Table 1.

The Harlick’s texture feature from GLCM

Feature	Formula	Description
Energy (angular second moment)	$\sum _i^M\sum _j^N{P}^2\left[i,j\right]$	Measure the local homogeneity and, therefore, show the opposite of the entropy. The energy value is high with the larger homogeneity of the texture.
Entropy	$-\sum _i^M\sum _j^{N}P\left[i,j\right]logP\left[i,j\right]$	Measure the randomness of a grey-level distribution. The Entropy is expected to be high if the grey-levels are distributed randomly through the image.
Correlation	$\sum _i^M\sum _j^N\frac{\left(i-\mu \right)\left(j-\mu \right)P\left[i,j\right]}{{\sigma }^2}$	Measure the joint probability occurrence of the certain pixel pairs. The correlation is expected to be high if the grey levels of the pixel pairs are highly correlated.
Contrast	$\sum _i^M\sum _j^N{\left(i-j\right)}^{2}P\left[i,j\right]$	Measure the local variations in the grey level co-occurrence matrix. The contrast is expected to be low if the grey levels of each pixel pair are similar. High contrast values are expected for heavy textures and low for smooth, soft textures
Variance	$\frac{1}{2}\sum _i^M\sum _j^N\left({\left(i-\mu \right)}^{2}P\left[i,j\right]+{\left(j-\mu \right)}^{2}P\left[i,j\right]\right)$	Variance shows how is spread out the distribution of grey levels. The variance is expected to be large if grey levels of image are spread out greatly
Sum mean (Mean)	$\frac{1}{2}\sum _i^M\sum _j^N\left(iP\left[i,j\right]+jP\left[i,j\right]\right)$	Presents the mean of the grey levels in the image. The sum mean is expected to be large if the sum of the grey levels of the image is high.
Inertia (second difference moment)	$\sum _i^M\sum _j^N{\left(i-j\right)}^{2}P\left[i,j\right]$	Inertia is very sensitive to large variation in GLCM. It is expected to be high in highly contrast regions and low for homogeneous regions.
Cluster Shade	$\sum _i^M\sum _j^N{\left(i+j-{\mu }_x-{\mu }_y\right)}^{3}P\left[i,j\right]$	Measure the skewness of GLCM and represent the perceptual concepts of uniformity. It expected to be high in the asymmetric image.
Cluster Tendency	$\sum _i^M\sum _j^N{\left(i+j-2\mu \right)}^{k}P\left[i,j\right]$	Measure the grouping of pixels that have similar grey levels.
Homogeneity	$\sum _i^M\sum _j^N\frac{P\left[i,j\right]}{1+\left|i-j\right|}$	Measures the uniformity of non-zero entry and closeness of the distribution of elements in GLCM. The homogeneity is expected to be high if GLCM concentrates along the diagonal.
Max Probability (MP)	${\mathit{Max}}_{i,j}^{M,N}P\left[i,j\right]$	Results the pixel pair that is most predominant in the image. The MP is expected to be high if the occurrence of the most predominant pixel pair is high.
Inverse variance	$\sum _i^M\sum _j^N\frac{P\left[i,j\right]}{1+{\left(i-j\right)}^2},i\ne j$	Also called Inverse Difference Moment, similar to homogeneity. It is expected low for inhomogeneous and high for the homogeneous image.

From [26, 30–33]