Table 4. Texture feature definitions.

Feature name	Equation
Contrast	$f={\displaystyle \sum _{n=0}^{N_{g-1}}{n}^2}\left\{\underset{\left|i-j\right|=n}{{\displaystyle \sum _{i=1}^{N_g}{\displaystyle \sum _{j=1}^{N_g}p\left(i,j\right)}}}\right\}$
Correlation	$f=\frac{{\displaystyle \sum {}_i}{\displaystyle \sum {}_j\left(ij\right)p\left(i,j\right)}-{\mu }_x{\mu }_y}{{\sigma }_x{\sigma }_y}$
Difference entropy	$f=-{\displaystyle \sum _{i=0}^{N_{g-1}}{p}_{x-y}\left(i\right)}\log \left[p_{x-y}\left(i\right)\right]$
Difference variance	$f=varianceof{p}_{x-y}$
Energy	$f=-{{\displaystyle \sum _i{\displaystyle \sum _j\left[p\left(i,j\right)\right]}}}^2$
Entropy	$f=-{\displaystyle \sum _i{\displaystyle \sum _{j}p\left(i,j\right)\log \left[p\left(i,j\right)\right]}}$
Homogeneity	$f={\displaystyle \sum _i{\displaystyle \sum _j\frac{p\left(i,j\right)}{1+{\left(i-j\right)}^2}}}$
IMC1	$f=\frac{HXY-HXY1}{\max \left(HX,HY\right)}$
IMC2	$f={\left\{1-\exp \left[-2\left(HXY2-HXY\right)\right]\right\}}^{1/2}$
	$HXY=-{\displaystyle \sum _i{\displaystyle \sum _{j}p\left(i,j\right)\log \left[p\left(i,j\right)\right]}}$
	$HXY1=-{\displaystyle \sum _i{\displaystyle \sum _{j}p\left(i,j\right)\log \left[p_x\left(i\right)p_y\left(j\right)\right]}}$
	$HXY2=-{\displaystyle \sum _i{\displaystyle \sum _j{p}_x\left(i\right)p_y\left(j\right)\log \left[p_x\left(i\right)p_y\left(j\right)\right]}}$
Maximum correlation coefficient	$f={\left(SecondlargesteigenvalueofQ\right)}^{1/2}$
	$Q\left(i,j\right)={\displaystyle \sum _k\frac{p\left(i,k\right)p\left(j,k\right)}{p_x\left(i\right)p_y\left(k\right)}}$
Sum average	$f={\displaystyle \sum _{i=2}^{2Ng}i{p}_{x+y}\left(i\right)}$
Sum entropy	$f=-{\displaystyle \sum _{i=2}^{2Ng}{\displaystyle \sum _{i=2}^{2Ng}{p}_{x+y}\left(i\right)}}\log \left[p_{x+y}\left(i\right)\right]$
Sum variance	$f=varianceof{p}_{x-y}$
Skewness	$f=\frac{\frac{1}{n}{\displaystyle \sum \begin{array}{l}n\\ i=i\end{array}}{\left(x_i-\overline{x}\right)}^3}{\sqrt{\frac{1}{n-1}{\displaystyle \sum \begin{array}{l}n\\ i=i\end{array}}{\left(x_i-\overline{x}\right)}^2}}$

Notation: p(i,j): (i,j)th entry in a normalized gray-tone spatial-dependence matrix; px(i): ith entry in the marginal-probability matrix obtained by summing the rows of p(i,j); Ng: Number of distinct gray levels in the quantized image; py(j): ${\displaystyle \sum \begin{array}{l}Ng\\ i-1\end{array}}p\left(i,j\right)$ ; px+y(k): ${\displaystyle \sum \begin{array}{l}Ng\\ \underset{i+j=k}{i=1}\end{array}}{\displaystyle \sum \begin{array}{l}Ng\\ j=1\end{array}}p\left(i,j\right)$; px-y(k): ${\displaystyle \sum \begin{array}{l}Ng\\ \underset{\left|i-j=k\right|}{i=1}\end{array}}{\displaystyle \sum \begin{array}{l}Ng\\ j=1\end{array}}p\left(i,j\right)$.