Visual discrimination of textures with identical third-order statistics

We found a new class of two-dimensional random textures with identical third-order statistics that can be effortlessly discriminated. Discrimination is based on local "granularity" differences between these iso-trigon texture pairs. This is the more surprising since it is commonly assumed that texture granularity (grain) is determined by the power spectrum which, in turn, can be obtained from the second-order statistics. Because textures with identical third-order statistics must have identical second-order statistics (i.e., identical power spectra), visible texture granularity is not controlled by power spectra, and not even by third-order statistics.