TABLE 1B.

The Textural Features Used in This Study (Version With Definitions)

Category	Features	Computation Formula	Notes
Distribution of image gray level (9,10)	Mean	$m=\frac{1}{n}{\displaystyle \sum _{(x,y)\in R}}[f(x,y)]$	f(x,y) represents the intensity value of a pixel located at (x,y). n means the total number of pixels within the ROI, k means the number of gray level value within the ROI, and p(li) means the probability of value li occurring in the ROI.
	Entropy	$e=-{\sum }_{i=1}^k[p(I_i)]{log}_2[p(I_i)]$
	Uniformity	$u={\sum }_{i=1}^k{[p(I_i)]}^2$
	Standard deviation	$s=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n}{[f_i(x,y)-m]}^2}$
	Smoothness	$R=1-\frac{1}{1+s^2}$
	Skewness	$S=\frac{n}{(n-1)(n-2)s^3}{\displaystyle \sum _{i=1}^n}{(I_i-m)}^3$
	Third moment (Tm)	${\mu }_3={\sum }_{i=1}^k{(I_i-m)}^{3}p(I_i)$
	Kurtosis	$K=\frac{n(n+1)}{(n-1)(n-2)(n-3)s^4}{\displaystyle \sum _{i=1}^n}{(I_i-m)}^4-3\frac{{(n-1)}^2}{(n-2)(n-3)}$
Auto-covariance coefficient (12)	Norm of vector (NOV)	$\text{Nov}=\sqrt{{\sum }_{\mathrm{\Delta }m=0,\mathrm{\Delta }n=0}^n\gamma {(\mathrm{\Delta }m,\mathrm{\Delta }n)}^2}$, where $\gamma (\mathrm{\Delta }m,\mathrm{\Delta }n)=\frac{A(\mathrm{\Delta }m,\mathrm{\Delta }n)}{A(0,0)},A(\mathrm{\Delta }m,\mathrm{\Delta }n)=\frac{1}{{\mathit{Count}}_{(\mathrm{\Delta }m,\mathrm{\Delta }n)}}·{\displaystyle \sum _{x0}^{M-1-\mathrm{\Delta }m}}{\displaystyle \sum _{y=0}^{N-1-\mathrm{\Delta }n}}[f_{in}(x,y)-{\overline{f}}_{in}]\times [f_{in}(x+\mathrm{\Delta }m,y+\mathrm{\Delta }n)-{\overline{f}}_{in}]$	fin(x, y) and fin(x+Δm,y+Δn) are gray levels of pixels (i, j) and (i+Δm, j+Δn) inside a ROI of size M × N. f̄in is the mean value of all pixels and Count(Δm,Δn) is the number of pixel pairs inside a ROI, with given distance (Δm, Δn) along the x and y axes, respectively.
Tamura features (13)	Contrast	Fcon = σ/(a4)1/4, where α4 = μ4/σ4	μ4 is the 4th moment of all pixels about the mean inside a ROI, and σ2 is the variance. θ is the gradient direction of a pixel, and Nθ(k) is the number of pixels with which (2k−1)π/2n < θ < (2k + 1)π/2n and the gradient norm |G| ≥ t (a preset thresholding). HD(φ) can be regarded as the histogram of θ, where np is the number of peaks, φp is the position of the pth peak, and wp is the range between peaks. PDd means the nxn local cooccurrence matrix with a given distance along a given direction. r is a normalizing factor and σxxx means the standard deviation of the feature Fxxx.
	Directionality	$H_D(k)=N_{\theta }(k)/{\sum }_{i=0}^{n-1}{N}_{\theta }(i)k=0,1,\cdots ,n-1$ $F_{\mathit{dir}}={\displaystyle \sum _p^{n_p}}{\displaystyle \sum _{\phi \in w_p}}{(\phi -{\phi }_p)}^2{H}_D(\phi )$
	Line-likeness	$F_{\mathit{lin}}={\displaystyle \sum _i^n}{\displaystyle \sum _j^n}{P}_{Dd}(i,j)cos\left[(i-j)\frac{2\pi }{n}\right]/{\displaystyle \sum _i^n}{\displaystyle \sum _j^n}{P}_{Dd}(i,j)$
	Regularity	Freg = 1 − r(σcrs + σcon + σdir + σlin) where $F_{\mathit{crs}}=\frac{1}{M\times N}{\displaystyle \sum _{i=1}^M}{\displaystyle \sum _{j=1}^N}{S}_{\mathit{best}}(i,j)$
Features derived from GLCM (14,15)	f1–f16 derived from the GLCM matrix	$M_{d,\theta }(i,j)={\sum }_{x=1}^M{\sum }_{y=1}^N\{\begin{array}{cc}1& if(x,y),(x^{\prime },y^{\prime })\epsilon R^2,f(x,y)=i\mathit{and}f(x^{\prime },y^{\prime })=j\\ 0& \mathit{otherwise}\end{array}$ f1: angular second moment, f2: contrast, f3: correlation, f4: sum of squares, f5: inverse difference moment, f6: sum average, f7: sum variance, f8: sum entropy, f9: entropy, f10: difference variance, f11: difference entropy, f12 & f13: information measures of correlation, f14: inertia, f15: cluster shade, and f16: cluster prominence.	f(x,y) represents the intensity value of a pixel located at (x,y). M × N is the size of the ROI. Md,θ(i,j) is the (i, j) element of the GLCM matrix, representing the relative frequency with which two pixels with given gray levels of i and j are separated by a given pixel distance of d along the direction of θ.
Features derived from GLGCM (16)	T1–T11 derived from the GLGCM matrix	${\text{M}}^{\prime }(\text{i},\text{j})={\sum }_{\text{x}=1}^{\text{M}}{\sum }_{\text{y}=1}^{\text{N}}\{\begin{array}{ll}1\hfill & \text{if}(\text{x},\text{y})\epsilon {\text{R}}^2,\text{f}(\text{x},\text{y})=\text{i}\text{and}{\text{f}}_{\text{g}}(\text{x},\text{y})=\text{j}\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$ T1: small grads dominance, T2: big grads dominance, T3: gray asymmetry, T4: grads asymmetry, T5: energy, T6: correlation, T7: gray entropy, T8: grads entropy, T9: entropy. T10: inertia, and T11: DifferMoment.	fg(x,y) represents the gradient image of f(x,y). M′(i,j) is the (i, j) element of the GLGCM matrix, representing the relative frequency with which a pixel with given gray level of i and gradient of j appeared in the ROI.

GLCM, gray level cooccurrence matrix; GLGCM, gray level-gradient co-occurrence matrix; grads, gradient; N, number of features; Tm, third moment.