Commit 42719d97 by Manuel Grizonnet

### DOC: after all copy also all haralick textures formulas in the software guide

parent 611eed98
 ... ... @@ -14,24 +14,168 @@ This example illustrates the use of the \doxygen{otb}{ScalarImageToTexturesFilte which computes the standard Haralick's textural features~\cite{Haralick1973}. The \doxygen{otb}{ScalarImageToTexturesFilter} class computes 8 local Haralick textures features. Their formulas are available in the \doxygen{otb}{ScalarImageToTexturesFilter} documentation (see section \textit{Detailed Description} in the doxygen). 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. \begin{table} \begin{center} \begin{tabular}{|c|c|} \hline & \\ Energy & $f_1 = \sum_{i,j}g(i, j)^2$ \\ & \\ \hline & \\ Entropy & $f_2 = -\sum_{i,j}g(i, j) \log_2 g(i, j)$, or 0 if $g(i, j) = 0$ \\ & \\ \hline & \\ Correlation & $f_3 = \sum_{i,j}\frac{(i - \mu)(j - \mu)g(i, j)}{\sigma^2}$ \\ & \\ \hline & \\ Difference Moment & $f_4 = \sum_{i,j}\frac{1}{1 + (i - j)^2}g(i, j)$ \\ & \\ \hline & \\ Inertia (a.k.a. Contrast) & $f_5 = \sum_{i,j}(i - j)^2g(i, j)$ \\ & \\ \hline & \\ Cluster Shade & $f_6 = \sum_{i,j}((i - \mu) + (j - \mu))^3 g(i, j)$ \\ & \\ \hline Cluster Prominence & $f_7 = \sum_{i,j}((i - \mu) + (j - \mu))^4 g(i, j)$ \\ & \\ \hline & \\ Haralick's Correlation & $f_8 = \frac{\sum_{i,j}(i, j) g(i, j) -\mu_t^2}{\sigma_t^2}$ \\ & \\ \hline \end{tabular} \itkcaption[Haralick features]{Haralick features~\cite{Haralick1973} available in \doxygen{otb}{ScalarImageToTexturesFilter}} \end{center} \label{tab:haralickStandardFeatures} \end{table} Note that more features are available in \doxygen{otb}{ScalarImageToAdvancedTexturesFilter} and in \doxygen{otb}{ScalarImageToHigherOrderTexturesFilter}. \doxygen{otb}{ScalarImageToHigherOrderTexturesFilter} computes 10 advanced texture features. Their formulas are available in the \doxygen{otb}{ScalarImageToAdvancedTexturesFilter} documentation (see section \textit{Detailed Description} in the doxygen). \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), and $\g_{x+y}(k) = \sum_{i}\sum_{j}g(i)$ 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{table} \begin{center} \begin{tabular}{|c|c|} \hline & \\ Mean & $f_{mean} = \sum_{i, j}i g(i, j)$ \\ & \\ \hline & \\ Sum of squares: Variance & $f_4 = \sum_{i, j}(i - \mu)^2 g(i, j)$ \\ & \\ \hline & \\ Dissimilarity & $f_5 = \sum_{i, j}(i - j) g(i, j)^2$ \\ & \\ \hline & \\ Sum average & $f_6 = -\sum_{i}i g_{x+y}(i)$ \\ & \\ \hline & \\ Sum Variance & $f_7 = \sum_{i}(i - f_8)^2 g_{x+y}(i)$ \\ & \\ \hline & \\ Sum Entropy & $f_8 = -\sum_{i}g_{x+y}(i) log (g_{x+y}(i))$ \\ & \\ \hline Difference variance & $f_{10} = variance of g_{x-y}(i)$ \\ & \\ \hline & \\ Difference entropy & $f_{11} = -\sum_{i}g_{x-y}(i) log (g_{x-y}(i))$ \\ & \\ \hline & \\ Information Measures of Correlation IC1 & $f_{12} = \frac{f_9 - HXY1}{H}$ \\ & \\ \hline & \\ Information Measures of Correlation IC2 & $f_{13} = \sqrt{1 - \exp{-2}|HXY2 - f_9|}$ \\ & \\ \hline \end{tabular} \itkcaption[Haralick features]{Haralick features~\cite{Haralick1973} available in \doxygen{otb}{ScalarImageToAdvancedTexturesFilter}} \end{center} \label{tab:haralickAdvancedFeatures} \end{table}. \doxygen{otb}{ScalarImageToHigherOrderTexturesFilter} computes 11 other local higher order statistics textures coefficients also based on the grey level run-length matrix. Formulas for these coefficients are also available in the doxygen documentation of the filter (see section \textit{Detailed Description} in the doxygen). 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. \begin{table} \begin{center} \begin{tabular}{|c|c|} \hline & \\ Short Run Emphasis & $SRE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j)}{j^2}$ \\ & \\ \hline & \\ Long Run Emphasis & $LRE = \frac{1}{n_r} \sum_{i, j}p(i, j) * j^2$ \\ & \\ \hline & \\ Grey-Level Nonuniformity & $GLN = \frac{1}{n_r} \sum_{i} \left( \sum_{j}{p(i, j)} \right)^2$ \\ & \\ \hline & \\ Run Length Nonuniformity & $RLN = \frac{1}{n_r} \sum_{j} \left( \sum_{i}{p(i, j)} \right)^2$ \\ & \\ \hline & \\ Low Grey-Level Run Emphasis & $LGRE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j)}{i^2}$ \\ & \\ \hline & \\ High Grey-Level Run Emphasis & $HGRE = \frac{1}{n_r} \sum_{i, j}p(i, j) * i^2$ \\ & \\ \hline Short Run Low Grey-Level Emphasis & $SRLGE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j)}{i^2 j^2}$ \\ & \\ \hline & \\ Short Run High Grey-Level Emphasis & $SRHGE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j) * i^2}{j^2}$ \\ & \\ \hline & \\ Long Run Low Grey-Level Emphasis & $LRLGE = \frac{1}{n_r} \sum_{i, j}\frac{p(i, j) * j^2}{i^2}$ \\ & \\ \hline & \\ Long Run High Grey-Level Emphasis & $LRHGE = \frac{1}{n_r} \sum_{i, j} p(i, j) i^2 j^2$ \\ & \\ \hline \end{tabular} \itkcaption[Haralick higher order features]{Haralick features~\cite{Haralick1973} available in \doxygen{otb}{ScalarImageToHigherOrderTexturesFilter}} \end{center} \label{tab:haralickHigherOrderFeatures} \end{table} \relatedClasses \begin{itemize} ... ...
 ... ... @@ -91,7 +91,7 @@ SetDocLongDescription( "sharpness homogeneity), Low Grey-Level Run Emphasis, High Grey-Level Run Emphasis, " "Short Run Low Grey-Level Emphasis, Short Run High Grey-Level Emphasis, Long Run Low " "Grey-Level Emphasis and Long Run High Grey-Level Emphasis.\n\n" "The documentation of textures (description are formulas) are available in corresponding doxygen documentation of filters (see section *Detailed Description* in doxygen):\n" "The documentation of textures (description are formulas) are available in the OTB Software Guide (section Textures) and also in corresponding doxygen documentation of filters (see section *Detailed Description* in doxygen):\n" "* **simple**: otbScalarImageToTexturesFilter\n" "* **advanced**: otbScalarImageToAdvancedTexturesFilter\n" "* **higher**: otbScalarImageToHigherOrderTexturesFilter"); ... ...
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