then subtracted from the focal length $f_l$ as calculated above, and
assigned to a new variable $\mathrm{dFocalPastPhm} = f_l - d_{hs}$. Since $f_l$ and
$d_{hs}$ are derived from the phantom dimension and the input focal length and field of view ratios, one can write,
+\latexonly{
\begin{equation}
\mathrm{dFocalPastPhm} = f_l -d_{hs}
= \sqrt{2}(l_p/2) f_{lR} - (l_p/2) f_{vR} = l_p(\sqrt{2}f_{lR} - f_{vR})
\end{equation}
+}
If this quantity is less than or equal to zero, then at least for some
projections the source is inside the phantom. Perhaps a figure will help at
this point. Consider first the case where $f_{vR} = f_{lR} =1 $, figure 3. The
square in the figure bounds the phantom and has sides $l_p$. For this case
then,
+\latexonly{
\[
f_l=\sqrt{2}l_p/2 = l_p/\sqrt{2},
\]
\[
\mathrm{dFocalPastPhm} = ({l_p}/{2}) (\sqrt{2}-1)
\]
+}
\begin{figure}
\includegraphics[height=0.5\textheight]{ctsimfig3.eps}
\caption{Equilinear and equiangluar geometry when focal length ratio =
the phantom rotated by 45 degrees, corresponding to the geometry of a
projection taken at that angle. Note that the fan beam now clips the top
and bottom corners of the bounding square. This illustrates that one may
-still be clipping the phantom, despite CTSim's best efforts. You have
+still be clipping the phantom, despite \ctsim\'s best efforts. You have
been warned.
\begin{figure}
\includegraphics[width=\textwidth]{ctsimfig5.eps}
than the spatial domain. The technique is comprised of two sequential steps:
filtering projections and then backprojecting the filtered projections. Though
these two steps are sequential, each view position can be processed individually.
-This parallelism is exploited in the MPI versions of \ctsim where the data from
+This parallelism is exploited in the MPI versions of \ctsim\ where the data from
all the views are spread about amongst all of the processors. This has been testing
in a 16-CPU cluster with good results.
\subsubsection{Filter projections}
The projections for a single view have their frequency data multipled by
-a filter of absolute(w). \ctsim permits four different ways to accomplish this
+a filter of absolute(w). \ctsim\ permits four different ways to accomplish this
filtering. Two of the methods use convolution of the projection data with the
inverse fourier transform of absolute(x). The other two methods perform an fourier
transform of the projection data and multiply that by the absolute(x) filter and
then perform an inverse fourier transform.
-\item{Backprojection of filtered projections}
\ No newline at end of file
+\subsubsection{Backprojection of filtered projections}
\ No newline at end of file
projects / ctsim.git / blobdiff