Table 1. Definitions of features.

Variable	Definition	Mathematical Formulaea
Minkowski functionals
Area	Summed designated (white) pixels.	Ai = pi
Perimeter	Summed pixel edges at the boundary between black and white pixels.	Ui = -4pi + 2ei
Perimeter 1b	Perimeter at grey-scale threshold 1 (i.e. all pixels are white). The edge length (or contour) of the segmented region of interest.	U0 = -4p0 + 2e0
Genus	Number of regions of connectedc white pixels minus the number of completely enclosed regions of black pixels.	χi = pi − ei + vi
Size
Total Area	Summed area at grey-scale threshold 1 (i.e. all pixels are white) for all slices of the tumour.	$T{A}_k={\displaystyle \sum _{j=1}^J}{\left(A_0\right)}_j$
Total Perimeter	Summed perimeter at grey-scale threshold 1 for all slices of the tumour. The summed edge length (or contour) of the segmented regions of interest from all slices of the tumour.	$T{P}_k={\displaystyle \sum _{j=1}^J}{\left(U_0\right)}_j$
Signal intensity
Mean	The mean raw signal intensity of all pixels from the segmented regions of interest from all slices of the tumour.	${\mu }_k=\frac{1}{T{A}_k}{\displaystyle \sum _{p=1}^{T{A}_k}}S{I}_P$
Standard Deviation	The standard deviation of the raw signal intensity of all pixels from the segmented regions of interest from all slices of the tumour.	${\sigma }_k=\sqrt{\frac{1}{T{A}_k}{\displaystyle \sum _{p=1}^{T{A}_k}}\left(S{I}_P- {\mu }_k\right)}$
Maximum	The maximum raw signal intensity of all pixels from the segmented regions of interest from all slices of the tumour.	${\wedge }_k= S{I}_{\left(T{A}_k\right)}$
Minimum	The minimum raw signal intensity of all pixels from the segmented regions of interest from all slices of the tumour.	${\vee }_k= S{I}_{\left(1\right)}$

^a Where p_i, e_i, and v_i are the numbers of pixels, edges, and vertices at grey-scale threshold i, respectively; j is the number of image slices through the tumour; k is the individual tumour; SI_p is the raw signal intensity for pixel p.

^b A segmented region of interest was displayed as a binary combination of black and white pixels at 11 different grey-scale thresholds (Fig 1). Perimeter 1 in Table 1 is the perimeter at grey-scale threshold 1, from a total of 11. Eleven different grey-scale thresholds were also used for genus. Ten different grey-scale thresholds were used for area because the 1^st value ≡ 1 when normalized and so was excluded.

^c Two pixels are connected if they are nearest neighbors or next-nearest neighbors to each other.