X-Git-Url: http://git.kpe.io/?p=ctsim.git;a=blobdiff_plain;f=doc%2Fctsim-concepts.tex;h=c7c3ffd39350bd3a66b965e2c8aa25e2b5dcc8c9;hp=3a01615190f08910ee6a0a81ae9201ac403d35c4;hb=751de723fd6e8a258a7a4730893efe937b7db971;hpb=47601e0ab94ccdc360824178cf068a05bcbdb0eb diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex index 3a01615..c7c3ffd 100644 --- a/doc/ctsim-concepts.tex +++ b/doc/ctsim-concepts.tex @@ -2,7 +2,7 @@ \setheader{{\it CHAPTER \thechapter}}{}{}{\ctsimheadtitle}{}{{\it CHAPTER \thechapter}}% \ctsimfooter% -\section{Overview}\label{conceptoverview}\index{Concepts,Overview}% +\section{Overview}\label{conceptoverview}\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 @@ -16,8 +16,8 @@ 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 \emph{phantom} and the \emph{scanner}. -\section{Phantoms}\label{conceptphantom}\index{Concepts,Phantoms}% -\subsection{Overview}\label{phantomoverview}\index{Concepts,Phantoms,Overview}% +\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 a one or more phantom elements. @@ -32,7 +32,7 @@ user-defined phantoms. The types of phantom elements and their definitions are taken with permission from G.T. Herman's 1980 book\cite{HERMAN80}. -\subsection{Phantom File}\label{phantomfile}\index{Concepts,Phantoms,File} +\subsection{Phantom File}\label{phantomfile}\index{Phantom file syntax} Each line in the text file describes an element of the phantom. Each line contains seven entries, in the following form: \begin{verbatim} @@ -50,7 +50,7 @@ coefficient of the object. Where objects overlap, the attenuations of the overlapped objects are summed. -\subsection{Phantom Elements}\label{phantomelements}\index{Concepts,Phantoms,Elements} +\subsection{Phantom Elements}\label{phantomelements}\index{Phantom elements} \subsubsection{ellipse} Ellipses use \texttt{dx} and \texttt{dy} to define the semi-major and @@ -88,14 +88,14 @@ The perimeter of the circle is then draw between those two points below the x-axis. The sector is then rotated and translated the same as a segment. -\subsection{Phantom Size} +\subsection{Phantom Size}\index{Phantom size} The overall dimensions of the phantom are increased by 1\% above the specified sizes to avoid clipping due to round-off errors from sampling the polygons of the phantom elements. So, if the phantom is defined as a rectangle of size 0.1 by 0.1, the actual phantom has extent 0.101 in each direction. -\section{Scanner}\label{conceptscanner}\index{Concepts,Scanner}% +\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 @@ -119,7 +119,7 @@ the \emph{view diameter}, \emph{scan diameter}, and \emph{focal length}. These variables are all input into \ctsim\ in terms of ratios rather than absolute values. -\subsubsection{Phantom Diameter} +\subsubsection{Phantom Diameter}\index{Phantom diameter} \begin{figure} $$\image{5cm;0cm}{scangeometry.eps}$$ \caption{\label{phantomgeomfig} Phantom Geometry} @@ -138,7 +138,7 @@ the diameter of the boundary square relationships are diagrammed in figure~\ref{phantomgeomfig}.} \latexignore{emph{Pd}.} -\subsubsection{View Diameter} +\subsubsection{View Diameter}\index{View diameter} The \emph{view diameter} is the area that is being processed during scanning of phantoms as well as during rasterization of phantoms. By default, the \emph{view diameter} \rtfsp is set equal @@ -159,7 +159,7 @@ This will lead to significant artifacts. Physically, this would be impossible and is analagous to inserting an object into the CT scanner that is larger than the scanner itself! -\subsubsection{Scan Diameter} +\subsubsection{Scan Diameter}\index{Scan diameter} By default, the entire \emph{view diameter} is scanned. For experimental purposes, it may be desirable to scan an area either larger or smaller than the \emph{view diameter}. Thus, the concept @@ -172,7 +172,7 @@ for all ordinary scanning, the \emph{scan ratio} is to \texttt{1}. If the \emph{scan ratio} is less than \texttt{1}, you can expect significant artifacts. -\subsubsection{Focal Length} +\subsubsection{Focal Length}\index{Focal length} The \emph{focal length}, \latexonly{$f$,}\latexignore{\emph{F},} is the distance of the X-ray source to the center of @@ -190,7 +190,7 @@ physically impossible and it analagous to have having the x-ray source inside of the \emph{view diameter}. -\subsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel} +\subsection{Parallel Geometry}\label{geometryparallel}\index{Parallel Geometry} As mentioned above, the focal length is not used in this simple geometry. The detector array is set to be the same size as the @@ -202,7 +202,7 @@ values of less than \texttt{1} are used for these two variables, significant distortions will occur. -\subsection{Divergent Geometries}\label{geometrydivergent}\index{Concepts,Scanner,Geometries,Divergent} +\subsection{Divergent Geometries}\label{geometrydivergent}\index{Divergent geometry} \subsubsection{Overview} Next consider the case of equilinear (second generation) and equiangular (third, fourth, and fifth generation) geometries. In these cases, @@ -297,7 +297,7 @@ length}. It is calculated as \latexonly{$4\,f \tan (\alpha / 2)$} \subsubsection{Examples of Geometry Settings} -\section{Reconstruction}\label{conceptreconstruction}\index{Concepts,Reconstruction}% +\section{Reconstruction}\label{conceptreconstruction}\index{Reconstruction Overview}% \subsection{Overview} \subsection{Direct Inverse Fourier} This method is not currently implemented in \ctsim, however it is @@ -306,7 +306,7 @@ accurate as filtered backprojection. The difference is due primarily because interpolation occurs in the frequency domain rather than the spatial domain. -\subsection{Filtered Backprojection} +\subsection{Filtered Backprojection}\index{Filtered backprojection} 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. @@ -338,7 +338,7 @@ Backprojection is the process of ``smearing'' the filtered projections over the reconstructing image. Various levels of interpolation can be specified. -\section{Image Comparison} +\section{Image Comparison}\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}.