*r.texture* assumes grey levels ranging from 0 to 255 as input.
The input has to be rescaled to 0 to 255 beforehand if the input map range
is outside of this range by using *r.rescale*.

In general, several variables constitute texture: differences in grey level values, coarseness as scale of grey level differences, presence or lack of directionality and regular patterns. A texture can be characterized by tone (grey level intensity properties) and structure (spatial relationships). Since textures are highly scale dependent, hierarchical textures may occur.

*r.texture* reads a GRASS raster map as input and calculates textural
features based on spatial dependence matrices for north-south, east-west,
northwest, and southwest directions using a side by side neighborhood (i.e.,
a distance of 1). The user should be sure to carefully set the resolution
(using *g.region*) before running this program, or the computer may
run out of memory. The output consists into four images for each textural
feature, one for every direction.

A commonly used texture model is based on the so-called grey level co-occurrence matrix. This matrix 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.

The following part offers brief explanations of texture measures (after Jensen 1996).

- Sum Average (SA)
- 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).
- Difference Entropy (DE)
- Sum Entropy (SE)
- Variance (VAR): A measure of gray tone variance within the moving window (second-order moment about the mean)
- Difference Variance (DV)
- Sum Variance (SV)

- Angular Second Moment (ASM, also called Uniformity):
This is a measure of local homogeneity and the opposite of Entropy.
High values of ASM occur when the pixels in the moving window are
very similar.

Note: The square root of the ASM is sometimes used as a texture measure, and is called Energy. - Inverse Difference Moment (IDM, also called Homogeneity): This measure relates inversely to the contrast measure. It is a direct measure of the local homogeneity of a digital image. Low values are associated with low homogeneity and vice versa.
- Contrast (CON):
This measure analyses the image contrast (locally gray-level variations) as
the linear dependency of grey levels of neighboring pixels (similarity). Typically high,
when the scale of local texture is larger than the
*distance*. - Correlation (COR):
This measure analyses the linear dependency of grey levels of neighboring
pixels. Typically high, when the scale of local texture is larger than the
*distance*. - Information Measures of Correlation (MOC)
- Maximal Correlation Coefficient (MCC)

g.region rast=ortho_2001_t792_1m -p r.texture -a ortho_2001_t792_1m prefix=ortho_texture # display g.region n=221461 s=221094 w=638279 e=638694 d.shadedmap drape=ortho_texture_ASM_0 rel=ortho_2001_t792_1m

- The method for finding the maximal correlation coefficient, which requires finding the second largest eigenvalue of a matrix Q, does not always converge. This is a known issue with this measure in general.

The code was taken by permission from *pgmtexture*, part of
PBMPLUS (Copyright 1991, Jef Poskanser and Texas Agricultural Experiment
Station, employer for hire of James Darrell McCauley). Manual page
of pgmtexture.

- Haralick, R.M., K. Shanmugam, and I. Dinstein (1973). Textural features for
image classification.
*IEEE Transactions on Systems, Man, and Cybernetics*, SMC-3(6):610-621. - Bouman, C. A., Shapiro, M. (1994). A Multiscale Random Field Model for Bayesian Image Segmentation, IEEE Trans. on Image Processing, vol. 3, no. 2.
- Jensen, J.R. (1996). Introductory digital image processing. Prentice Hall. ISBN 0-13-205840-5
- Haralick, R. (May 1979).
*Statistical and structural approaches to texture*, Proceedings of the IEEE, vol. 67, No.5, pp. 786-804 - Hall-Beyer, M. (2007). The GLCM Tutorial Home Page (Grey-Level Co-occurrence Matrix texture measurements). University of Calgary, Canada

C. Basco - RCOST (Research Centre on Software Technology - Viale Traiano - 82100 Benevento)

M. Ceccarelli - Facolta di Scienze, Universita del Sannio, Benevento

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