### 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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