-Herman\cite{HERMAN80}.
-$d$ is the standard error, $e$ is the maximum error, and
-$r$ is the maximum error of a 2 by 2 pixel area.
-
-To compare two images, $A$ and $B$, each of which has $n$ columns and $m$ rows,
-these values are calculated as below.
-
-
-\latexonly{
-\begin{equation}
-d = \frac{\sum_{i=0}^{n}{\sum_{j=0}^{m}{(A_{ij} - B_{ij})^2}}}{m n}
-\end{equation}
-\begin{equation}
-r = \max(|A_{ij} - B{ij}|)
-\end{equation}
-}
+Herman\cite{HERMAN80}. They are:
+\begin{description}
+\item[$d$] The normalized root mean squared distance measure.
+\item[$r$] The normalized mean absolute distance measure.
+\item[$e$] The worst case distance measure over a $2\times2$ area.
+\end{description}
+
+These measurements are defined in equations \ref{dequation} through \ref{bigrequation}.
+In these equations, $p$ denotes the phantom image, $r$ denotes the reconstruction
+image, and $\bar{p}$ denotes the average pixel value for $p$. Each of the images have a
+size of $m \times n$. In equation \ref{eequation} $[n/2]$ and $[m/2]$ denote the largest
+integers less than $n/2$ and $m/2$, respectively.
+
+\latexignore{These formulas are shown in the print documentation of \ctsim.}
+%
+%Tex2RTF can not handle the any subscripts or superscripts for the inner summation unless
+% have a space character before the \sum
+\latexonly{\begin{equation}\label{dequation} d =\sqrt{\frac{\displaystyle \sum_{i=1}^{n}{ \sum_{j=1}^{m}{(p_{i,j} - r_{i,j})^2}}}{\displaystyle \sum_{i=1}^{n}{ \sum_{j=1}^{m}{(p_{i,j} - \bar{p})^2}}}}\end{equation}}
+\latexonly{\[\label{requation}r = \frac{ \displaystyle \sum_{i=1}^{n}{ \sum_{j=1}^{m}{|p_{i,j} - r_{i,j}|}}}{ \displaystyle \sum_{i=1}^{n}{ \sum_{j=1}^{m}{|p_{i,j}|}}}\]}
+\latexonly{\begin{equation}\label{eequation}e = \max_{1 \le k \le [n/2] \atop 1 \le l \le [m/2]}(|P_{k,l} - R_{k,l}|)\end{equation}}
+\latexonly{where}
+\latexonly{\[\label{bigpequation}P_{k,l} = \textstyle \frac{1}{4} (p_{2k,2l} + p_{2k+1,2l} + p_{2k,2l+l} + p_{2k+1,2l+1})\]}
+\latexonly{\begin{equation}\label{bigrequation}R_{k,l} = \textstyle \frac{1}{4} (r_{2k,2l} + r_{2k+1,2l} + r_{2k,2l+1} + r_{2k+1,2l+1})\end{equation}}
projects / ctsim.git / blobdiff