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

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index 29a0fad3b1d294fc0f2819c0c22ced9fd42a3f35..12cdc3f603942ad4ccc1abfe63b1bb3d912e81b7 100644 (file)
--- a/doc/ctsim-concepts.tex
+++ b/doc/ctsim-concepts.tex
@@ -119,10 +119,6 @@ length}. These variables are input into \ctsim\ in terms of
 ratios rather than absolute values.
 
 \subsubsection{Phantom Diameter}\index{Phantom!Diameter}
 ratios rather than absolute values.
 
 \subsubsection{Phantom Diameter}\index{Phantom!Diameter}

-\begin{figure}
-$$\image{5cm;0cm}{scangeometry.eps}$$
-\caption{\label{phantomgeomfig} Phantom Geometry}
-\end{figure}

 The phantom diameter is automatically calculated by \ctsim\ from
 the phantom definition. The maximum of the phantom length and
 height is used to define the square that completely surrounds the
 The phantom diameter is automatically calculated by \ctsim\ from
 the phantom definition. The maximum of the phantom length and
 height is used to define the square that completely surrounds the


@@ -134,9 +130,13 @@ Pythagorean theorem and is
 \latexonly{\begin{equation}p_d = p_l \sqrt{2}\end{equation}}
 CT scanners collect projections around a
 circle rather than a square. The diameter of this circle is
 \latexonly{\begin{equation}p_d = p_l \sqrt{2}\end{equation}}
 CT scanners collect projections around a
 circle rather than a square. The diameter of this circle is

-the diameter of the boundary square \latexonly{$p_d$.  These
-relationships are diagrammed in figure~\ref{phantomgeomfig}.}
-\latexignore{emph{Pd}.}
+the diameter of the boundary square \latexonly{$p_d$.}
+\latexignore{\emph{Pd}.}
+\latexonly{These relationships are diagrammed in figure~\ref{phantomgeomfig}.}
+\begin{figure}
+\centerline{\image{5cm;0cm}{scangeometry.eps}}
+\latexonly{\caption{\label{phantomgeomfig} Phantom Geometry}}
+\end{figure}

 
 \subsubsection{View Diameter}\index{View diameter}
 The \emph{view diameter} is the area that is being processed
 
 \subsubsection{View Diameter}\index{View diameter}
 The \emph{view diameter} is the area that is being processed


@@ -194,7 +194,7 @@ physically impossible and it analagous to have having the x-ray
 source inside of the \emph{view diameter}.
 
 
 source inside of the \emph{view diameter}.
 
 

-\subsection{Parallel Geometry}\label{geometryparallel}\index{Parallel geometry}
+\subsection{Parallel Geometry}\label{geometryparallel}\index{Parallel geometry}\index{Scanner!Parallel}

 
 The simplest geometry, parallel, was used in \mbox{$1^{st}$} generation
 scanners. As mentioned above, the focal length is not used in this simple
 
 The simplest geometry, parallel, was used in \mbox{$1^{st}$} generation
 scanners. As mentioned above, the focal length is not used in this simple


@@ -208,6 +208,7 @@ significant distortions will occur.
 
 
 \subsection{Divergent Geometries}\label{geometrydivergent}\index{Equilinear geometry}\index{Equiangular geometry}
 
 
 \subsection{Divergent Geometries}\label{geometrydivergent}\index{Equilinear geometry}\index{Equiangular geometry}

+\index{Scanner!Equilinear}\index{Scanner!Equiangular}

 \subsubsection{Overview}
 Next consider the case of equilinear (second generation) and equiangular
 (third, fourth, and fifth generation) geometries. In these cases,
 \subsubsection{Overview}
 Next consider the case of equilinear (second generation) and equiangular
 (third, fourth, and fifth generation) geometries. In these cases,


@@ -217,8 +218,8 @@ source produces a fan beam which is read by a linear array of detectors.  If
 the detectors occupy an arc of a circle, then the geometry is equiangular.
 \latexonly{These configurations are shown in figure~\ref{divergentfig}.}
 \begin{figure}
 the detectors occupy an arc of a circle, then the geometry is equiangular.
 \latexonly{These configurations are shown in figure~\ref{divergentfig}.}
 \begin{figure}

-\image{10cm;0cm}{divergent.eps}
-\caption{\label{divergentfig} Equilinear and equiangular geometries.}
+\centerline{\image{10cm;0cm}{divergent.eps}}
+\latexonly{\caption{\label{divergentfig} Equilinear and equiangular geometries.}}

