X-Git-Url: http://git.kpe.io/?a=blobdiff_plain;f=doc%2Fctsim-concepts.tex;h=1b53d60671da122a033dee3f618b4582452542c2;hb=0730f9f3adbf326b9d4bac754634399ad688efd1;hp=63d478c20ae2bae6e15a4f508efcd64ed4ae25a0;hpb=07353e6f00d4b1b0c7a9b57b9b42043da29489ba;p=ctsim.git diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex index 63d478c..1b53d60 100644 --- a/doc/ctsim-concepts.tex +++ b/doc/ctsim-concepts.tex @@ -2,11 +2,11 @@ \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 -simulated. That projection data can be reconstructed using various +simulated. This projection data can be reconstructed using various user-controlled algorithms producing an image of the phantom object. These reconstructions can be visually and statistically compared to the original phantom object. @@ -18,7 +18,6 @@ concerned with are the \helprefn{phantom}{conceptphantom} and the \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. @@ -58,18 +57,18 @@ meanings depending on the element type. \subsubsection{ellipse} Ellipses use \texttt{dx} and \texttt{dy} to define the semi-major and -semi-minor axis lengths, with the center of the ellipse at \texttt{(cx,cy)}. +semi-minor axis lengths with the center of the ellipse at \texttt{(cx,cy)}. Of note, the commonly used phantom described by 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)}, -with a base half-width of \texttt{dx} and a height of \texttt{dy}. +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. \subsubsection{segment} @@ -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}% -\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 @@ -108,7 +106,8 @@ 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. -In general, the geometry for a scan all starts with the size of +\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 it's reconstructions. Since CT scanners scan a circular area, the @@ -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} -\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. @@ -303,7 +301,7 @@ length}. This length, \latexonly{\begin{equation} d_l = 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} \centerline{\image{10cm;0cm}{equilinear.eps}} \latexonly{\caption{\label{equilinearfig} Equilinear geometry}} \end{figure} @@ -358,11 +356,11 @@ 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: -\begin{twocollist} -\twocolitem{\textbf{$d$}}{The normalized root mean squared distance measure.} -\twocolitem{\textbf{$r$}}{The normalized mean absolute distance measure.} -\twocolitem{\textbf{$e$}}{The worst case distance measure over a \latexonly{$2\times2$}\latexignore{\emph{2 x 2}} pixel area.} -\end{twocollist} +\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{itemize} These measurements are defined in equations \ref{dequation} through \ref{bigrequation}. In these equations, $p$ denotes the phantom image, $r$ denotes the reconstruction