Feature Family  Specific
Features  Parameter
Name  Range  Default  Description, Formula and Comments 
Intensity Features
(FirstOrder Statistics) 

Minimum

Maximum

Mean

Standard Deviation

Variance

Skewness

Kurtosis
 N.A.  N.A.  N.A. 

Minimum Intensity = \( Min (I_{k}). \) where \( I_{k} \) is the intensity of pixel or voxel at index k.

Maximum Intensity = \( Max (I_{k}). \) where \( I_{k} \) is the intensity of pixel or voxel at index k.

Mean= \( \frac{\sum(X_{i})}{N} \) where N is the number of voxels/pixels.

Standard Deviation = \( \sqrt{\frac{\sum(X\mu)^{2}}{N}}\) where \(\mu\) is the mean of the data.

Variance = \( \frac{\sum(X\mu)^{2}}{N} \) where \(\mu\) is the mean intensity.

Skewness = \( \frac{\sum_{i=1}^{N}(X_{i}  \bar{X})^{3}/N} {s^{3}} \) where \(\bar{X}\) is the mean, s is the standard deviation and N is the number of pixels/voxels.

Kurtosis = \( \frac{\sum_{i=1}^{N}(X_{i}  \bar{X})^{4}/N}{s^{4}} \) where \(\bar{X}\) is the mean, s is the standard deviation and N is the number of pixels/voxels.
All features in this family are extracted from the raw intensities. 
Histogram
based 
 Num_Bins  N.A.  10 

Uses number of bins as input and the number of pixels in each bin would be the output.
All features in this family are extracted from the discretized intensities. 
Volumetric 
 Dimensions
Axis  2D:3D
x,y,z  3D
z 

Volume/Area (depending on image dimension) and number of voxels/pixels in the ROI.

Morphologic 

Elongation

Perimeter

Roundness

Eccentricity
 Dimensions
Axis  2D:3D
x,y,z  3D
z 

Elongation = \( \sqrt{\frac{i_{2}}{i_{1}}} \) where i_{n} are the second moments of particle around its principal axes.

Perimeter = \( 2 \pi r \) where r is the radius of the circle enclosing the shape.

Roundness = \( As/Ac = (Area of a shape)/(Area of circle) \) where circle has the same perimeter.

Eccentricity = \( \sqrt{1  \frac{a*b}{c^{2}}} \) where c is the longest semiprincipal axis of an ellipsoid fitted on an ROI, and a and b are the 2nd and 3rd longest semiprincipal axes of the ellipsoid.

Local Binary
Pattern (LBP)   Radius
Neighborhood  N.A.
2:4:8  N.A.
8 

The LBP codes are computed using N sampling points on a circle of radius R and using mapping table.

Grey Level
Cooccurrence
Matrix
(GLCM) 

Energy (Angular Second Moment)

Contrast (Inertia)

Joint Entropy

Homogeneity (Inverse Difference Moment)

Correlation

Variance

SumAverage

Variance

Auto
Correlation
 Num_Bins
Num_Directions
Radius
Dimensions
Offset
Axis  N.A.
3:13
N.A.
2D:3D
Individual/Average/Combined
x,y,z  10
13
2
3D
Average
z  For a given image, a Grey Level Cooccurrence Matrix is created and \( g(i,j) \) represents an element in matrix

Energy = \( \sum_{i,j}g(i, j)^2 \)

Contrast = \( \sum_{i,j}(i  j)^2g(i, j) \)

Joint Entropy = \( \sum_{i,j}g(i, j) \log_2 g(i, j) \)

Homogeneity = \( \sum_{i,j}\frac{1}{1 + (i  j)^2}g(i, j) \)

Correlation = \( \sum_{i,j}\frac{(i  \mu)(j  \mu)g(i, j)}{\sigma^2} \)

Sum Average = \( \sum_{i,j}i \cdot g(i, j) = \sum_{i,j}j \cdot g(i, j)\)(due to matrix symmetry)

Variance = \( \sum_{i,j}(i  \mu)^2 \cdot g(i, j) = \sum_{i,j}(j  \mu)^2 \cdot g(i, j)\) (due to matrix symmetry)

AutoCorrelation = \(\frac{\sum_{i,j}(i, j) g(i, j)\mu_t^2}{\sigma_t^2}\) where \(\mu_t\) and \(\sigma_t\) are the mean and standard deviation of the row (or column, due to symmetry) sums.
All features are estimated within the ROI in an image, considering 26connected neighboring voxels in the 3D volume. Note that the creation of the GLCM and its corresponding aforementioned features for all offsets are calculated using an existing ITK filter. The Individual option gives features for each individual offset, Average estimates the average across all offsets and assigns a single value for each feature and Combined combines the GLCM matrices generated across offsets and calculates a single set of features from this matrix. 
Grey Level
RunLength
Matrix
(GLRLM) 

SRE

LRE

GLN

RLN

LGRE

HGRE

SRLGE

SRHGE

LRLGE

LRHGE
 Num_Bins
Num_Directions
Radius
Dimensions
Axis
Offset
Distance_Range  N.A.
3:13
N.A.
2D:3D
x,y,z
Individual/Average/Combined
1:5  10
13
2
3D
z
Average
1  For a given image, a runlength matrix \( P(i; j)\) is defined as the number of runs with pixels of gray level i and run length j.

