NGTDM Features

Neighbouring Gray Tone Difference Matrix analysis for local texture pattern characterization

Overview

The Neighbouring Gray Tone Difference Matrix (NGTDM) quantifies the difference between a gray value and the average gray value of its neighbors within a specified distance. This texture analysis method captures local intensity variations and spatial patterns by analyzing how each voxel's intensity relates to its surrounding neighborhood, providing essential descriptors for characterizing tissue heterogeneity in medical imaging.

NGTDM features excel at capturing fine-scale texture patterns and local intensity variations by comparing each voxel with its immediate neighborhood. These features are particularly sensitive to subtle changes in tissue structure, making them invaluable for detecting early disease progression, tumor characterization, and quantitative assessment of heterogeneity in radiomics research.

Extracted Features

The following NGTDM-based texture features are computed:

Coarseness

Measures the spatial rate of change in intensity; higher values indicate coarser textures with larger homogeneous regions.

Coarseness = 1 / Σi pi · si
Contrast

Quantifies the intensity contrast between a voxel and its neighbors; higher values indicate larger differences and more heterogeneous patterns.

Contrast = (1 / (Ng(Ng - 1))) · Σi,j pi · pj · (i - j)²
Busyness

Measures rapid changes in intensity between neighboring voxels; higher values indicate more heterogeneous and busy textures.

Busyness = Σi pi · si / Σi,j |i - j| · pi · pj
Complexity

Evaluates local intensity variations considering differences among all gray levels; higher values indicate more complex and intricate texture patterns.

Complexity = Σi,j |i - j| / Nv · (pi · si + pj · sj)
Strength

Measures the perceptual strength of the texture patterns; higher values indicate more prominent and well-defined structures within the region.

Strength = Σi,j (pi + pj) · (i - j)² / Σi si

Notation Legend

The following symbols are used in the formulas above:

  • G : Number of gray levels in the quantized image.
  • i, j : Gray level indices, ranging from 1 to G.
  • p_i : Probability of gray level i in the region of interest (ROI).
  • s_i : Sum of absolute differences between gray level i and the average of its neighbors.
  • N_g : Total number of gray levels (same as G).
  • N : Number of voxels (or pixels) in the ROI.
  • f(i,j) : Frequency or probability of occurrence of gray level pair (i,j).
  • Δ(i) : Difference between gray level i and the average of its neighboring voxels.

Calculation Methodology

  1. Discretize the image based on n_bins or bin_width parameters to create quantized intensity levels for consistent analysis.
  2. Compute the NGTDM matrix using calculate_ngtdm_matrix, which evaluates the neighborhood of each voxel and calculates intensity differences.
  3. Calculate coefficients using calculate_ngtdm_coefficients, deriving probability distributions (p_i) and difference measures (s_i).
  4. Extract individual features using their corresponding mathematical formulas: coarseness, contrast, busyness, complexity, and strength.

Clinical Applications

NGTDM features are particularly valuable for capturing local texture patterns and assessing heterogeneity within regions of interest in medical imaging. These features have demonstrated clinical utility in tumor grading, response prediction to therapy, prognostic modeling, and tissue characterization across various imaging modalities including CT, MRI, and PET. Their sensitivity to fine-scale texture variations makes them essential tools in precision medicine and quantitative imaging biomarker development.