User:Mcstrother/Texture

In image analysis and processing, texture statistics are quantitative measures of local variation of pixel intensity around a given pixel in the image.

Examples of Texture Statistics
http://www.itk.org/Doxygen38/html/classitk_1_1Statistics_1_1GreyLevelCooccurrenceMatrixTextureCoefficientsCalculator.html

"Energy" $$ \sum_{i,j}g(i, j)^2$$

"Entropy" $$ -\sum_{i,j}g(i, j) \log_2 g(i, j)$$, or 0 if $$g(i, j) = 0$$

"Correlation"$$ \sum_{i,j}\frac{(i - \mu)(j - \mu)g(i, j)}{\sigma^2} $$

"Difference Moment" $$ \sum_{i,j}\frac{1}{1 + (i - j)^2}g(i, j) $$

"Inertia"(sometimes called "contrast.") $$ \sum_{i,j}(i - j)^2g(i, j) $$

"Cluster Shade" $$ \sum_{i,j}((i - \mu) + (j - \mu))^3 g(i, j) $$

"Cluster Prominence" $$ \sum_{i,j}((i - \mu) + (j - \mu))^4 g(i, j) $$

Above, $$ \mu = $$ (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 summetry) $$ g(i, j) $$ is the element in cell i, j of a a normalized grey level cooccurrence matrix.

=References=

http://www.mathworks.com/access/helpdesk/help/toolbox/images/index.html?/access/helpdesk/help/toolbox/images/f11-27972.html