Weber–Fechner behavior in symmetry perception?

The literature contains several allusions to the idea that detection of (mirror) symmetry in the presence of noise follows the Weber–Fechner law. This law usually applies to first-order structures, such as length, weight, or pitch, and it holds that just-noticeable differences in a signal vary in proportion to the strength of the signal. Symmetry, however, is a higher order structure, and this theoretical note starts from the idea that, in noisy symmetry, the regularity-to-noise ratio defines the strength of the signal to be considered. We argue that the detectability of the symmetry follows a psychophysical law that also holds for Glass patterns. This law deviates from the Weber–Fechner law in that it implies that, in the middle range of noise proportions, the sensitivity to variations in the regularity-to-noise ratio is disproportionally higher than in both outer ranges