 \end{figure}
 
 
 \end{figure}
 
 


@@ -231,11 +232,11 @@ the \emph{focal length}:
 \latexignore{\centerline{\emph{alpha = 2 x asin (
 (Sd / 2) / f)}}}
 \latexonly{\begin{equation}\label{alphacalc}\alpha = 2 \sin^{-1}
 \latexignore{\centerline{\emph{alpha = 2 x asin (
 (Sd / 2) / f)}}}
 \latexonly{\begin{equation}\label{alphacalc}\alpha = 2 \sin^{-1}

-((s_d / 2) / f)\end{equation}
- This is illustrated in figure~\ref{alphacalcfig}.}
+((s_d / 2) / f)\end{equation}}
+\latexonly{This is illustrated in figure~\ref{alphacalcfig}.}

 \begin{figure}
 \begin{figure}

-\image{10cm;0cm}{alphacalc.eps}
-\caption{\label{alphacalcfig} Calculation of $\alpha$}
+\centerline{\image{10cm;0cm}{alphacalc.eps}}
+\latexonly{\caption{\label{alphacalcfig} Calculation of $\alpha$}}

 \end{figure}
 
 
 \end{figure}
 
 


@@ -282,13 +283,15 @@ the \emph{scan diameter} increases the detector array size.
 
 For equiangular geometry, the detectors are spaced around a circle
 covering an angular distance of
 
 For equiangular geometry, the detectors are spaced around a circle
 covering an angular distance of

-\latexonly{$2\,\alpha$.}\latexignore{\emph{2 \alpha}.} The dotted
-circle in
+\latexonly{$2\,\alpha$.}\latexignore{\emph{2 \alpha}.}
+The dotted circle
+\latexonly{in figure~\ref{equiangularfig}}
+indicates the positions of the detectors in this case.
+

 \begin{figure}
 \begin{figure}

-\image{10cm;0cm}{equiangular.eps}
-\caption{\label{equiangularfig}Equiangular geometry}
+\centerline{\image{10cm;0cm}{equiangular.eps}}
+\latexonly{\caption{\label{equiangularfig}Equiangular geometry}}

 \end{figure}
 \end{figure}

-figure~\ref{equiangularfig} indicates the positions of the detectors in this case.

 
 For equilinear geometry, the detectors are space along a straight
 line. The length of the line depends upon
 
 For equilinear geometry, the detectors are space along a straight
 line. The length of the line depends upon


@@ -296,11 +299,11 @@ line. The length of the line depends upon
 length}. It is calculated as
 \latexonly{\begin{equation}4\,f \tan (\alpha / 2)\end{equation}}
 \latexignore{\\\centerline{\emph{4 x F x tan(\alpha/2)}}}
 length}. It is calculated as
 \latexonly{\begin{equation}4\,f \tan (\alpha / 2)\end{equation}}
 \latexignore{\\\centerline{\emph{4 x F x tan(\alpha/2)}}}

+\latexonly{This geometry is shown in figure~\ref{equilinearfig}.}

 \begin{figure}\label{equilinearfig}
 \begin{figure}\label{equilinearfig}

-\image{10cm;0cm}{equilinear.eps}
-\caption{\label{equilinearfig} Equilinear geometry}
+\centerline{\image{10cm;0cm}{equilinear.eps}}
+\latexonly{\caption{\label{equilinearfig} Equilinear geometry}}

 \end{figure}
 \end{figure}

-\latexonly{This geometry is shown in figure~\ref{equilinearfig}.}

 
 
 \section{Reconstruction}\label{conceptreconstruction}\index{Reconstruction Overview}%
 
 
 \section{Reconstruction}\label{conceptreconstruction}\index{Reconstruction Overview}%


@@ -347,7 +350,7 @@ Backprojection is the process of ``smearing'' the filtered
 projections over the reconstructing image. Various levels of
 interpolation can be specified.
 
 projections over the reconstructing image. Various levels of
 interpolation can be specified.
 

-\section{Image Comparison}\index{Image comparison}
+\section{Image Comparison}\label{conceptimagecompare}\index{Image!Comparison}

 Images can be compared statistically. Three measurements can be calculated
 by \ctsim. They are taken from the standard measurements used by
 Herman\cite{HERMAN80}. They are:
 Images can be compared statistically. Three measurements can be calculated
 by \ctsim. They are taken from the standard measurements used by
 Herman\cite{HERMAN80}. They are: