Commit c9d5f956 authored by Manuel Grizonnet's avatar Manuel Grizonnet

DOC: reformat table with haralick formulas

parent 33ee340e
......@@ -15,15 +15,21 @@ which computes the standard Haralick's textural features~\cite{Haralick1973}.
The \doxygen{otb}{ScalarImageToTexturesFilter} class computes 8 local Haralick
textures features presented in table~\ref{tab:haralickStandardFeatures},
where $\mu_t$ and $\sigma_t$ are the mean and standard deviation of the row
(or column, due to symmetry) sums, $ \mu = $ (weighted pixel average)
$ = \sum_{i,j}i \cdot g(i, j) =\sum_{i,j}j \cdot g(i, j) $ due to matrix summetry, and
$ \sigma = $ (weighted pixel variance) $ = \sum_{i,j}(i - \mu)^2 \cdot g(i, j) =\sum_{i,j}(j - \mu)^2 \cdot g(i, j) $
due to matrix symmetry.
where :
\begin{itemize}
\item $\mu_t$ and $\sigma_t$ are the mean and standard deviation of the row
(or column, due to symmetry) sums
\item $ \mu = $ (weighted pixel average)
$ = \sum_{i,j}i \cdot g(i, j) =\sum_{i,j}j \cdot g(i, j) $ due to matrix
symmetry
\item $ \sigma = $ (weighted pixel variance) $ = \sum_{i,j}(i - \mu)^2 \cdot g(i, j) =\sum_{i,j}(j - \mu)^2 \cdot g(i, j) $
due to matrix symmetry
\end{itemize}
\begin{table}
\begin{center}
\begin{tabular}{|c|c|}
\begin{tabular}[h!]{|c|c|}
\hline
& \\
Energy & $ f_1 = \sum_{i,j}g(i, j)^2 $ \\
......@@ -68,15 +74,20 @@ Note that more features are available in
\doxygen{otb}{ScalarImageToAdvancedTexturesFilter} computes 10 advanced
texture features presented presented in table~\ref{tab:haralickAdvancedFeatures},
where $ \mu = $ (weighted pixel average) = $ \sum_{i, j}i \cdot g(i, j) =
\sum_{i,j}j \cdot g(i, j) $ (due to matrix symmetry).
$N_{g}$ : Number of distinct gray levels in the quantized image.
where:
$ g_{x+y}(k) = \sum_{i}\sum_{j}g(i) $ where $ i+j=k $ and $ k = 2, 3, .., 2N_{g} $ and $ g_{x-y}(k) = \sum_{i}\sum_{j}g(i) $ where $ i-j=k $ and $ k = 0, 1, ..,N_{g}-1 $
\begin{itemize}
\item $ \mu = $ (weighted pixel average) = $ \sum_{i, j}i \cdot g(i, j) =
\sum_{i,j}j \cdot g(i, j) $ (due to matrix symmetry)
\item $N_{g}$ : Number of distinct gray levels in the quantized image
\item $ g_{x+y}(k) = \sum_{i}\sum_{j}g(i) $ where $ i+j=k $ and $ k = 2, 3, .., 2N_{g} $ and $ g_{x-y}(k) = \sum_{i}\sum_{j}g(i) $ where $ i-j=k $ and $ k = 0, 1, ..,N_{g}-1 $
\end{itemize}
\begin{table}
\begin{center}
\begin{tabular}{|c|c|}
\begin{tabular}[h!]{|c|c|}
\hline
& \\
Mean & $ f_{mean} = \sum_{i, j}i g(i, j) $ \\
......@@ -121,18 +132,23 @@ Information Measures of Correlation IC2 & $ f_{13} = \sqrt{1 - \exp{-2}|HXY2 - f
\itkcaption[Haralick features]{Haralick features~\cite{Haralick1973} available in \doxygen{otb}{ScalarImageToAdvancedTexturesFilter}}
\end{center}
\label{tab:haralickAdvancedFeatures}
\end{table}.
\end{table}
\doxygen{otb}{ScalarImageToHigherOrderTexturesFilter} computes 11
\doxygen{otb}{ScalarImageToHigherOrderTexturesFilter} computes 10
other local higher order statistics textures coefficients also based on the grey
level run-length matrix. Formulas for these coefficients are presented in
table~\ref{tab:haralickHigherOrderFeatures},where $p(i, j)$ is the element in
cell i, j of a normalized Run Length Matrix, $n_r$ is the total number of runs
and $n_p$ is the total number of pixels.
table~\ref{tab:haralickHigherOrderFeatures},where:
\begin{itemize}
\item $p(i, j)$ is the element in cell i
\item j of a normalized Run Length Matrix
\item $n_r$ is the total number of runs
\item $n_p$ is the total number of pixels
\end{itemize}
\begin{table}
\begin{center}
\begin{tabular}{|c|c|}
\begin{tabular}[h!]{|c|c|}
\hline
& \\
Short Run Emphasis & $ SRE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j)}{j^2} $ \\
......
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