Table 2.

Selected Second-Order Features

Name	Description	Mathematical Description
Energy⁎	Also defined as Angular Second Moment. This feature describes the homogeneity of an image. 0 represents complete heterogeneity. 1 represents complete homogeneity [42].	${\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{P}_{ij}^2}}$
Local homogeneity⁎	Measures the relation of GLCM intensities to the diagonal GLCM matrix. A value of 1 represents total homogeneity. A value of 0 represents nonhomogeneity [42].	${\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N\frac{P_{ij}}{1+{\left(i-j\right)}^2}}}$
Entropy⁎	Measures the pair contributions and information content.	${\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{P}_{ij}log{P}_{ij}}}$
Correlation⁎	Measures correlation between co-occurrence matrix values.	$\frac{{\sum }_i{\sum }_j\left(ij\right)P\left(i,j\right)-{\mu }_x{\mu }_y}{{\sigma }_x{\sigma }_y}$
SRE†	Measures short run distribution (short run emphasis).	$\frac{1}{n}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j-1}^N\frac{R\left(i,j\right)}{j^2}}}$
LRE†	Measures long run distribution (long run emphasis).	$\frac{1}{n}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^{N}R\left(i,j\right)j^2}}$
RPC†	Ratio of total number of runs to total number of pixels in the image. Measures homogeneity and run distribution (run percentage).	$\frac{n}{n_p}$
LGRE†	Measures low gray-level distribution (low gray-level run emphasis).	$\frac{1}{n}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N\frac{R\left(i,j\right)}{i^2}}}$
SRLGE†	Measures short runs and low gray-level distribution (short run low gray-level emphasis).	$\frac{1}{n}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N\frac{R\left(i,j\right)}{i^2{j}^2}}}$
LRLGE†	Measures long runs and low gray-level distribution (long run low gray-level emphasis).	$\frac{1}{n}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^{N}R\left(i,j\right)i^2{j}^2}}$
RLNU†	Measures the nonuniformity of the run lengths (run length nonuniformity).	$\frac{1}{n}{{\displaystyle \sum _{{}^{i=1}}^N\left({\displaystyle \sum _{j=1}^{M}R\left(i,j\right)}\right)}}^2$
GLNU†	Measures the nonuniformity of the gray levels (gray-level nonuniformity).	$\frac{1}{n}{\displaystyle \sum _{j=1}^M{\left({\displaystyle \sum _{i=1}^{N}R\left(i,j\right)}\right)}^2}$

^⁎Where P(i,j) is an element of the gray-level co-occurrence matrix. GLCM features were originally developed by Haralick et al. [14], [41].

^†Where R(I,j) is an element of the RLM, n is the total number of runs, n_p is the number of pixels in the image, N is the longest run, and M is the number of gray levels. RLM features were originally developed by Galloway et al. [44], Chu et al. [45], and Dasarathy and Holder [46].