Conjoint measurement of perceived transparency and perceived contrast in variegated checkerboards

One fundamental question in vision research is how the retinal input is segmented into perceptually relevant variables. A striking example of this segmentation process is transparency perception, in which luminance information in one location contributes to two perceptual variables: the properties of the transparent medium itself and of what is being seen in the background. Previous work by Robilotto et al. (2002, 2004) suggested that perceived transparency is closely related to perceived contrast, but how these two relate to retinal luminance has not been established. Here we studied the relationship between perceived transparency, perceived contrast, and image luminance using maximum likelihood conjoint measurement (MLCM). Stimuli were rendered images of variegated checkerboards that were composed of multiple reflectances and partially covered by a transparent overlay. We systematically varied the transmittance and reflectance of the transparent medium and measured perceptual scales of perceived transparency. We also measured scales of perceived contrast using cut-outs of the transparency stimuli that did not contain any geometrical cues to transparency. Perceptual scales for perceived transparency and contrast followed a remarkably similar pattern across observers. We tested the empirically observed scales against predictions from various contrast metrics and found that perceived transparency and perceived contrast were equally well predicted by a metric based on the logarithm of Michelson or Whittle contrast. We conclude that judgments of perceived transparency and perceived contrast are likely to be supported by a common mechanism, which can be computationally captured as a logarithmic contrast.