Excluded Radiomic Features¶
Some commonly know features are not supported (anymore) in PyRadiomics. These features are listed here, so as to provide a complete overview, as well as argumentation for why these features are excluded from PyRadiomics
Excluded GLCM Features¶
For included features and class definition, see Gray Level Co-occurrence Matrix (GLCM) Features.
1. Sum Variance¶
Sum Variance is a measure of heterogeneity that places higher weights on neighboring intensity level pairs that deviate more from the mean.
This feature has been removed, as it is mathematically identical to Cluster Tendency (see
getClusterTendencyFeatureValue()
).
The mathematical proof is as follows:
- As defined in GLCM, \(p_{x+y}(k) = \sum^{N_g}_{i=1}\sum^{N_g}_{j=1}{p(i,j)},\text{ where }i+j=k, k \in \{2, 3, \dots, 2N_g\}\)
- Starting with cluster tendency as defined in GLCM:
Note
Because inside the sum \(\sum^{2N_g}_{k=2}\), \(k\) is a constant, and so are \(\mu_x\) and \(\mu_y\), \(\big(k-(\mu_x+\mu_y)\big)^2\) is constant and can be taken outside the inner sum \(\sum^{N_g}_{i=1}\sum^{N_g}_{j=1}\).
- Using (1.) and (2.)
- As defined in GLCM, \(p_x(i) = \sum^{N_g}_{j=1}{P(i,j)}\) and \(\mu_x = \sum^{N_g}_{i=1}{p_x(i)i}\), therefore \(\mu_x = \sum^{N_g}_{i=1}\sum^{N_g}_{j=1}{P(i,j)i}\)
- Similarly as in (4.), \(\mu_y = \sum^{N_g}_{j=1}\sum^{N_g}_{i=1}{P(i,j)j}\)
- Using (4.) and (5.), \(\mu_x\) and \(\mu_y\) can then be combined as follows:
- Combining (3.) and (6.) yields the following formula:
Q.E.D