Table 6.

GLRLM, GLSZM, and NGTDM feature definitions and NPS peak frequency and maximum intensity corrections.

Features	Original feature formula $F$$(v,Ng,K)$	Corr. feature formula	Corr. feature formula
GLRLM features
Low gray-level run emphasis	$\frac{1}{n}\sum _{i=1}^M\sum _{J=1}^{Ng}\frac{R(i,j)}{i^2}$	$F(v,Ng,K)/f_{\text{peak}}(K)$	$F(v,Ng,K)/I_{\max }^2(K)$
Short run low gray-level emphasis	$\frac{1}{n}\sum _{i=1}^M\sum _{J=1}^{Ng}\frac{R(i,j)}{i^2{j}^2}$	$F(v,Ng,K)/f_{\text{peak}}(K)$	$F(v,Ng,K)/I_{\max }^2(K)$
Long run low gray-level emphasis	$\frac{1}{n}\sum _{i=1}^M\sum _{J=1}^{Ng}\frac{R(i,j)j^2}{i^2}$	$F(v,Ng,K)/f_{\text{peak}}(K)$	$F(v,Ng,K)/I_{\max }^2(K)$
GLSZM Features
Small-area emphasis	$\frac{1}{\mathrm{\Omega }}\sum _{i=1}^m\sum _{j=1}^n\frac{z(i,j)}{j^2}$	$F(v,Ng,K)/{[f_{\text{peak}}(K)]}^2$	$F(v,Ng,K)/I_{\max }^4(K)$
High-intensity small-area emphasis	$\frac{1}{\mathrm{\Omega }}\sum _{i=1}^m\sum _{j=1}^n{i}^2$, $j^2$, $z(i,j)$	$F(v,Ng,K)/{[f_{\text{peak}}(K)]}^2$	$F(v,Ng,K)/I_{\max }^4(K)$
Size-zone variability	$\frac{1}{\mathrm{\Omega }}\sum _{i=1}^m{\left[\sum _{j=1}^n\frac{z(i,j)}{i^2}\right]}^2$	$F(v,Ng,K)/\sqrt{f_{\text{peak}}(K)}$	$F(v,Ng,K)/I_{\mathrm{max.}}(K)$
NGTDM feature
Coarseness	${[ϵ+\sum _{i=0}^{Nh}{p}_{i}M(i)]}^{-1}$	$F(v,Ng,K)/\sqrt{f_{\text{peak}}(K)}$	$F(v,Ng,K)/I_{\mathrm{max.}}(K)$

GLRLM: $R(i,j)$ is the $(i,j)$’th entry in the given run-length matrix, and $Ng$ is the number of discrete gray levels in the image. $M$ is the longest run, and n is the total number of runs.

GLSZM: In size zone matrix $z(i,j)$ rows $i$ indicate gray levels and columns indicating zone sizes. $Ng$ is the number of gray levels, and the largest zone size is indicated by m. $\mathrm{\Omega }$ is the total number of unique connected zones.

NGTDM: $P_i$ is the probability of occurrence of voxel of intensity $I$, and $M(i)$ is the NGTDM value of intensity $i$. $N_h$ is the highest gray-level value present in the ROI.