What's constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns

"Contrast constancy" refers to the ability to perceive objects as maintaining a constant contrast independent of size or distance. When tested with high contrast sinusoidal gratings, contrast constancy has been shown to hold for a wide range of spatial frequencies, suggesting that sensitivity is constant across the spectrum at suprathreshold. In this study, we show that contrast constancy also holds for relatively broadband patterns. We describe how the frequency spectra of such functions change as the patterns scale in size. In particular, we emphasize how these changes in the spectra depend on whether the functions are localized (coherent phase) or spatially distributed (incoherent phase). In Fourier terms, the scaling properties depend on the phase spectra of the patterns. Contrast constancy is shown to hold for both localized Gabor patches (coherent phase spectra) and bandpass noise patterns (incoherent phase spectra). Constancy holds over a wide range of suprathreshold contrasts; in fact, matching is quite accurate as soon as the pattern is suprathreshold. These results are explained with a model in which mechanism bandwidths increase with frequency (constant in octaves) and peak spectral sensitivity is equal across frequency out to around 16 c/deg. In the case of the Gabor stimuli, perceived contrast is assumed to be mediated by a mechanism centered on the patch. For the bandpass noise, contrast is determined by the average response of units distributed across the stimulus. This model can account for the matching data without assuming that the contrast-response gain of the underlying channels changes with spatial frequency. Neither does the model assume "response pooling". In addition to explaining the experimental results, the model also predicts that perceived contrast will be approximately constant across scale for scenes whose spectra fall as 1/f, as is typical of natural scenes.