The grey-level zone length matrix (GLZLM) provides information on the size of homogeneous zones for each grey-level in 3 dimensions. It is also named Grey Level Size Zone Matrix (GLSZM).
From this matrix, 11 texture indices can be computed. Element \((i,j)\) of GLZLM corresponds to the number of homogeneous zones of \(j\) voxels with the intensity \(i\) in an image and is called \(GLZLM(i,j)\) thereafter.
GLZLM_SZE, GLZLM_LZE, Short-Zone Emphasis or Long-Zone Emphasis is the distribution of the short or the long homogeneous zones in an image.
\begin{equation}
GLZLM\_SZE=\frac{1}{H} \sum_{i} \sum_{j} \frac{GLZLM(i,j)}{j^{2}}
\end{equation}
\begin{equation}
GLZLM\_LZE=\frac{1}{H} \sum_{i} \sum_{j} GLZLM(i,j)\cdot j^{2}
\end{equation}
where \(H\) corresponds to the number of homogeneous zones in the Volume of Interest.
GLZLM_LGZE, GLZLM_HGZE, Low Gray-level Zone Emphasis or High Gray-level Zone Emphasis is the distribution of the low or high grey-level zones.
\begin{equation}
GLZLM\_LGZE=\frac{1}{H} \sum_{i} \sum_{j} \frac{GLZLM(i,j)}{i^{2}}
\end{equation}
\begin{equation}
GLZLM\_HGZE=\frac{1}{H} \sum_{i} \sum_{j} GLZLM(i,j)\cdot i^{2}
\end{equation}
GLZLM_SZLGE, GLZLM_SZHGE, Short-Zone Low Gray-level Emphasis or Short-Zone High Gray-level Emphasis is the distribution of the short homogeneous zones with low or high grey-levels.
\begin{equation}
GLZLM\_SZLGE=\frac{1}{H} \sum_{i} \sum_{j} \frac{GLZLM(i,j)}{i^{2}\cdot j^{2}}
\end{equation}
\begin{equation}
GLZLM\_SZHGE=\frac{1}{H} \sum_{i} \sum_{j} \frac{GLZLM(i,j)\cdot i^{2}}{j^{2}}
\end{equation}
GLZLM_LZLGE, GLZLM_LZHGE, Long-Zone Low Gray-level Emphasis or Long-Zone High Gray-level Emphasis is the distribution of the long homogeneous zones with low or high grey-levels.
\begin{equation}
GLZLM\_LZLGE=\frac{1}{H} \sum_{i} \sum_{j} \frac{GLZLM(i,j)\cdot j^{2}}{i^{2}}
\end{equation}
\begin{equation}
GLZLM\_LZHGE=\frac{1}{H} \sum_{i} \sum_{j} GLZLM(i,j)\cdot i^{2} \cdot j^{2}
\end{equation}
GLZLM_GLNUz, GLZLM_ZLNU, Gray-Level Non-Uniformity for zone or Zone Length Non-Uniformity is the non-uniformity of the grey-levels or the length of the homogeneous zones.
\begin{equation}
GLZLM\_GLNUz=\frac{1}{H} \sum_{i} \left( \sum_{j} GLZLM(i,j)\right) ^{2}
\end{equation}
\begin{equation}
GLZLM\_ZLNU=\frac{1}{H} \sum_{j} \left( \sum_{i} GLZLM(i,j)\right) ^{2}
\end{equation}
GLZLM_ZP, Zone Percentage measures the homogeneity of the homogeneous zones.
\begin{equation}
GLZLM\_ZP=\frac{H}{\sum_{i} \sum_{j}(j\cdot GLZLM(i,j))}
\end{equation}