Table 1: $\chi ^2$ for the three Minkowski functionals for different resolutions and thresholds.
Resolution Area (%) $\chi_{\rm data}^2$ Degrees of freedom $\langle \chi^2 \rangle$ $\sqrt{\langle (\chi^2 -\langle \chi^2 \rangle)^2\rangle}$ $P(\chi^2\le \chi_{\rm data}^2)$

32 100 43.62 33 33.55 10.05 0.868

64 100 44.39 39 40.55 10.33 0.679

128 32 50.59 45 46.29 10.79 0.688

32, 64 100, 100 85.14 72 73.88 14.29 0.804

32, 64, 128 100, 100, 32 134.05 117 120.30 18.40 0.791

**Table 1:** $\chi ^2$ for the three Minkowski functionals for different resolutions and thresholds.
Resolution	Area (%)	$\chi_{\rm data}^2$	Degrees of freedom	$\langle \chi^2 \rangle$	$\sqrt{\langle (\chi^2 -\langle \chi^2 \rangle)^2\rangle}$	$P(\chi^2\le \chi_{\rm data}^2)$
32	100	43.62	33	33.55	10.05	0.868
64	100	44.39	39	40.55	10.33	0.679
128	32	50.59	45	46.29	10.79	0.688
32, 64	100, 100	85.14	72	73.88	14.29	0.804
32, 64, 128	100, 100, 32	134.05	117	120.30	18.40	0.791

Source LaTeX | All tables | In the text