@@ -52,8 +52,8 @@ <h2>NOTES</h2>
5252or for the identification of objects in < a href ="i.segment.html "> i.segment</ a > ,
5353and/or for the characterization of these objects and thus, for example, as one
5454of the raster inputs of the
55- < a href ="https://grass.osgeo.org/grass8 /manuals/addons/i.segment.stats.html ">
56- i.segment.stats </ a > addon.
55+ < a href ="https://grass.osgeo.org/grass-stable /manuals/addons/i.segment.stats.html "> i.segment.stats </ a >
56+ addon.
5757
5858< p >
5959In general, several variables constitute texture: differences in grey level values,
@@ -68,32 +68,61 @@ <h2>NOTES</h2>
6868is a two-dimensional histogram of grey levels for a pair of pixels which are
6969separated by a fixed spatial relationship. The matrix approximates the joint
7070probability distribution of a pair of pixels. Several texture measures are
71- directly computed from the grey level co-occurrence matrix.
71+ directly computed from the Grey Level Co-occurrence Matrix (GLCM).
72+
73+ The provided measures can be categorized under first-order and
74+ second-order statistics, with each playing a unique role in texture
75+ analysis. First-order statistics consider the distribution of
76+ individual pixel values without regard to spatial relationships, while
77+ second-order statistics, particularly those derived from the Grey Level
78+ Co-occurrence Matrix (GLCM), consider the spatial relationship of
79+ pixels.
7280
7381< p >
7482The following part offers brief explanations of the Haralick et al texture
7583measures (after Jensen 1996).
7684
7785< h3 > First-order statistics in the spatial domain</ h3 >
7886< ul >
79- < li > Sum Average (SA)</ li >
87+ < li > Sum Average (SA):
88+ Sum Average measures the average gray level intensity of the sum of
89+ pixel pairs within the moving window. It reflects the average intensity
90+ of pixel pairs at specific distances and orientations, highlighting the
91+ overall brightness level within the area.</ li >
8092
8193< li > Entropy (ENT):
8294 This measure analyses the randomness. It is high when the values of the
8395 moving window have similar values. It is low when the values are close
84- to either 0 or 1 (i.e. when the pixels in the local window are uniform).</ li >
96+ to either 0 or 1 (i.e. when the pixels in the local window are
97+ uniform).</ li >
8598
86- < li > Difference Entropy (DE)</ li >
99+ < li > Difference Entropy (DE):
100+ This metric quantifies the randomness or unpredictability in the
101+ distribution of differences between the grey levels of pixel pairs. It
102+ is a measure of the entropy of the pixel-pair difference histogram,
103+ capturing texture granularity.</ li >
87104
88- < li > Sum Entropy (SE)</ li >
105+ < li > Sum Entropy (SE): Similar to Difference Entropy, Sum Entropy measures
106+ the randomness or unpredictability, but in the context of the sum of the
107+ grey levels of pixel pairs. It evaluates the entropy of the pixel-pair
108+ sum distribution, providing insight into the complexity of texture in
109+ terms of intensity variation.</ li >
89110
90111< li > Variance (VAR):
91- A measure of gray tone variance within the moving window (second-order
92- moment about the mean)</ li >
93-
94- < li > Difference Variance (DV)</ li >
95-
96- < li > Sum Variance (SV)</ li >
112+ A measure of gray tone variance within the moving window (second-order
113+ moment about the mean)</ li >
114+
115+ < li > Difference Variance (DV):
116+ This is a measure of the variance or spread of the differences in grey
117+ levels between pairs of pixels within the moving window. It quantifies
118+ the contrast variability between pixels, indicating texture smoothness
119+ or roughness.</ li >
120+
121+ < li > Sum Variance (SV):
122+ In contrast to Difference Variance, Sum Variance measures the variance
123+ of the sum of grey levels of pixel pairs. It assesses the variability
124+ in the intensity levels of pairs of pixels, contributing to an
125+ understanding of texture brightness or intensity variation.</ li >
97126</ ul >
98127
99128Note that measures "mean", "kurtosis", "range", "skewness", and "standard
@@ -128,9 +157,19 @@ <h3>Second-order statistics in the spatial domain</h3>
128157 pixels. Typically high, when the scale of local texture is larger than the
129158 < em > distance</ em > .</ li >
130159
131- < li > Information Measures of Correlation (MOC)</ li >
132-
133- < li > Maximal Correlation Coefficient (MCC)</ li >
160+ < li > Information Measures of Correlation (MOC):
161+ These measures evaluate the complexity of the texture in terms of the
162+ mutual dependence between the grey levels of pixel pairs. They
163+ quantify how one pixel value informs or correlates with another,
164+ offering insight into pattern predictability and structure regularity.</ li >
165+
166+ < li > Maximal Correlation Coefficient (MCC):
167+ This statistic measures the highest correlation between any two
168+ features of the texture, providing a single value that summarizes the
169+ degree of linear dependency between grey levels in the texture. It's
170+ often used to assess the overall correlation in the image, indicating
171+ how predictable the texture patterns are from one pixel to the
172+ next.</ li >
134173</ ul >
135174
136175< p >
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