Table 1. Results of the hkaAICnorm MATLAB script on the noise-free pattern that underlies Fig. 1 ▸ for geometric model selections by G-AIC value minimization using inequality (9b).

Plane symmetry group to which the image data have been symmetrized	Sum of squared residuals of complex Fourier coefficients	Sum of squared residuals of Fourier coefficient amplitudes	No. of Fourier coefficients in the geometric model of the image data
p2	0.0042	none	956
p1m1	1.8799	0.0052	937
p11m	1.8642	0.0052	937
p1g1	0.0094	0.0052	934
p11g	0.0081	0.0052	934
c1m1	0.0103	0.0053	924
c11m	0.0110	0.0053	924
p3	2.5290	1.3339	954
p2gg	0.0096	0.0052	931
c2mm	0.0119	0.0053	924
p4	0.0065	0.0021	948
p4mm	1.9558	0.0063	918
p4gm	0.0102	0.0061	912