GLDM Features

Gray Level Dependence Matrix analysis for spatial texture characterization

Overview

The Gray Level Dependence Matrix (GLDM) quantifies the spatial dependence of gray levels in medical images by measuring how many neighboring voxels share similar intensity values. This texture analysis method provides powerful descriptors of local homogeneity and heterogeneity patterns that are essential for radiomics feature extraction.

GLDM features capture fine-to-coarse texture patterns by analyzing the size of connected regions with similar intensity values. These features are particularly effective at distinguishing between homogeneous and heterogeneous tissue regions in 3D medical imaging data.

Extracted Features

The following GLDM-based texture features are computed:

Small Dependence Emphasis (SDE)

Highlights fine textures by emphasizing small dependence regions with few connected neighbors.

SDE = Σi,j P(i,j) / j2
Large Dependence Emphasis (LDE)

Emphasizes coarse textures by highlighting large dependence regions with many connected neighbors.

LDE = Σi,j j2 · P(i,j)
Gray Level Non-Uniformity (GLNU)

Measures variability of gray level distributions across dependence regions.

GLNU = Σi ( Σj P(i,j) )2
Dependence Non-Uniformity (DNU)

Quantifies variability in the size distribution of dependence regions.

DNU = Σj ( Σi P(i,j) )2
Dependence Non-Uniformity Normalized (DNUN)

Normalized version of DNU, providing scale-invariant dependence size variability.

DNUN = Σj ( Σi P(i,j) )2 / Nz
Gray Level Variance (GLV)

Variance of gray level values across the GLDM, measuring intensity dispersion.

GLV = Σi,j (i - μ)2 · P(i,j)
Dependence Variance (DV)

Variance of dependence sizes, quantifying the spread of connected region sizes.

DV = Σi,j (j - μd)2 · P(i,j)
Dependence Entropy (DE)

Measures randomness of voxel dependencies, quantifying texture complexity.

DE = - Σi,j P(i,j) · log2(P(i,j))
Low Gray Level Emphasis (LGLE)

Emphasizes regions with low intensity values in the dependence matrix.

LGLE = Σi,j P(i,j) / i2
High Gray Level Emphasis (HGLE)

Emphasizes regions with high intensity values in the dependence matrix.

HGLE = Σi,j i2 · P(i,j)
Small Dependence Low Gray Level Emphasis (SDLGLE)

Joint measure emphasizing small dependence regions with low intensity values.

SDLGLE = Σi,j P(i,j) / (i2 · j2)
Small Dependence High Gray Level Emphasis (SDHGLE)

Joint measure emphasizing small dependence regions with high intensity values.

SDHGLE = Σi,j (i2 · P(i,j)) / j2
Large Dependence Low Gray Level Emphasis (LDLGLE)

Joint measure emphasizing large dependence regions with low intensity values.

LDLGLE = Σi,j (j2 · P(i,j)) / i2
Large Dependence High Gray Level Emphasis (LDHGLE)

Joint measure emphasizing large dependence regions with high intensity values.

LDHGLE = Σi,j i2 · j2 · P(i,j)

Notation Legend

The following symbols are used in the GLDM formulas above:

  • P(i,j) = normalized probability of dependence of size j at gray level i
  • Nz = total number of dependence zones in the image
  • i = gray level intensity value
  • j = dependence size (number of connected neighboring voxels with the same gray level)
  • μi = mean gray level in the GLDM
  • μj = mean dependence size in the GLDM
  • Σi,j = summation over all i (gray levels) and j (dependence sizes)
  • log₂ = base-2 logarithm

Calculation Methodology

  1. Discretize the image into gray levels using n_bins or bin_width parameters to create a quantized intensity representation.
  2. Compute the GLDM matrix using calculate_gldm_matrix, which counts the number of dependent neighbors for each gray level across all spatial directions.
  3. Calculate coefficients with calculate_gldm_coefficients, including probability distributions pd, pg, index vectors ivector, jvector, and the total number of zones Nz.
  4. Extract individual features using their corresponding mathematical formulas, including SDE, LDE, GLNU, DV, DE, and all joint emphasis measures.

Clinical Applications

GLDM features are widely used in radiomics to capture texture patterns in 3D medical images, providing quantitative measures of tissue homogeneity, coarseness, and gray level distribution. These features have demonstrated clinical value in tumor characterization, treatment response assessment, and prognostic modeling across various imaging modalities.