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.