Wallach’s ratio principle under affine representation

Motivated by Heller (2014) and supplementing the results found there, the main objective of this paper is to study the near-miss to Wallach’s ratio principle and the near-miss to illumination invariance, assuming more general psychophysical representations than in the previous works. We employ a model-creation technique founded on functional equations to study the affine and gain-control type representations of these phenomena, respectively.