DEFINITION OF TEXTURE FEATURES
Input volume: Volume of interest V (x, y, z) with isotropic voxel size. The
necessity for isotropically resampling V to a given voxel dimension prior to
texture analysis results from the fact that: 1) Global features are computed
from histograms counting the number of gray-levels in 3D space; and 2) all
higher-order texture measurements explicitly or implicitly involve a distance
parameter in the matrix computation (GLCM, GLRLM, GLSZM and NGTDM).
For this parameter to be meaningful in 3D space and in order for the orientation
dependence of the tumour to be minimized, isotropic resolution is required.
Global texture features (first-order gray-level statistics).
Let P define the first-order histogram of a volume V (x, y, z) with isotropic voxel
size. P (i) represents the number of voxels with gray-level i, and N
g
represents
the number of gray-level bins set for P . The i
th
entry of the normalized his-
togram is then defined as:
p(i) =
P (i)
P
N
g
i=1
P (i)
.
The Global texture features are then defined as:
• Variance:
σ
2
=
N
g
X
i=1
(i − µ)
2
p(i)
• Skewness:
s = σ
−3
N
g
X
i=1
(i − µ)
3
p(i)
• Kurtosis
k = σ
−4
N
g
X
i=1
(i − µ)
4
p(i)
− 3
Gray-Level Co-occurence Matrix (GLCM) texture features.
Let P define the GLCM of a quantized volume V (x, y, z) with isotropic voxel
size. P(i, j) represents the number of times voxels of gray-level i were neighbours
with voxels of gray-level j in V , and N
g
represents the pre-defined number of
quantized gray-levels set in V . Only one GLCM of size N
g
× N
g
is computed
per volume V by simultaneously adding up the frequency of co-occurences of all
voxels with their 26-connected neighbours in 3D space, with all voxels (including
1
