When an undulating surface bearing a painted texture is illuminated the resulting shading pattern produces in-phase modulations of the mean luminance (LM) and luminance amplitude (AM) of the texture. Experimentally, in-phase combinations of LM and AM (LM+AM) are seen as undulating surfaces whereas anti-phase combinations (LM-AM) are more ambiguous; being seen as undulating when presented alone but as flat when presented in a plaid with LM+AM. AM is a second-order cue and its influence on shape-from-shading can be explained with a bottom-up layer decomposition model containing second-order mechanisms. However, the role of second-order vision in layer decomposition has not been established. If second-order vision is involved in layer decomposition then the perceptual differences between LM+AM and LM-AM should depend on the properties of the carrier texture in a way that is consistent with the known properties of second-order vision. Here we find a preference for carrier frequencies 3 octaves above the modulation frequency and take this as an indication that second-order (filter-rectify-filter) mechanisms are involved in processing our LM/AM mixes. We introduce a modified model which takes into account the selectivity of second-order vision for carrier frequency.
Sun, P., & Schofield, A. (2011). The efficacy of local luminance amplitude in disambiguating the origin of luminance signals depends on carrier frequency: Further evidence for the active role of second-order vision in layer decomposition. Vision Research, 51(5), 496-507. https://doi.org/10.1016/j.visres.2011.01.008