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## Grey-Level Zone Length Matrix (GLZLM)

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} 