First order statistics - cerr/CERR GitHub Wiki

First order statistics describe the grey-level intensity distribution within the region of interest (ROI). These features have been implemented in accordance with the IBSI Sec 4.3.

Note: Discretization is not required. However, intensity-based statistical features are not meaningful if the intensity scale is arbitrary. Hence normalization of intensities to standard units is required for modalities such as MR.

List of available features

Let X_k be the intensity of k^th voxel within the region of interest.

Min : The lowest intensity in X.
Max : The highest intensity in X.
10th percentile : The 10th percentile of X. This is more robust to outliers than the minimum grey level.
90th percentile : The 90th percentile of X. This is more robust to outliers than the maximum grey level.
Median , M : The sample median of X.
$Mean, \ \mu =\frac{\sum_{k=1}^{N_v} X_k}{N_v}$
$Range = \max(X) - \min(X)$
$Variance = \frac{\sum_{k=1}^{N_v}(X_k - \mu)^2}{N_v}$
$Standard \ deviation = \sqrt{Variance}$
$Skewness = \frac{\frac{\sum_{k=1}^{N_v}(X_k - \mu)^3}{N_v}} {(\frac{\sum_{k=1}^{N_v}(X_k - \mu)^2}{Nv})^{3/2})}$
$Kurtosis = \frac{\frac{\sum_{k=1}^{N_v}(X_k - \mu)^4}{N_v}} {(\frac{\sum_{k=1}^{N_v}(X_k - \mu)^2}{Nv})^2)} - 3$
$Energy = \sum_{k=1}^{N_v} X_k^2$
$Total \ energy = \sum_{k=1}^{N_v} X_k^2 \times voxelVolume$
$Root \ Mean \ Square = \sqrt{}\frac{\sum_{k=1}^{N_v} X_k^2}{N_v}$
$Mean \ absolute \ deviation = \frac{\sum_{k=1}^{N_v}|X_{gl,k}-\mu|}{N_v}$
$Median\ absolute \ deviation = \frac{\sum_{k=1}^{N_v}|X_k-median|}{N_v}$
$Robust \ mean \ absolute \ deviation = \frac{\sum_{k=1}^{N_{v,10-90}}|X_{10-90,k}-\bar{X}_{10-90,k}|}{N_{v,10-90}}\\$
$Robust \ median \ absolute \ deviation = \frac{\sum_{k=1}^{N_{v,10-90}}|X_{10-90,k}-median(X_{10-90})|}{N_{v,10-90}}\\$
$Inter-Quartile \ Range = P_{75} - P_{25}$
where P₂₅ and P₇₅ are the 25^th and 75^th percentiles of X, respectively
$Quartile \ coefficient \ of \ Dispersion = \frac{P_{75}-P_{25}}{P_{75}+P_{25}}$
$Coefficient \ of \ Variation = \frac{\sigma}{\mu}$
$Entropy = - \sum_{k=1}^{N_g_l} p_{gl}\times log2(p_{gl})$ for the set of grey levels X_gl = {X_gl,1, X_gl,2, . . . , X_gl,Nv} of Nv voxels in the region of interest. X is discretized into bins of uniform width specified by the binWidth parameter. The smallest bin includes 0 and the largest bin includes X_max.

Sample function call

% planC object
global planC

% Structure index
structNum = 1;

% Intensity offset for the Energy feature. For example, 1000 for CT scans, 0 for PET SUVs.
ctOffset = 1000;

% Bin-width for Entropy feature. For example, 25 HU for CT scans, 0.2 for PET SUVs.
binWidth = 25; 

% Call the first order feature calculation function
statsFeatureS = radiomics_first_order_stats(planC,structNum,ctOffset,binWidth);

First order statistics - cerr/CERR GitHub Wiki

List of available features

Sample function call

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