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[ctsim.git] / doc / ctsim-concepts.tex

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index 27d342a33b72062f926b846809afc8a727379829..3f0bb1640554d5fe31f0415e017792f94566b778 100644 (file)
--- a/doc/ctsim-concepts.tex
+++ b/doc/ctsim-concepts.tex
@@ -2,7 +2,7 @@
 \setheader{{\it CHAPTER \thechapter}}{}{}{\ctsimheadtitle}{}{{\it CHAPTER \thechapter}}
 \ctsimfooter
 
 \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
 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


@@ -18,7 +18,6 @@ concerned with are the \helprefn{phantom}{conceptphantom} and the
 \helprefn{scanner}{conceptscanner}.
 
 \section{Phantoms}\label{conceptphantom}
 \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.
 
 \ctsim\ uses geometrical objects to describe the object being
 scanned. A phantom is composed of one or more phantom elements.


@@ -63,12 +62,12 @@ Of note, the commonly used phantom described by
 Shepp and Logan\cite{SHEPP74} uses only ellipses.
 
 \subsubsection{rectangle}
 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}
 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.
 
 and a base half-width of \texttt{dx} and a height of \texttt{dy}.
 Rotations are then applied about the center of the base.
 


@@ -100,7 +99,6 @@ defined as a rectangle of size 0.1 by 0.1, the phantom size is
 0.101 in each direction.
 
 \section{Scanner}\label{conceptscanner}\index{Scanner!Concepts}%
 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
 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


@@ -108,6 +106,7 @@ construction of the scanner and can not be changed. \ctsim,
 being a very flexible simulator, gives tremendous options in
 setting up the geometry for a scan.
 
 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
 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


@@ -212,7 +211,6 @@ significant distortions will occur.
 
 \subsection{Divergent Geometries}\label{geometrydivergent}\index{Equilinear geometry}\index{Equiangular geometry}
 \index{Scanner!Equilinear}\index{Scanner!Equiangular}
 
 \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.
 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.


@@ -359,10 +357,10 @@ by \ctsim. They are taken from the standard measurements used by
 Herman\cite{HERMAN80}. They are:
 
 \begin{itemize}\itemsep=0pt
 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
 
 These measurements are defined in equations \ref{dequation} through \ref{bigrequation}.
 In these equations, $p$ denotes the phantom image, $r$ denotes the reconstruction