Table 7.

Best set of derived features after applying filter methods and recursive feature elimination.

Feature Name	Description	Equation
Skewness	It measures the asymmetry of the distribution of values about the Mean value.	Skew = $\frac{{\mu }_3}{{\sigma }_3}=\frac{\frac{1}{N_p}{{\displaystyle \sum }}_{i=1}^{N_p}{\left(X\left(i\right)-\overline{X}\right)}^3}{{\left(\sqrt{\frac{1}{N_p}{{\displaystyle \sum }}_{i=1}^{N_p}{\left(X\left(i\right)-\overline{X}\right)}^2}\right)}^3}$
Entropy	It measures the uncertainty or randomness in the image values.	Entropy = $-{{\displaystyle \sum }}_{i=1}^{N_g}p\left(i\right)lo{g}_2\left(p\left(i\right)+ \in \right)$
Total Energy	It is the measure of the magnitude of voxel values in an image.	Total Energy = $V_{voxel}{{\displaystyle \sum }}_{i=1}^{N_p}{\left(X\left(i\right)+c\right)}^2$
Interquartile Range	It measures the percentile of image data present between 25th percent to 75th percent.	IQR = $P_{75}-P_{25}$
Mesh Volume [38]	It measures the Volume of ROI.	$\begin{array}{c}{V}_i=\frac{O_{a_i}·\left(O_{b_i}\times O_{c_i}\right)}{6}\\ V= {\displaystyle {\displaystyle \sum }_{i=1}^{N_f}}{V}_i\end{array}$
Surface Area	It measures the extrinsic surface are of the ROI	$\begin{array}{c}{A}_i= \frac{1}{2} \left|a_i{b}_i \times a_i{c}_i\right|\\ A= {\displaystyle {\displaystyle \sum }_{i=1}^{N_f}}{A}_i\end{array}$
Major Axis Length	It measures the largest axis length of the ROI enclosing ellipsoid using the largest principal component.	Major axis = $4\sqrt{{\lambda }_{major}}$
Minor Axis Length	It measures the second- largest axis length of the ROI enclosing ellipsoid using the largest principal component.	Minor axis = $4\sqrt{{\lambda }_{minor}}$
Autocorrelation	It measures the magnitude of the fineness and coarseness of texture.	Auto_corr = ${{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_g}p\left(i, j\right)i$
Cluster Prominence	It measures the skewness and asymmetry of the Gray Level Co-occurrence Matrix.	CP = ${{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_g}{\left(i+j-{\mu }_x-{\mu }_y\right)}^{4}p\left(i,j\right)$
Difference Entropy	It is a measure of the randomness/variability in neighborhood intensity value differences.	DE = ${{\displaystyle \sum }}_{k=0}^{N_g-1}{p}_{x-y}\left(k\right)lo{g}_2(p_{x-y}\left(k\right)+\in )$
Inverse Difference Moment	IDM measures the local homogeneity of an image.	IDM = ${{\displaystyle \sum }}_{k=0}^{N_g-1}\frac{p_{x-y}\left(k\right)}{1+k^2}$
Small Area High Gray Level Emphasis (SAHGLE)	It measures the proportion in the image of the joint distribution of smaller size zones with higher gray level values	SAHGLE = $\frac{{{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_s}\frac{P\left(i, j\right)i^2}{j^2}}{N_z}$
Gray Level Non-Uniformity [16]	It measures the similarity of gray level intensity values in the images, where a lower GLN value correlates with a greater similarity in intensity values	GLN = $\frac{{{\displaystyle \sum }}_{i=1}^{N_g}{\left({{\displaystyle \sum }}_{j=1}^{N_r}P(i,j|\theta )\right)}^2}{N_r\left(\theta \right)}$
Gray Level Variance	It measures the variance in gray level intensity for the runs	GLV = ${{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_r}p\left(i,j|\theta \right){\left(i-\mu \right)}^2$
Run Entropy	It measures the randomness in the distribution of run length and gray levels.	RE = ${{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_r}p\left(i,j|\theta \right){\log }_2\left(p\left(i,j|\theta \right)+\in \right)$
Long Run High Gray Level Emphasis (LRHGLE)	It measures the joint distribution of long-run lengths with higher gray-level values.	LRHGLRE = $\frac{{{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_r}P\left(i,j|\theta \right)i^2{j}^2}{N_r\left(\theta \right)}$
Coarseness	It measures the average difference between the center voxel and its neighborhood and is an indication of the spatial rate of change	Coarseness = $\frac{1}{{{\displaystyle \sum }}_{i=1}^{N_g}{p}_i{s}_i}$
Small Dependence Emphasis	It measures the small dependencies, with a greater value indicative of smaller dependence and less homogeneous textures.	SDE = $\frac{{{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_d}\frac{P\left(i, j\right)}{i^2}}{N_z}$
Dependence Non-Uniformity	It measures the similarity of dependence throughout the image, with a lower value indicating more homogeneity among dependencies in the image.	DN = $\frac{{{\displaystyle \sum }}_{j=1}^{N_d}{\left({{\displaystyle \sum }}_{i=1}^{N_g}P\left(i,j\right)\right)}^2}{N_z}$