First-order Features - Radiomics.jl

Overview

First-order features describe the statistical properties of voxel intensities within a region of interest (ROI). These features characterize the distribution of intensity values without considering the spatial arrangement of voxels, providing fundamental quantitative descriptors for radiomics analysis.

First-order statistics are intensity-based features that capture the overall texture and heterogeneity of the ROI through statistical moments and distribution characteristics. They serve as essential baseline features in radiomics pipelines and medical image analysis workflows.

Extracted Features

Radiomics.jl computes the following comprehensive set of first-order statistical features:

Energy

Sum of squared voxel intensities, measuring the magnitude of voxel values in the ROI.

E = Σ X(i)²

Total Energy

Energy multiplied by the voxel volume, accounting for spatial resolution in the energy measurement.

E_total = V_voxel × Σ X(i)²

Entropy

Measure of uncertainty or randomness in the voxel intensity distribution, quantifying image complexity.

H = -Σ p(i) × log₂(p(i))

Minimum / Maximum

The minimum and maximum voxel values within the ROI, defining the intensity range.

min(X), max(X)

10th / 90th Percentile

Intensity values corresponding to the 10th and 90th percentiles of the distribution.

P₁₀, P₉₀

Mean

Average intensity value across all voxels in the ROI, representing central tendency.

μ = (1/N) × Σ X(i)

Median

Middle value of the sorted intensity distribution, robust to outliers.

M = X((N+1)/2)

Interquartile Range

Difference between the 75th and 25th percentiles, measuring the spread of the middle 50% of data.

IQR = P₇₅ - P₂₅

Range

Difference between maximum and minimum voxel values, indicating total intensity variation.

R = max(X) - min(X)

Mean Absolute Deviation

Average absolute deviation from the mean, quantifying average variability.

MAD = (1/N) × Σ |X(i) - μ|

Robust Mean Absolute Deviation

Mean absolute deviation calculated from values between the 10th and 90th percentiles, reducing outlier influence.

rMAD = (1/N₁₀₋₉₀) × Σ |X(i) - μ₁₀₋₉₀|

Root Mean Squared

Square root of the mean of squared voxel values, measuring the quadratic mean intensity.

RMS = √[(1/N) × Σ X(i)²]

Standard Deviation

Standard deviation of voxel values, quantifying dispersion around the mean.

σ = √[(1/N) × Σ (X(i) - μ)²]

Skewness

Measure of asymmetry of the voxel intensity distribution relative to the mean.

γ₁ = (1/N) × Σ [(X(i) - μ)/σ]³

Kurtosis

Measure of the "tailedness" of the distribution, indicating the presence of outliers.

γ₂ = (1/N) × Σ [(X(i) - μ)/σ]⁴

Variance

Variance of voxel values, representing the squared standard deviation.

σ² = (1/N) × Σ (X(i) - μ)²

Uniformity

Measure of the uniformity of voxel intensities, with higher values indicating more homogeneous regions.

U = Σ p(i)²

Notation Legend

The following symbols are used in the formulas above:

X(i) = intensity value of voxel i
N = total number of voxels in the ROI
μ = mean intensity value
σ = standard deviation
p(i) = probability (normalized frequency) of intensity value i
P₁₀, P₂₅, P₇₅, P₉₀ = 10th, 25th, 75th, and 90th percentiles
V_voxel = volume of a single voxel
Σ = summation over all voxels in the ROI

Clinical Significance

First-order features provide quantitative information about the texture and heterogeneity of medical images within the ROI. These features are essential for radiomics analysis and have demonstrated value in:

Tumor characterization and classification
Treatment response assessment
Prognostic biomarker discovery
Quantitative imaging phenotyping
Computer-aided diagnosis systems