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docs: r.texture manual texture measure explanations (#3458)
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This PR attempts to complete missing texture measure explanations.
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neteler committed Feb 28, 2024
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or for the identification of objects in <a href="i.segment.html">i.segment</a>,
and/or for the characterization of these objects and thus, for example, as one
of the raster inputs of the
<a href="https://grass.osgeo.org/grass8/manuals/addons/i.segment.stats.html">
i.segment.stats</a> addon.
<a href="https://grass.osgeo.org/grass-stable/manuals/addons/i.segment.stats.html">i.segment.stats</a>
addon.

<p>
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
separated by a fixed spatial relationship. The matrix approximates the joint
probability distribution of a pair of pixels. Several texture measures are
directly computed from the grey level co-occurrence matrix.
directly computed from the Grey Level Co-occurrence Matrix (GLCM).

The provided measures can be categorized under first-order and
second-order statistics, with each playing a unique role in texture
analysis. First-order statistics consider the distribution of
individual pixel values without regard to spatial relationships, while
second-order statistics, particularly those derived from the Grey Level
Co-occurrence Matrix (GLCM), consider the spatial relationship of
pixels.

<p>
The following part offers brief explanations of the Haralick et al texture
measures (after Jensen 1996).

<h3>First-order statistics in the spatial domain</h3>
<ul>
<li> Sum Average (SA)</li>
<li> Sum Average (SA):
Sum Average measures the average gray level intensity of the sum of
pixel pairs within the moving window. It reflects the average intensity
of pixel pairs at specific distances and orientations, highlighting the
overall brightness level within the area.</li>

<li> Entropy (ENT):
This measure analyses the randomness. It is high when the values of the
moving window have similar values. It is low when the values are close
to either 0 or 1 (i.e. when the pixels in the local window are uniform).</li>
to either 0 or 1 (i.e. when the pixels in the local window are
uniform).</li>

<li> Difference Entropy (DE)</li>
<li> Difference Entropy (DE):
This metric quantifies the randomness or unpredictability in the
distribution of differences between the grey levels of pixel pairs. It
is a measure of the entropy of the pixel-pair difference histogram,
capturing texture granularity.</li>

<li> Sum Entropy (SE)</li>
<li> Sum Entropy (SE): Similar to Difference Entropy, Sum Entropy measures
the randomness or unpredictability, but in the context of the sum of the
grey levels of pixel pairs. It evaluates the entropy of the pixel-pair
sum distribution, providing insight into the complexity of texture in
terms of intensity variation.</li>

<li> Variance (VAR):
A measure of gray tone variance within the moving window (second-order
moment about the mean)</li>

<li> Difference Variance (DV)</li>

<li> Sum Variance (SV)</li>
A measure of gray tone variance within the moving window (second-order
moment about the mean)</li>

<li> Difference Variance (DV):
This is a measure of the variance or spread of the differences in grey
levels between pairs of pixels within the moving window. It quantifies
the contrast variability between pixels, indicating texture smoothness
or roughness.</li>

<li> Sum Variance (SV):
In contrast to Difference Variance, Sum Variance measures the variance
of the sum of grey levels of pixel pairs. It assesses the variability
in the intensity levels of pairs of pixels, contributing to an
understanding of texture brightness or intensity variation.</li>
</ul>

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
<em>distance</em>.</li>

<li> Information Measures of Correlation (MOC)</li>

<li> Maximal Correlation Coefficient (MCC)</li>
<li> Information Measures of Correlation (MOC):
These measures evaluate the complexity of the texture in terms of the
mutual dependence between the grey levels of pixel pairs. They
quantify how one pixel value informs or correlates with another,
offering insight into pattern predictability and structure regularity.</li>

<li> Maximal Correlation Coefficient (MCC):
This statistic measures the highest correlation between any two
features of the texture, providing a single value that summarizes the
degree of linear dependency between grey levels in the texture. It's
often used to assess the overall correlation in the image, indicating
how predictable the texture patterns are from one pixel to the
next.</li>
</ul>

<p>
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