Table 2. Summary description and relevant formulae for the independent first, second and fractal features analyzed.

Parameter	Description	Formula
First order: histogram statistics provide an indication of central tendency (coefficient of variation) and variability (kurtosis, energy and entropy)
Coefficient of Variation (CoV)	Indicates how large the standard deviation is in relation to the mean	σ μ
Kurtosis	Describes the “peak” of a distribution. Kurtosis >3: sharper peak than a normal distribution Kurtosis <3: flatter peak than a normal distribution Kurtosis = 3: normal distribution	$\frac{n}{(n-1)(n-2)(n-3)}\frac{{\displaystyle {\sum }_{(x,y)\in R}{[a(x,y)-a]}^4}}{{[sd(a)]}^4}-3\frac{{(n-1)}^2}{(n-2)(n-3)}$ where n = the total number of voxels in the region-on-interest, R within the image a(x,y); sd = standard deviation; ā is the mean value within R
Energy	Measures voxel signal distribution. High energy is noted in homogeneous voxels	${\displaystyle {\sum }_{i=1}^{\mathit{\text{imax}}}[p(i)}{]}^2$ where i is the voxel value (between i = 1 to imax in the region of interest and p(i) the probability of the occurrence of that voxel value
Entropy	Measures voxel randomness. Low entropy is noted in homogeneous voxels	${\displaystyle {\sum }_{i=1}^{i\mathit{\text{max}}}[p(i)}\mathit{\text{ln}}[p(i)]$ where i is the voxel value (between i = 1 to imax in the region of interest and p(i) the probability of the occurrence of that voxel value
Second order: Gray Level Co-occurrence matrix (GLCM) statistics are computed after the original texture image D is re-quantized into an image G with reduced number of gray level, Ng by scanning the intensity of each voxel and its neighbour, defined by displacement d and angle θ. A displacement, d could take a value of 1,2,3,…n whereas an angle, θ is limited 0°, 45°, 90° and 135°. The GLCM p(i; j|d; θ) is a second order joint probability density function of gray level pairs in the image for each element in the co-occurrence matrix by dividing each element with Ng. Finally, scalar secondary features are extracted from this co-occurrence matrix
GLCM: Correlation	Measures gray level intensity linear dependence between the voxels (i,j) at the specified positions relative to each other	${\displaystyle {\sum }_i{\displaystyle {\sum }_j(ij)p(i,j)}}$ where i is the voxel value (between i = 1 to imax in the region of interest; j is the voxel value (between j = 1 to jmax in the region of interest; and p(i,j) the probability of the occurrence of that voxel value i relative to j
GLCM: Cluster prominence	Measures asymmetry. A low cluster prominence value indicates small variations in gray-scale	${\displaystyle {\sum }_i{\displaystyle {\sum }_j{(i+j-{\mu }_x-{\mu }_y)}^{4}p(i,j)}}$ where i is the voxel value (between i = 1 to imax in the region of interest; j is the voxel value (between j = 1 to jmax in the region of interest; p(i,j) is the probability of the occurrence of that voxel value i relative to j; μx is the mean of px and μy is the mean of py
Fractal features describe self-similar fractal shapes
Mean fractal dimension	Measures the texture of a fractal, a self similar pattern. A higher fractal dimension corresponds to greater roughness	$\overline{D}=\frac{{\displaystyle {\sum }_{i=1}^N{D}_i}}{N}$ where N is the number of slices and Di is the fractal dimension for the ith slice
Standard deviation	Measures the standard deviation of a fractal computed by a differential box counting algorithm	$\sigma =\sqrt{{\displaystyle {\sum }_{i=1}^N{D}_i^2}/N-{\left(\frac{{\displaystyle {\sum }_{i=1}^N{D}_i}}{N}\right)}^2}$ where N is the number of slices and Di is the fractal dimension for the ith slice
Lacunarity	Measures the amount of “gaps” in the image/object. If a fractal has large “gaps”, it has high lacunarity	$\frac{\left[{\displaystyle {\sum }_{i=1}^N{D}_i^2/N}\right]}{\left[{\left(\frac{{\displaystyle {\sum }_{i=1}^N{D}_i}}{N}\right)}^2\right]}-1$ where N is the number of slices and Di is the fractal dimension for the ith slice
Hurst component	Measures the density of the image/object i.e. how much the image/object occupies the space that contains it. A small value corresponds to coarse texture	$H=3-\overline{D}$ where $\overline{D}$ is the mean fractal dimension