Gray-Level Co-occurrence Matrix (GLCM)

Measures textural uniformity—the sum of squared GLCM entries.

• High ASM: Image has constant or periodic pixel patterns (few dominant gray-tone transitions)
• Low ASM: Pixel intensities are randomly distributed across the matrix
• Energy is the square root of ASM, providing a more linear scaling
• Clinical relevance: Homogeneous tumors often exhibit higher ASM values, correlating with less aggressive phenotypes in certain cancers
• Formula: ASM = Σᵢⱼ p(i,j)² where p(i,j) is the normalized co-occurrence probability

Quantifies the local intensity variation and the depth of texture grooves.

• High contrast: Large differences between neighboring pixel intensities (sharp edges, noise)
• Low contrast: Smooth, visually flat regions with minimal intensity variation
• Weighted by distance: Squared difference (i-j)² amplifies contributions from far-apart gray levels
• Clinical relevance: Malignant lesions often show higher contrast due to heterogeneous internal architecture
• Related term: Inertia—identical mathematical formulation, emphasizing resistance to intensity change

Measures the linear dependency of gray levels on those of neighboring pixels.

• Range: -1 to +1, where +1 indicates perfect positive linear relationship
• High correlation: Predictable, structured texture with directional patterns
• Low correlation: Uncorrelated, chaotic pixel arrangements
• Directionally sensitive: Values change based on the spatial offset angle (0°, 45°, 90°, 135°)
• Clinical relevance: Quantifies tissue anisotropy—fibrotic tissue shows directional correlation patterns distinct from normal parenchyma

Weighs the closeness of GLCM elements to the diagonal, indicating local similarity.

• High homogeneity: Matrix elements cluster near the diagonal—adjacent pixels have similar intensities
• Low homogeneity: Wide distribution of intensity pairs, indicating rough texture
• Inverse weighting: 1/(1+(i-j)²) gives higher weight to small intensity differences
• Clinical relevance: Benign masses often demonstrate greater internal homogeneity than malignant counterparts
• Related metric: Inverse Difference Normalized (IDN) removes dependence on total number of gray levels

Measures the randomness and information content of the texture pattern.

• High entropy: Broad distribution of co-occurrence probabilities—complex, unstructured texture
• Low entropy: Concentrated probabilities—simple, repetitive patterns
• Theoretical basis: Derived from information theory; -Σ p(i,j) × log(p(i,j))
• Clinical relevance: High entropy in tumor ROIs often indicates necrosis, hemorrhage, or aggressive growth patterns
• Distinction: GLCM entropy captures spatial disorder, unlike first-order entropy which ignores pixel relationships

Higher-order measures of matrix asymmetry and tailedness.

• Cluster Shade: Measures skewness of the GLCM—positive values indicate dominance of low-intensity pairs, negative values indicate high-intensity dominance
• Cluster Prominence: Measures kurtosis—high values indicate a peaked distribution with heavy tails (dominant clusters)
• Clinical relevance: Cluster prominence is a key discriminator in tumor grading, with aggressive lesions showing prominent high-intensity clusters
• Calculation: Both use cubed and fourth-power deviations from the mean, making them sensitive to outliers in the co-occurrence distribution