Gray-Level Run Length Matrix (GLRLM)

A metric that quantifies the distribution of short runs of consecutive, identical pixel intensities. A high SRE value indicates fine, granular textures with rapid intensity fluctuations, often associated with heterogeneous tumor microenvironments. It is calculated by dividing each run count by its squared length, giving greater weight to shorter runs.

• Formula: Σ [p(i,j) / j²] / Σ p(i,j)
• Interpretation: High SRE = Fine texture; Low SRE = Coarse texture
• Clinical Relevance: High SRE in lung CT nodules has been correlated with malignancy and poorer prognosis.

A metric that measures the distribution of long runs of consecutive, identical pixel intensities. A high LRE value indicates coarse, structurally homogeneous textures with broad, uniform regions. It is calculated by multiplying each run count by the square of its length, emphasizing longer runs.

• Formula: Σ [p(i,j) × j²] / Σ p(i,j)
• Interpretation: High LRE = Coarse, uniform texture; Low LRE = Fine texture
• Clinical Relevance: High LRE in breast MRI has been associated with benign fibroglandular tissue, whereas low LRE suggests invasive carcinoma.

A metric that assesses the similarity of gray-level intensity values throughout the run-length distribution. A low GLN value indicates that runs are evenly distributed across all gray levels, signifying greater intensity uniformity. High GLN suggests that specific intensities dominate the texture.

• Formula: Σ [Σ p(i,j)]² / Σ p(i,j)
• Interpretation: Low GLN = Uniform intensity distribution; High GLN = Dominant intensities
• Clinical Relevance: GLN is a robust predictor of overall survival in head and neck cancer when extracted from FDG-PET scans.

A metric that evaluates the similarity of run lengths across the image. A low RLN value indicates that the lengths of runs are evenly distributed, suggesting a heterogeneous mix of fine and coarse textures. High RLN implies that the texture is dominated by runs of a single, specific length.

• Formula: Σ [Σ p(i,j)]² / Σ p(i,j)
• Interpretation: Low RLN = Even mix of run lengths; High RLN = Dominant run length
• Clinical Relevance: RLN is sensitive to structural anisotropy and is frequently used to differentiate between necrotic cores and viable tumor peripheries in glioblastoma.

A measure of overall homogeneity that calculates the fraction of the total number of runs over the total number of pixels in the region of interest. A high RP value indicates a highly homogeneous texture dominated by long runs, while a low RP suggests a chaotic, short-run texture.

• Formula: Σ p(i,j) / N_p
• Interpretation: High RP = Homogeneous; Low RP = Heterogeneous
• Clinical Relevance: RP is often inversely correlated with tumor grade, where lower RP values indicate higher cellular pleomorphism and aggressive pathology.

A joint metric that quantifies the distribution of runs dominated by low intensity values (dark regions). It is calculated by dividing each run count by the square of its gray level. A high LGRE indicates that short, dark runs are prevalent, often corresponding to hypoxic or necrotic tissue.

• Formula: Σ [p(i,j) / i²] / Σ p(i,j)
• Interpretation: High LGRE = Dark, hypodense texture
• Clinical Relevance: Combined with SRE, the LGRE metric helps identify necrotic cores in non-small cell lung cancer on contrast-enhanced CT.

The critical preprocessing step of binning continuous voxel intensities into a finite number of discrete gray levels before matrix calculation. The number of bins directly impacts GLRLM sensitivity—too few bins suppress fine texture, while too many create sparse, noisy matrices. Common strategies include fixed bin number (e.g., 8, 16, 32 levels) and fixed bin width (e.g., 25 HU in CT). The Image Biomarker Standardisation Initiative (IBSI) recommends consistent discretization protocols to ensure cross-study reproducibility.

A primary GLRLM-derived metric that quantifies the distribution of short consecutive runs of identical pixel intensities. SRE is calculated by dividing each run length count by the square of its run length, then summing and normalizing. A high SRE value indicates fine, granular textures with frequent intensity changes—characteristic of heterogeneous tumor microenvironments. Conversely, low SRE suggests coarse, homogeneous regions. SRE is often combined with Long Run Emphasis (LRE) and Run Percentage (RP) to form a comprehensive texture signature.

A complementary second-order statistical method that quantifies texture by calculating the frequency of specific pairs of pixel intensities occurring at a defined spatial offset and direction. While GLRLM captures run-length continuity, GLCM captures spatial dependence between pixel pairs. Key GLCM features include Contrast (local intensity variation), Homogeneity (closeness of element distribution to the diagonal), and Correlation (linear dependency of gray levels). Together, GLRLM and GLCM provide orthogonal texture characterizations.

A texture matrix that quantifies the size of homogeneous connected regions (zones) of identical voxel intensity, independent of rotational orientation. Unlike GLRLM, which measures one-dimensional collinear runs, GLSZM measures two-dimensional or three-dimensional contiguous zones. This rotation-invariance makes GLSZM particularly valuable for analyzing tumors where orientation is arbitrary. Derived features include Zone Percentage (ZP) and Large Zone Emphasis (LZE), which correlate with coarse, uniform tissue architecture.

A GLRLM feature measuring the similarity of run lengths throughout the image. RLN is calculated by summing the squares of each run length's total count, then normalizing. Low RLN values indicate greater homogeneity in run length distribution—most runs have similar lengths. High RLN values suggest heterogeneous run length mixtures, often seen in complex, irregular tissue patterns. RLN is directionally dependent and is typically averaged across all 13 angular directions (in 3D) or 4 directions (in 2D) for a rotationally robust metric.