re = /(?<=\W)\$[a-zA-Z_\\\{\}= +']+\$/m
str = '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}'
# Print the match result
str.scan(re) do |match|
puts match.to_s
end
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 Ruby, please visit: http://ruby-doc.org/core-2.2.0/Regexp.html