Table 4 Texture features considered, together with their significance, equations and models.
From: Texture-based markers from structural imaging correlate with motor handicap in Parkinson’s disease
Feature | Description | Equation |
|---|---|---|
First-order statistics | ||
Mean | Mean image grey level values | |
SD | Standard deviation of grey level values | |
Kurtosis (Kurt) | Kurtosis is a measure of whether the data are heavy-tailed or light-tailed, relative to a normal distribution. Positive kurtosis indicates a peaked distribution, while negative kurtosis indicates a flat distribution | \(\mathrm{Kurt}=\mathrm{E}\left[{\left(\frac{\mathrm{X}-\mathrm{Mean}}{\mathrm{SD}}\right)}^{4}\right]\) |
Skewness (Skew) | Skewness quantifies the lack of symmetry: it is zero for a symmetric distribution and negative for left-skewed data | \(\mathrm{Skew}=\mathrm{E}\left[{\left(\frac{\mathrm{X}-\mathrm{Mean}}{\mathrm{SD}}\right)}^{3}\right]\) |
Second-order statistics | ||
Homogeneity contrast (Cont) | Uniformity of texture intensity (a measure of the closeness of the distribution of elements in the co-occurrence matrix) Contrast represents the degree to which the texture intensity levels differ between voxels (i.e. local intensity variations). It will favour contributions from p(i,j) away from the diagonal | \(\mathrm{Homogeneity}= \sum_{\mathrm{i}=0}^{\mathrm{G}-1}\sum_{\mathrm{j}=0}^{\mathrm{G}-1}{(\mathrm{P}(\mathrm{i},\mathrm{j}))}^{2}\) \(\mathrm{Contrast}= \sum_{\mathrm{i}=0}^{\mathrm{G}-1}\sum_{\mathrm{j}=0}^{\mathrm{G}-1}{(\mathrm{i}-\mathrm{j})}^{2}\cdot \mathrm{P}(\mathrm{i},\mathrm{j})\) |
Entropy (Ent) | Entropy represents the degree of uncertainty (a measure of randomness) | \(\mathrm{Entropy}=-{\sum }_{\mathrm{i}=0}^{\mathrm{G}-1}{\sum }_{\mathrm{j}=0}^{\mathrm{G}-1}\mathrm{P}\left(\mathrm{i},\mathrm{j}\right)\cdot \mathrm{log}(\mathrm{P}(\mathrm{i},\mathrm{j}))\) |
Correlation (Corr) | Correlation represents the degree of mutual dependency between pixels | \(\mathrm{Correlation}={\sum }_{\mathrm{i}=0}^{\mathrm{G}-1}{\sum }_{\mathrm{j}=0}^{\mathrm{G}-1}\frac{\left\{\mathrm{i}\cdot \mathrm{j}\right\}\cdot \mathrm{P}\left(\mathrm{i},\mathrm{j}\right)-\left\{{\upmu }_{\mathrm{x}}\cdot {\upmu }_{\mathrm{y}}\right\}}{{\upsigma }_{\mathrm{x}}\cdot {\upsigma }_{\mathrm{y}}}\) |
Sum of squares (SumSqr) | Sum of squares also called variance gives a high weighting to elements that differ from the average value | \(\mathrm{SumSQR}=\sum_{\mathrm{i}=0}^{\mathrm{G}-1}\sum_{\mathrm{j}=1}^{\mathrm{G}-1}(\mathrm{i}-\upmu )^{2}\mathrm{P}(\mathrm{i},\mathrm{j})\) |
Sum average (SumA) Sum variation (SumV) | Sum average measures the relationship between occurrences of pairs with lower intensity values and occurrences of pairs with higher intensity values. Quantifies brightness Sum variation represents the global variation in the sum of the grey-levels of voxel-pairs distribution | \(\mathrm{SumAvg}=\sum_{\mathrm{I}=1}^{2\mathrm{G}}\mathrm{i}{\cdot \mathrm{P}}_{\mathrm{x}+\mathrm{y}}(\mathrm{j})\) \(\mathrm{SumV}=\sum_{\mathrm{I}=1}^{2\mathrm{G}}{\left(\mathrm{i}-\mathrm{SumAvg}\right)}^{2}{\cdot \mathrm{P}}_{\mathrm{x}+\mathrm{y}}(\mathrm{i})\) |
Inverse difference moment (IDM) | The IDM corresponds to small contributions from in-homogeneous areas (i ̸ = j). The value is low for in-homogeneous images and relatively high for homogeneous images | \(\mathrm{IDM}= \sum_{\mathrm{i}=0}^{\mathrm{G}-1}\frac{\mathrm{P}\left(\mathrm{i},\mathrm{j}\right)}{1+{\left(i-j\right)}^{2}}\) |
