The neighborhood grey-level difference matrix (NGLDM) corresponds to the difference of grey-level between one voxel and its 26 neighbours in 3 dimensions (8 in 2D). Three texture indices can be computed from this matrix. An element \((i,1)\) of NGLDM corresponds to the probability of occurrence of level \(i\) and an element \((i,2)\) is equal to:
\begin{equation}
NGLDM(i,2)= \sum_{p}\sum_{q} \left\lbrace
\begin{array}{ll}
|\overline{M}(p,q)-i| \mbox{~if $I(p,q)=i$} \\
0 \mbox{~else}
\end{array}
\right.
\end{equation}
where \(\overline{M}(p,q)\) is the average of intensities over the 26 neighbour voxels of voxel \((p,q)\).
NGLDM_Coarseness is the level of spatial rate of change in intensity.
\begin{equation}
NGLDM\_Coarseness=\frac{1}{\sum_{i} NGLDM(i,1) \cdot NGLDM(i,2)}
\end{equation}
NGLDM_Contrast is the intensity difference between neighbouring regions.
\begin{equation}
NGLDM\_Contrast=\left[ \sum_{i} \sum_{j} NGLDM(i,1) \cdot NGLDM(j,1) \cdot (i-j)^{2} \right] \cdot \frac{\sum_{i} NGLDM(i,2)}{E \cdot G \cdot (G-1)}
\end{equation}
where E corresponds to the number of voxels in the Volume of Interest and G the number of grey-levels.
NGLDM_Busyness is the spatial frequency of changes in intensity.
\begin{equation}
\begin{split}
NGLDM\_Busyness=\frac{\sum_{i} NGLDM(i,1) \cdot NGLDM(i,2)}{\sum_{i} \sum_{j} \left | i \cdot NGLDM(i,1) - j \cdot NGLDM(j,1) \right | } \\
with~ NGLDM(i,1)\neq 0,~ NGLDM(j,1)\neq 0
\end{split}
\end{equation}