Short Run Emphasis (SRE) = \( \frac{1}{n_r}\sum_{i,j}^{N}\frac{p(i,j)}{j^2} \)

Long Run Emphasis (LRE) = \( \frac{1}{n_r}\sum_{j}^{N}p(i,j) \cdot j^2\)

Grey Level Nonuniformity (GLN) = \( \frac{1}{n_r}\sum_{i}^{M}\Big(\sum_{j}^{N}p(i,j) \Big)^2 \)

Run Length Nonuniformity (RLN) = \( \frac{1}{n_r}\sum_{j}^{N}\Big(\sum_{i}^{M}p(i,j) \Big)^2 \)

Low GreyLevel Run Emphasis (LGRE)= \( \frac{1}{n_r}\sum_{i}^{M}\frac{p_g(i)}{i^2} \)

High GreyLevel Run Emphasis (HGRE)= \( \frac{1}{n_r}\sum_{i}^{M}p_g(i) \cdot i^2 \)

Short Run Low GreyLevel Emphasis (SRLGE)= \(\frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j)}{i^2 \cdot j^2} \)

Short Run High GreyLevel Emphasis (SRLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot i^2 }{j^2}\)

Long Run Low GreyLevel Emphasis (LRLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot j^2 }{i^2} \)

Long Run High GreyLevel Emphasis (LRHGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}p(i,j) \cdot i^2 \cdot j^2 \)
All features are estimated within the ROI in an image, considering 26connected neighboring voxels in the 3D volume. Note that the creation of the GLRLM and its corresponding aforementioned features for all offsets are calculated using an existing ITK filter. The Individual option gives features for each individual offset, Average estimates the average across all offsets and assigns a single value for each feature and Combined combines the GLRLM matrices generated across offsets and calculates a single set of features from this matrix. 
Neighborhood
GreyTone
Difference
Matrix
(NGTDM) 

Coarseness

Contrast

Busyness

Complexity

Strength
 Num_Bins
Num_Directions
Dimensions
Axis
Distance_Range  N.A.
3:13
2D:3D
x,y,z
1:5  10
13
3D
N.A.
1 

Coarseness = \( \Big[ \epsilon + \sum_{i=0}^{G_{k}} p_{i}s(i) \Big]\)

Contrast = \( \Big[\frac{1}{N_{s}(N_{s}1)}\sum_{i}^{G_{k}}\sum_{j}^{G_{k}}p_{i}p_{j}(ij)^2\Big]\Big[\frac{1}{n^2}\sum_{i}^{G_{k}}s(i)\Big] \)

Busyness = \( \Big[\sum_{i}^{G_{k}}p_{i}s(i)\Big]\Big/ \Big[\sum_{i}^{G_{k}}\sum_{j}^{G_{k}}i p_{i}  j p_{j}\Big] \)

Complexity = \( \sum_{i}^{G_{k}}\sum_{j}^{G_{k}} \Big[ \frac{(ij)}{(n^{2}(p_{i}+p_{j}))} \Big] \Big[ p_{i}s(i)+p_{j}s(j) \Big]\)

Strength = \( \Big[\sum_{i}^{G_{k}}\sum_{j}^{G_{k}}(p_{i}+p_{j})(ij)^{2}\Big]/\Big[\epsilon + \sum_{i}^{G_{k}} s(i)\Big]\)
Where \(p_{i}\) is the probability of occurrence of a voxel of intensity i and \(s(i)\) represents the NGTDM value of intensity i calculated as: \( \sum │i  Ai│\). Ai indicates the average intensity of the surrounding voxels without including the central voxel.

Grey Level
SizeZone
Matrix
(GLSZM) 

SZE

LZE

GLN

ZSN

ZP

LGZE

HGZE

SZLGE

SZHGE

LZLGE

LZHGE

GLV

ZLV
 Num_Bins
Num_Directions
Radius
Dimensions
Axis
Distance_Range  N.A.
3:13
N.A.
2D:3D
x,y,z
1:5  10
13
2
3D
z
4  For a given image, a runlength matrix \( P(i; j)\) is defined as the number of runs with pixels of gray level i and run length j.

Small Zone Emphasis (SZE) = \( \frac{1}{n_r}\sum_{i,j}^{N}\frac{p(i,j)}{j^2} \)

Large Zone Emphasis(LZE) = \( \frac{1}{n_r}\sum_{j}^{N}p(i,j) \cdot j^2\)

GrayLevel Nonuniformity (GLN) = \( \frac{1}{n_r}\sum_{i}^{M}\Big(\sum_{j}^{N}p(i,j) \Big)^2 \)

ZoneSize Nonuniformity (ZSN) = \( \frac{1}{n_r}\sum_{j}^{N}\Big(\sum_{i}^{M}p(i,j) \Big)^2 \)

Zone Percentage (ZP) = \( \frac{n_{r}}{n_p} \) where \( n_r \) is the total number of runs and \( n_p \) is the number of pixels in the image.

Low GreyLevel Zone Emphasis (LGZE)= \( \frac{1}{n_r}\sum_{i}^{M}\frac{p_g(i)}{i^2} \)

High GreyLevel Zone Emphasis (HGZE)= \( \frac{1}{n_r}\sum_{i}^{M}p_g(i) \cdot i^2 \)

Short Zone Low GreyLevel Emphasis (SZLGE)= \(\frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j)}{i^2 \cdot j^2} \)

Short Zone High GreyLevel Emphasis (SZLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot i^2 }{j^2}\)

Long Zone Low GreyLevel Emphasis (LZLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot j^2 }{i^2} \)

Long Zone High GreyLevel Emphasis (LZHGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}p(i,j) \cdot i^2 \cdot j^2 \)
All features are estimated within the ROI in an image, considering 26connected neighboring voxels in the 3D volume. 