First-Order Statistics

The arithmetic average of all voxel intensity values within the segmented ROI. This metric provides a baseline measure of overall tissue density or signal activity.

• Clinical relevance: Distinguishes hypo-intense from hyper-intense lesions
• Calculation: Sum of all voxel intensities divided by total voxel count
• Limitation: Highly sensitive to outliers and does not capture heterogeneity
• Example: A mean Hounsfield Unit of 35 in a lung nodule suggests ground-glass opacity rather than solid tissue

Variance measures the spread of intensity values around the mean, while standard deviation is its square root. These metrics quantify the degree of dispersion within the ROI.

• High variance indicates heterogeneous tissue with mixed densities
• Low variance suggests homogeneous tissue composition
• Clinical application: Tumor heterogeneity often correlates with malignancy and treatment resistance
• Standard deviation is expressed in the original intensity units, making it more interpretable than variance

A measure of the asymmetry of the intensity histogram distribution. Skewness indicates whether the tail of the distribution extends toward higher or lower intensity values.

• Positive skew: Tail extends toward higher intensities; mean > median
• Negative skew: Tail extends toward lower intensities; mean < median
• Zero skew: Symmetric distribution around the mean
• Clinical insight: Skewness shifts can indicate the presence of enhancing or necrotic sub-regions within tumors

A measure of the 'peakedness' or tailedness of the intensity histogram relative to a normal distribution. Kurtosis quantifies the concentration of values around the mean versus the extremes.

• High kurtosis (leptokurtic): Sharp peak with heavy tails; indicates a dense core with outlier voxels
• Low kurtosis (platykurtic): Flat distribution; suggests uniform heterogeneity
• Excess kurtosis is often reported, where a normal distribution equals zero
• Example: A necrotic tumor core surrounded by an enhancing rim produces high kurtosis values

A measure of the inherent randomness or unpredictability in the intensity distribution. Higher entropy indicates greater heterogeneity and disorganization within the ROI.

• Calculation: Based on Shannon's information theory applied to the intensity histogram
• Maximum entropy occurs when all intensity bins are equally probable
• Minimum entropy occurs when all voxels share the same intensity value
• Clinical significance: High entropy in glioblastomas correlates with poorer overall survival and genetic heterogeneity

Order statistics that describe the intensity values at specific cumulative distribution thresholds, along with the overall intensity range.

• 10th and 90th percentiles: Robust alternatives to minimum and maximum, less sensitive to outlier voxels
• Interquartile range (IQR): Difference between 25th and 75th percentiles; robust measure of dispersion
• Intensity range: Maximum minus minimum; highly sensitive to noise and artifacts
• Median: The 50th percentile; robust central tendency measure unaffected by extreme values

Morphological descriptors that quantify the three-dimensional geometric properties of a segmented region of interest. Unlike first-order statistics, these metrics are independent of intensity values and focus purely on form.

• Volume: Total number of voxels multiplied by voxel dimensions
• Sphericity: How closely the ROI approximates a perfect sphere
• Compactness: Ratio of volume to surface area
• Maximum 3D Diameter: The largest pairwise Euclidean distance between surface mesh vertices

A second-order statistical method that quantifies texture by calculating the frequency of specific pairs of pixel intensities occurring at a defined spatial offset. While first-order statistics ignore spatial relationships, GLCM captures directional patterns.

• Generates matrices for multiple angles (0°, 45°, 90°, 135°)
• Derives features like contrast, homogeneity, and correlation
• Sensitive to the chosen distance offset and discretization bin width

A first-order statistical measure of the randomness or inherent unpredictability in the distribution of voxel intensity values. High entropy indicates a heterogeneous, noisy region with many intensity levels; low entropy suggests a homogeneous, uniform texture.

• Calculated as: -Σ p(i) * log₂(p(i)) where p(i) is the probability of intensity i
• Often correlates with tumor heterogeneity and treatment resistance
• Highly dependent on the number of discretization bins chosen

The process of binning continuous voxel intensity values into a finite number of discrete gray levels. This is a critical preprocessing step that directly impacts the reproducibility of first-order and texture features.

• Fixed Bin Width: Bins of constant Hounsfield Unit width (e.g., 25 HU)
• Fixed Bin Count: A constant number of bins across all ROIs
• IBSI guidelines recommend reporting discretization parameters for reproducibility

An independent international collaboration providing consensus-based reference values and standardized nomenclature for radiomic feature computation. IBSI ensures that first-order statistics calculated in different software packages yield identical results.

• Publishes benchmark datasets with ground-truth feature values
• Defines mathematical formulas for 174 radiomic features
• Critical for multi-center clinical trial harmonization

A feature scaling technique that standardizes radiomic feature values by centering them to a mean of zero and scaling to a standard deviation of one. Essential before feeding first-order statistics into machine learning classifiers.

• Formula: z = (x - μ) / σ
• Preserves the shape of the distribution while removing scale effects
• Prevents features with larger numeric ranges from dominating model training