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docs: r.texture manual texture measure explanations (#3458)
This PR attempts to complete missing texture measure explanations.
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raster/r.texture/r.texture.html

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@@ -52,8 +52,8 @@ <h2>NOTES</h2>
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or for the identification of objects in <a href="i.segment.html">i.segment</a>,
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and/or for the characterization of these objects and thus, for example, as one
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of the raster inputs of the
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<a href="https://grass.osgeo.org/grass8/manuals/addons/i.segment.stats.html">
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i.segment.stats</a> addon.
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<a href="https://grass.osgeo.org/grass-stable/manuals/addons/i.segment.stats.html">i.segment.stats</a>
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addon.
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<p>
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In general, several variables constitute texture: differences in grey level values,
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is a two-dimensional histogram of grey levels for a pair of pixels which are
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separated by a fixed spatial relationship. The matrix approximates the joint
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probability distribution of a pair of pixels. Several texture measures are
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directly computed from the grey level co-occurrence matrix.
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directly computed from the Grey Level Co-occurrence Matrix (GLCM).
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The provided measures can be categorized under first-order and
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second-order statistics, with each playing a unique role in texture
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analysis. First-order statistics consider the distribution of
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individual pixel values without regard to spatial relationships, while
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second-order statistics, particularly those derived from the Grey Level
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Co-occurrence Matrix (GLCM), consider the spatial relationship of
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pixels.
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<p>
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The following part offers brief explanations of the Haralick et al texture
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measures (after Jensen 1996).
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<h3>First-order statistics in the spatial domain</h3>
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<ul>
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<li> Sum Average (SA)</li>
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<li> Sum Average (SA):
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Sum Average measures the average gray level intensity of the sum of
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pixel pairs within the moving window. It reflects the average intensity
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of pixel pairs at specific distances and orientations, highlighting the
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overall brightness level within the area.</li>
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<li> Entropy (ENT):
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This measure analyses the randomness. It is high when the values of the
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moving window have similar values. It is low when the values are close
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to either 0 or 1 (i.e. when the pixels in the local window are uniform).</li>
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to either 0 or 1 (i.e. when the pixels in the local window are
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uniform).</li>
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<li> Difference Entropy (DE)</li>
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<li> Difference Entropy (DE):
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This metric quantifies the randomness or unpredictability in the
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distribution of differences between the grey levels of pixel pairs. It
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is a measure of the entropy of the pixel-pair difference histogram,
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capturing texture granularity.</li>
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<li> Sum Entropy (SE)</li>
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<li> Sum Entropy (SE): Similar to Difference Entropy, Sum Entropy measures
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the randomness or unpredictability, but in the context of the sum of the
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grey levels of pixel pairs. It evaluates the entropy of the pixel-pair
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sum distribution, providing insight into the complexity of texture in
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terms of intensity variation.</li>
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<li> Variance (VAR):
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A measure of gray tone variance within the moving window (second-order
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moment about the mean)</li>
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<li> Difference Variance (DV)</li>
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<li> Sum Variance (SV)</li>
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A measure of gray tone variance within the moving window (second-order
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moment about the mean)</li>
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<li> Difference Variance (DV):
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This is a measure of the variance or spread of the differences in grey
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levels between pairs of pixels within the moving window. It quantifies
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the contrast variability between pixels, indicating texture smoothness
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or roughness.</li>
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<li> Sum Variance (SV):
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In contrast to Difference Variance, Sum Variance measures the variance
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of the sum of grey levels of pixel pairs. It assesses the variability
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in the intensity levels of pairs of pixels, contributing to an
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understanding of texture brightness or intensity variation.</li>
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</ul>
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Note that measures "mean", "kurtosis", "range", "skewness", and "standard
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pixels. Typically high, when the scale of local texture is larger than the
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<em>distance</em>.</li>
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<li> Information Measures of Correlation (MOC)</li>
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<li> Maximal Correlation Coefficient (MCC)</li>
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<li> Information Measures of Correlation (MOC):
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These measures evaluate the complexity of the texture in terms of the
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mutual dependence between the grey levels of pixel pairs. They
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quantify how one pixel value informs or correlates with another,
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offering insight into pattern predictability and structure regularity.</li>
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<li> Maximal Correlation Coefficient (MCC):
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This statistic measures the highest correlation between any two
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features of the texture, providing a single value that summarizes the
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degree of linear dependency between grey levels in the texture. It's
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often used to assess the overall correlation in the image, indicating
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how predictable the texture patterns are from one pixel to the
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next.</li>
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</ul>
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<p>

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