In the visualization panes, the "Z" axis is the center; and "Y" and "X" are to its left and right, respectively. "Z" represents the Axial view for RAI-to-LPS images.
Feature Family | Specific
Features | Parameter
Name | Range | Default | Description, Formula and Comments |
First
Order
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.
|
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.
|
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 semi-principal axis of an ellipsoid fitted on an ROI, and a and b are the 2nd and 3rd longest semi-principal 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
Co-occurrence
Matrix
(GLCM) |
-
Energy
-
Contrast
-
Entropy
-
Homogeneity
-
Correlation
-
Variance
-
SumAverage
-
Variance
-
Auto
Correlation
| Num_Bins
Num_Directions
Radius
Dimensions
Offset
Axis | N.A.
3:13
N.A.
2D:3D
Average/Individual
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 = \( \sum_{i,j}(i - j)^2g(i, j) \)
-
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 summetry)
-
Variance = \( \sum_{i,j}(i - \mu)^2 \cdot g(i, j) = \sum_{i,j}(j - \mu)^2 \cdot g(i, j)\) (due to matrix summetry)
-
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 26-connected neighboring voxels in the 3D volume.
|
Grey Level
Run-Length
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
Average/Individual
1:5 | 10
13
2
3D
z
Average
1 | For a given image, a run-length 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 Non-uniformity (GLN) = \( \frac{1}{n_r}\sum_{i}^{M}\Big(\sum_{j}^{N}p(i,j) \Big)^2 \)
-
Run Length Non-uniformity (RLN) = \( \frac{1}{n_r}\sum_{j}^{N}\Big(\sum_{i}^{M}p(i,j) \Big)^2 \)
-
Low Grey-Level Run Emphasis (LGRE)= \( \frac{1}{n_r}\sum_{i}^{M}\frac{p_g(i)}{i^2} \)
-
High Grey-Level Run Emphasis (HGRE)= \( \frac{1}{n_r}\sum_{i}^{M}p_g(i) \cdot i^2 \)
-
Short Run Low Grey-Level Emphasis (SRLGE)= \(\frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j)}{i^2 \cdot j^2} \)
-
Short Run High Grey-Level Emphasis (SRLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot i^2 }{j^2}\)
-
Long Run Low Grey-Level Emphasis (LRLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot j^2 }{i^2} \)
-
Long Run High Grey-Level 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 26-connected neighboring voxels in the 3D volume. |
Neighborhood
Grey-Tone
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 = \( \Big[\frac{1}{N_{s}(N_{s}-1)}\sum_{i}^{G_{k}}\sum_{j}^{G_{k}}p_{i}p_{j}(i-j)^2\Big]\Big[\frac{1}{n^2}\sum_{i}^{G_{k}}s(i)\Big] \)
-
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 = \( \sum_{i}^{G_{k}}\sum_{j}^{G_{k}} \Big[ \frac{(|i-j|)}{(n^{2}(p_{i}+p_{j}))} \Big] \Big[ p_{i}s(i)+p_{j}s(j) \Big]\)
-
Strength = \( \Big[\sum_{i}^{G_{k}}\sum_{j}^{G_{k}}(p_{i}+p_{j})(i-j)^{2}\Big]/\Big[\epsilon + \sum_{i}^{G_{k}} s(i)\Big]\)
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
Size-Zone
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 run-length 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) = \( \frac{1}{n_r}\sum_{j}^{N}p(i,j) \cdot j^2\)
-
Gray-Level Nonuniformity (GLN) = \( \frac{1}{n_r}\sum_{i}^{M}\Big(\sum_{j}^{N}p(i,j) \Big)^2 \)
-
Zone-Size 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 Grey-Level Zone Emphasis (LGZE)= \( \frac{1}{n_r}\sum_{i}^{M}\frac{p_g(i)}{i^2} \)
-
High Grey-Level Zone Emphasis (HGZE)= \( \frac{1}{n_r}\sum_{i}^{M}p_g(i) \cdot i^2 \)
-
Short Zone Low Grey-Level Emphasis (SZLGE)= \(\frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j)}{i^2 \cdot j^2} \)
-
Short Zone High Grey-Level Emphasis (SZLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot i^2 }{j^2}\)
-
Long Zone Low Grey-Level Emphasis (LZLGE) = \( \frac{1}{n_r}\sum_{i}^{M}\sum_{j}^{N}\frac{p(i,j) \cdot j^2 }{i^2} \)
-
Long Zone High Grey-Level 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 26-connected neighboring voxels in the 3D volume.
|