Fig. 2

Sets of synthetic (256 times 256 pixel) test images arranged in columns where the first image is the one without noise and the second and third images were created by adding independent Gaussian noise of mean zero and a standard deviation of 10 and 50% of the maximal pixel intensity to the corresponding image in the top row. The images are numbered to provide for straightforward references below. Note that there are pronounced motif-based and translational pseudo-symmetries of the first kind in the test images #7 to #9. (In the two noisy images of this series, i.e., #8 and #9, as well as in all noisy images of the other three series, there are of course pseudo-symmetries of the second kind due to the addition of noise to the noise-free images in the top row.) Because image #10 features a metric specialization (see footnote 3), images #11 and #12 feature pronounced translational pseudo-symmetries of a “special” (see footnote 2) kind. Genuine pseudo-symmetries, the effects of added Gaussian noise on genuine symmetries, and the metric specialization lead to a somewhat “squarish” visual appearance of the images #7 to #12 and present challenges to lattice parameter extraction algorithms