GLSZM Features

Gray Level Size Zone Matrix analysis for homogeneous region characterization

Overview

The Gray Level Size Zone Matrix (GLSZM) quantifies the size of homogeneous zones for each gray level in a region of interest. This texture analysis method identifies connected regions with the same intensity value and characterizes their size distribution, providing powerful descriptors for distinguishing between fine and coarse texture patterns in medical imaging.

GLSZM features are particularly effective at capturing spatial organization of intensity values by analyzing the size distribution of homogeneous zones. These features excel at characterizing tissue heterogeneity and texture coarseness, making them essential for radiomics analysis in oncology and quantitative imaging research.

Extracted Features

The following GLSZM-based texture features are computed:

Small Area Emphasis (SAE)

Measures the distribution of small homogeneous zones; higher values indicate finer, more heterogeneous textures.

SAE = Σi,j P(i,j) / j²
Large Area Emphasis (LAE)

Measures the distribution of large homogeneous zones; higher values indicate coarser, more homogeneous textures.

LAE = Σi,j j² · P(i,j)
Gray Level Non-Uniformity (GLN)

Measures the variability of gray levels across zones; lower values indicate more uniform gray level distribution.

GLN = Σi [Σj P(i,j)]²
Gray Level Non-Uniformity Normalized (GLNN)

Normalized version of GLN, providing scale-invariant gray level variability measurement.

GLNN = GLN / N_zones
Size Zone Non-Uniformity (SZN)

Measures variability of zone sizes; lower values indicate more uniform zone size distribution.

SZN = Σj [Σi P(i,j)]²
Size Zone Non-Uniformity Normalized (SZNN)

Normalized version of SZN for consistent comparison across different ROI sizes.

SZNN = SZN / N_zones
Zone Percentage (ZP)

Ratio of number of zones to total number of voxels; indicates texture density and homogeneity.

ZP = N_zones / N_voxels
Gray Level Variance (GLV)

Variance of gray level intensities across zones, quantifying intensity dispersion.

GLV = Σi,j (i - μ_g)² · P(i,j)
Zone Variance (ZV)

Variance of zone sizes, measuring the heterogeneity of homogeneous region distribution.

ZV = Σi,j (j - μ_s)² · P(i,j)
Zone Entropy (ZE)

Measures randomness in zone distribution, quantifying texture complexity and disorder.

ZE = - Σi,j P(i,j) · log₂(P(i,j))
Low Gray Level Zone Emphasis (LGLZE)

Emphasizes zones with low gray level values, highlighting darker homogeneous regions.

LGLZE = Σi,j P(i,j) / i²
High Gray Level Zone Emphasis (HGLZE)

Emphasizes zones with high gray level values, highlighting brighter homogeneous regions.

HGLZE = Σi,j i² · P(i,j)
Small Area Low Gray Level Emphasis (SALGLE)

Joint measure emphasizing small zones with low gray levels, capturing fine dark textures.

SALGLE = Σi,j P(i,j) / (i² · j²)
Small Area High Gray Level Emphasis (SAHGLE)

Joint measure emphasizing small zones with high gray levels, capturing fine bright textures.

SAHGLE = Σi,j (i² / j²) · P(i,j)
Large Area Low Gray Level Emphasis (LALGLE)

Joint measure emphasizing large zones with low gray levels, capturing coarse dark textures.

LALGLE = Σi,j (j² / i²) · P(i,j)
Large Area High Gray Level Emphasis (LAHGLE)

Joint measure emphasizing large zones with high gray levels, capturing coarse bright textures.

LAHGLE = Σi,j (i² · j²) · P(i,j)

Notation Legend

The following symbols are used in the formulas above:

  • P(i,j) = normalized GLSZM probability for gray level i and zone size j
  • i = gray level value
  • j = zone size
  • N_zones = total number of zones in the ROI
  • N_voxels = total number of voxels in the ROI
  • μ_g = mean gray level over all zones
  • μ_s = mean zone size over all zones
  • Σi,j = summation over all gray levels i and zone sizes j

Calculation Methodology

  1. Discretize the image based on n_bins or bin_width parameters to create quantized intensity levels.
  2. Compute the GLSZM matrix using calculate_glszm_matrix, which identifies connected components of identical intensity values.
  3. Calculate coefficients using calculate_glszm_coefficients, deriving probability distributions and statistical measures.
  4. Extract individual features using their corresponding mathematical formulas, including small_area_emphasis, zone_entropy, and all joint emphasis measures.

Clinical Applications

GLSZM features are particularly useful for characterizing texture patterns in medical images, capturing both the size and intensity distribution of homogeneous zones. These features have demonstrated clinical value in tumor heterogeneity assessment, response prediction, and prognostic modeling across various imaging modalities including CT, MRI, and PET imaging.