using System;
using System.Text.RegularExpressions;
public class Example
{
public static void Main()
{
string pattern = @"(?<=\W)\$[a-zA-Z_\\\{\}= +']+\$";
string input = @"We try to quantitatively capture these characteristics by defining a set of indexes, which can be computed using the mosaic image and the corresponding ground truth:
\begin{itemize}
\item $\mu_{A_T}$ and $\sigma_{A_T}$, the mean and standard deviation of the tiles area $A_T$, respectively;
\item $\rho_\text{filler}$, the ratio between the filler area and the overall mosaic are, computed as $\rho_\text{filler}=\frac{\sum_{T \in \mathcal{T} A_T}}{A}$, being $A$ the area of the mosaic;
\item \todo{does it worth?};
\item \todo{does it worth?};
\item $\mu_{C_T}$, the mean of the tiles \emph{color dispersion} $C_T$, being $C_T = \sigma_R+\sigma_G+\sigma_B$, where $\sigma_R$, $\sigma_G$ and $\sigma_B$ are the standard deviation of the red, green and blue channel values of the pixels within the tile $T$.
After applying a method to an image, we compare the segmented image (i.e., the result) against the ground truth and assess the performance according to the following three metrics:
\begin{itemize}
\item average tile precision $P$
\item average tile recall $R$
\item tile count error $C$
\end{itemize}
Let $T$ be a tile on the ground truth $\mathcal{T}$ with area $A_T$.
Let $T'$ be the tile in the segmented image which mostly overlaps $T$ and let $A_{T'}$ be the area of $T$; let $A_{T \cap T'}$ be the overlapping area between $T$ and $T'$.
Let $n$ and $n'$ the number of tiles respectively in the ground truth and in the segmented image.
Metrics are defined as:
\begin{align}
P &= \frac{1}{n} \sum_{T \in \mathcal{T}} \frac{A_{T \cap T'}}{A_{T'}} \\
R &= \frac{1}{n} \sum_{T \in \mathcal{T}} \frac{A_{T \cap T'}}{A_T} \\
C &= \frac{|n-n'|}{n}
\end{align}
We try to quantitatively capture these characteristics by defining a set of indexes, which can be computed using the mosaic image and the corresponding ground truth:
\begin{itemize}
\item $\mu_{A_T}$ and $\sigma_{A_T}$, the mean and standard deviation of the tiles area $A_T$, respectively;
\item $\rho_\text{filler}$, the ratio between the filler area and the overall mosaic are, computed as $\rho_\text{filler}=\frac{\sum_{T \in \mathcal{T} A_T}}{A}$, being $A$ the area of the mosaic;
\item \todo{does it worth?};
\item \todo{does it worth?};
\item $\mu_{C_T}$, the mean of the tiles \emph{color dispersion} $C_T$, being $C_T = \sigma_R+\sigma_G+\sigma_B$, where $\sigma_R$, $\sigma_G$ and $\sigma_B$ are the standard deviation of the red, green and blue channel values of the pixels within the tile $T$.
After applying a method to an image, we compare the segmented image (i.e., the result) against the ground truth and assess the performance according to the following three metrics:
\begin{itemize}
\item average tile precision $P$
\item average tile recall $R$
\item tile count error $C$
\end{itemize}
Let $T$ be a tile on the ground truth $\mathcal{T}$ with area $A_T$.
Let $T'$ be the tile in the segmented image which mostly overlaps $T$ and let $A_{T'}$ be the area of $T$; let $A_{T \cap T'}$ be the overlapping area between $T$ and $T'$.
Let $n$ and $n'$ the number of tiles respectively in the ground truth and in the segmented image.
Metrics are defined as:
\begin{align}
P &= \frac{1}{n} \sum_{T \in \mathcal{T}} \frac{A_{T \cap T'}}{A_{T'}} \\
R &= \frac{1}{n} \sum_{T \in \mathcal{T}} \frac{A_{T \cap T'}}{A_T} \\
C &= \frac{|n-n'|}{n}
\end{align}";
RegexOptions options = RegexOptions.Multiline;
foreach (Match m in Regex.Matches(input, pattern, options))
{
Console.WriteLine("'{0}' found at index {1}.", m.Value, m.Index);
}
}
}
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for C#, please visit: https://msdn.microsoft.com/en-us/library/system.text.regularexpressions.regex(v=vs.110).aspx