Gray-Level Size Zone Matrix (GLSZM)

A zone is defined as a connected group of voxels sharing the exact same discretized gray-level intensity. Connectivity is typically assessed in 3D using 26-connectivity (all adjacent voxels sharing a face, edge, or corner) or in 2D using 8-connectivity. Unlike the Gray-Level Run Length Matrix (GLRLM), which measures linear runs in specific directions, GLSZM is rotationally invariant—the shape and orientation of the zone do not matter, only its size. This makes GLSZM particularly suited for capturing structural heterogeneity in tumors where necrotic cores or cystic regions form irregular, non-directional clusters.

The GLSZM is a two-dimensional matrix where:

• Rows (Ng): Represent each discretized gray-level value present in the ROI.
• Columns (Ns): Represent each possible zone size, from 1 up to the maximum zone size found.
• Element P(i,j): Contains the total count of zones with gray level i and size j.

The matrix is fundamentally different from GLCM and GLRLM because a single large homogeneous region contributes only one count to the matrix, regardless of how many voxels it contains. This makes GLSZM highly sensitive to the presence of large uniform areas rather than frequent small textures.

Several quantitative features are extracted from the normalized GLSZM to characterize tissue architecture:

• Small Zone Emphasis (SZE): Measures the distribution of small zones. Higher values indicate finer, more granular textures.
• Large Zone Emphasis (LZE): Measures the distribution of large zones. Higher values indicate coarser, more homogeneous structural regions.
• Zone Size Non-Uniformity (ZSNU): Quantifies the variability of zone sizes across the image. Lower values mean more uniformity in zone size distribution.
• Gray-Level Non-Uniformity (GLNU): Measures the variability of gray-level intensities among zones. Higher values indicate greater heterogeneity in intensity values.
• Zone Percentage (ZP): The ratio of the number of zones to the total number of voxels, indicating textural coarseness.

GLSZM features have demonstrated significant prognostic value in oncology imaging:

• Tumor Heterogeneity: Large Zone Emphasis correlates with necrotic or cystic regions in tumors, which are often associated with aggressive phenotypes and poor prognosis.
• Treatment Response: Changes in Zone Size Non-Uniformity during therapy can indicate tumoral structural reorganization before volumetric shrinkage is visible.
• Histological Correlates: High Gray-Level Non-Uniformity has been linked to increased cellularity and nuclear atypia on histopathology.
• Non-Small Cell Lung Cancer: GLSZM features have been validated as independent predictors of overall survival and distant metastasis in multiple cohorts.

GLSZM calculation is highly sensitive to pre-processing parameters, which must be standardized per IBSI guidelines:

• Intensity Discretization: The number of gray-level bins directly impacts zone formation. Fixed bin width (e.g., 25 HU) is preferred over fixed bin count for cross-scanner reproducibility.
• Voxel Resampling: Non-isotropic voxels distort zone size measurements. Resampling to isotropic 1×1×1 mm³ or 2×2×2 mm³ voxels is mandatory.
• HU Rescaling: For CT, absolute Hounsfield Unit rescaling ensures consistent tissue density thresholds across scanners.
• Outlier Filtering: Extreme intensity outliers can fragment zones artificially. 3-sigma outlier removal or intensity clipping is often applied.

While both matrices quantify homogeneous regions, they capture fundamentally different structural properties:

• GLRLM: Counts directional runs of consecutive pixels. A long, thin structure aligned with the measurement direction produces a long run. The same structure measured perpendicularly produces short runs. GLRLM is directionally dependent.
• GLSZM: Counts connected zones regardless of shape or orientation. A long, thin structure produces a zone equal to its total area, independent of measurement angle. GLSZM is rotationally invariant.
• Practical Impact: GLSZM is preferred for quantifying blob-like or irregular heterogeneous regions (necrosis, cysts), while GLRLM excels at capturing linear or directional structures (fibrotic bands, vascular tracts).

A precursor texture matrix that quantifies consecutive runs of identical gray levels in a specific direction. While GLSZM measures the size of connected zones regardless of angle, GLRLM captures directional coarseness. A homogeneous tissue will yield long runs in GLRLM and large zones in GLSZM, but GLSZM provides a rotationally invariant alternative that is often more robust to patient positioning.

A mandatory pre-processing step where continuous Hounsfield Unit values are binned into a finite number of gray levels. The bin width directly controls GLSZM matrix dimensions:

• Fine discretization (e.g., 64 bins): Preserves subtle texture but increases matrix sparsity
• Coarse discretization (e.g., 8 bins): Reduces noise but may merge distinct tissue zones IBSI guidelines recommend a fixed bin width of 25 HU for CT radiomics to ensure cross-study comparability.

A complementary texture matrix that quantifies the difference between a voxel's intensity and its surrounding neighbors. While GLSZM counts connected homogeneous zones, NGTDM measures local intensity variation. A tissue with large GLSZM zones (high homogeneity) will typically exhibit low NGTDM busyness values. Using both matrices together provides a more complete texture signature.

A second-order statistical method that captures pairwise spatial relationships between voxel intensities at defined offsets. Unlike GLSZM's focus on connected region size, GLCM quantifies contrast, correlation, and local patterns. A tumor with large GLSZM zones may still exhibit high GLCM contrast if zone boundaries are sharp, making the two matrices complementary for capturing intratumoral heterogeneity.

A statistical batch-effect correction method that removes scanner-induced variability from GLSZM features. Without harmonization, identical tissue scanned on different CT models can produce divergent zone size metrics. ComBat estimates and removes the additive and multiplicative scanner effects while preserving biological variability, enabling multi-center radiomic studies to pool GLSZM data reliably.