Perceived contrast of gratings and plaids: non-linear summation across oriented filters

Plaids composed of two orthogonal sine-wave gratings appeared to be of lower contrast than single gratings of the same Michelson luminance contrast. This effect for plaids was obtained at all spatial frequencies (1-16 c/deg) and contrast levels (2-32%). Contrast-matching data plotted as a function of the angle between plaid components (0-90 deg) and as a function of spatial frequency and standard contrast level were consistent with a model in which the response of each orientation-tuned spatial frequency channel is a threshold-corrected power function of contrast, and is followed by quadratic summation of responses across all channels. The best-fitting contrast-response exponent in the main experiment was 0.63. Analysis of several other data-sets suggested a slightly higher value, 0.80. The same model gave a good account of contrast-matching between simple and compound (two-component) one dimensional gratings, accounting in particular for the apparent increase in contrast summation exponent at low contrasts reported by Quick, Hamerly and Reichert [(1976) Vision Research, 16, 351-355]. The model can, with one further assumption, account for the finding that contrast-matching between sine-wave and square-wave gratings depended only on the amplitude at the fundamental frequency. Comparison with contrast discrimination studies suggests that internal noise (variance of a channel's contrast-response) is not constant, but increases approximately in proportion to the mean response.