Table 1 Definitions of QUS measurements and their mathematical formulas
QUS measurements computed from a grayscale histogram | Mathematical formulas | |
First order statistics | ||
Echogenicity Mean (\( \overline{\mathrm{x}} \)) | Mean of grayscale values of micro pixels encompassed within the ROI (from 0 (black) to 255 (white) inclusively). | \( \overline{\mathrm{x}} = {\displaystyle {\sum}_{\mathrm{x}=1}^{\mathrm{M}}}{\displaystyle {\sum}_{\mathrm{y}=1}^{\mathrm{N}}}\frac{\mathrm{I}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{M}\mathrm{N}} \) |
Variance (σ2) | Dispersion around the mean of the grayscale values of micro pixels encompassed within the ROI. | \( {\upsigma}^2=\frac{{\displaystyle {\sum}_{\mathrm{X}=1}^{\mathrm{M}}}{\displaystyle {\sum}_{\mathrm{y}-1}^{\mathrm{N}}}{\left\{\mathrm{I}\left(\mathrm{x},\mathrm{y}\right)-\overline{\mathrm{x}}\right\}}^2}{\mathrm{M}\mathrm{N}} \) |
Skewness (Sk) | Reflects the asymmetry of the grey level frequency distribution curve around its mean. A high coefficient (in absolute value) translates in a shifted distribution relative to the mean, while a zero coefficient indicates a symmetric distribution. In a positively skewed distribution, pixels intensities are biased toward lower values (shifted distribution to the left). In a negatively skewed distribution, pixels intensities are biased toward higher values (shifted distribution to the right). | \( {\mathrm{S}}_{\mathrm{k}}=\frac{1}{\mathrm{M}\mathrm{N}}\frac{{\displaystyle {\sum}_{\mathrm{x}=1}^{\mathrm{M}}}{\displaystyle {\sum}_{\mathrm{y}=1}^{\mathrm{N}}}{\left\{\mathrm{I}\left(\mathrm{x},\mathrm{y}\right)-\overline{\mathrm{x}}\right\}}^3}{\upsigma^3} \) |
Kurtosis (Kt) | Reflects the flatness of the grey level frequency distribution curve around its mean. A diffuse distribution will translate in a lower kurtosis value. Distribution concentrated around its mean will translate in a higher kurtosis value. | \( {\mathrm{K}}_{\mathrm{t}}=\frac{1}{\mathrm{M}\mathrm{N}}\frac{{\displaystyle {\sum}_{\mathrm{x}=1}^{\mathrm{M}}}{\displaystyle {\sum}_{\mathrm{y}=1}^{\mathrm{N}}}{\left\{\mathrm{I}\left(\mathrm{x},\mathrm{y}\right)-\overline{\mathrm{x}}\right\}}^4}{\upsigma^4} \) |
Entropy (E) | Reflects disorder in a ROI. It considers the number of grey levels in a ROI, and the proportions of each grey level. There is an increased entropy when multiple grey level values are present in the ROI. Vice-versa, entropy equals zero if an image has a single grey level value for all its micro pixels. | \( \mathrm{E}=-{\displaystyle {\sum}_{\mathrm{i}=0}^{255}}{\displaystyle {\sum}_{\mathrm{j}=0}^{255}}\mathrm{p}\left(\mathrm{i},\mathrm{j}\right){ \log}_2\left(\mathrm{p}\left(\mathrm{i},\mathrm{j}\right)\right) \) |
QUS Measurements computed from a co-occurence matrix | ||
Texture parameters | ||
Contrast (I con ) | Contrast measures the difference of intensity between the grey level values of neighboring micro pixels. There is a reduced contrast in a constant image with lesser local variations of the grey level intensities. On the contrary, contrast is higher in an image containing a large amount of local sudden variations in the values of grey level intensities. | \( {\mathrm{I}}_{\mathrm{con}}={\displaystyle {\sum}_{\mathrm{i}=0}^{255}}{\displaystyle {\sum}_{\mathrm{j}=1}^{255}}{\left|\mathrm{i}-\mathrm{j}\right|}^2\ \mathrm{p}\left(\mathrm{i},\mathrm{j}\right) \) |
Energy (I eng ) | Energy is linked to the regularity and consistency of the patterns in an image. High energy is measured in a constant and steady picture. Vice-versa, low energy is found in an image in which the contacts of grey level values are diverse, uncoordinated and random. | \( {\mathrm{I}}_{\mathrm{eng}}={\displaystyle {\sum}_{\mathrm{i}=0}^{255}}{\displaystyle {\sum}_{\mathrm{j}=0}^{255}}\mathrm{p}{\left(\mathrm{i},\mathrm{j}\right)}^2 \) |
Homogeneity (I hmg ) | Homogeneity is increased in an image with a large number of pixels having the same grey level values, with little grayscale transition (i.e., increased when there is a large area of the same color). | \( {\mathrm{I}}_{\mathrm{hmg}}={\displaystyle {\sum}_{\mathrm{i}=0}^{255}}{\displaystyle {\sum}_{\mathrm{j}=0}^{255}}\frac{1}{1+{\left(\mathrm{i}-\mathrm{j}\right)}^2}\mathrm{p}\left(\mathrm{i},\mathrm{j}\right) \) |