GLRLM Features

Gray Level Run Length Matrix analysis for texture characterization

Overview

The Gray Level Run Length Matrix (GLRLM) quantifies the length of consecutive runs of voxels with the same intensity value in medical images. This texture analysis method provides powerful descriptors for distinguishing between fine and coarse texture patterns, making it essential for radiomics feature extraction and tissue characterization.

GLRLM features capture directional texture patterns by analyzing run lengths across multiple orientations. The features are computed in 2D and 3D and averaged across directions to provide rotationally invariant descriptors that effectively characterize local and regional texture heterogeneity.

Extracted Features

The following GLRLM-based texture features are computed:

Short Run Emphasis (SRE)

Measures the distribution of short runs; higher values indicate more short runs and finer textures.

SRE = Σi,j P(i,j) / j2
Long Run Emphasis (LRE)

Measures the distribution of long runs; higher values indicate coarser, more homogeneous textures.

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

Measures similarity of gray level values; 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 uniformity measurement.

GLNN = GLN / Nr
Run Length Non-Uniformity (RLN)

Measures similarity of run lengths; lower values indicate more uniform run length distribution.

RLN = Σj ( Σi P(i,j) )2
Run Length Non-Uniformity Normalized (RLNN)

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

RLNN = RLN / Nr
Run Percentage (RP)

Measures the distribution of runs relative to the total number of voxels; indicates texture density and homogeneity.

RP = Nr / Np
Gray Level Variance (GLV)

Measures variance in gray level intensities across runs, quantifying intensity dispersion.

GLV = Σi,j P(i,j) · (i − μi)2
Run Variance (RV)

Measures variance in run lengths, quantifying the heterogeneity of texture patterns.

RV = Σi,j P(i,j) · (j − μj)2
Run Entropy (RE)

Measures disorder or randomness in run lengths and gray levels, indicating texture complexity.

RE = −Σi,j P(i,j) · log₂(P(i,j))
Low Gray Level Run Emphasis (LGLRE)

Emphasizes runs with low gray level values, highlighting darker regions in the image.

LGLRE = Σi,j P(i,j) / i2
High Gray Level Run Emphasis (HGLRE)

Emphasizes runs with high gray level values, highlighting brighter regions in the image.

HGLRE = Σi,j i2 · P(i,j)
Short Run Low Gray Level Emphasis (SRLGLE)

Joint measure emphasizing short runs with low gray level values, capturing fine dark textures.

SRLGLE = Σi,j P(i,j) / (i2 · j2)
Short Run High Gray Level Emphasis (SRHGLE)

Joint measure emphasizing short runs with high gray level values, capturing fine bright textures.

SRHGLE = Σi,j (i2 · P(i,j)) / j2
Long Run Low Gray Level Emphasis (LRLGLE)

Joint measure emphasizing long runs with low gray level values, capturing coarse dark textures.

LRLGLE = Σi,j (j2 · P(i,j)) / i2
Long Run High Gray Level Emphasis (LRHGLE)

Joint measure emphasizing long runs with high gray level values, capturing coarse bright textures.

LRHGLE = Σi,j i2 · j2 · P(i,j)

Notation Legend

The following symbols are used in the GLRLM formulas above:

  • P(i,j) = normalized probability of a run of length j at gray level i
  • i = gray level intensity value
  • j = run length (number of consecutive voxels/pixels with the same gray level)
  • Nr = total number of runs in the region of interest (ROI)
  • Np = total number of pixels or voxels in the ROI
  • μi = mean gray level across the GLRLM
  • μj = mean run length across the GLRLM
  • Σi,j = summation over all gray levels i and run lengths j
  • log₂ = base-2 logarithm

Clinical Applications

GLRLM features are especially useful for capturing coarse and fine textures in medical images. These metrics are computed over multiple directions and averaged to obtain robust, rotationally invariant values for regions of interest. They have demonstrated clinical value in tumor characterization, treatment response assessment, and outcome prediction across various imaging modalities including CT, MRI, and PET.