Conjoint measurement of perceived transparency and perceived contrast in variegated checkerboards

Abstract

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.

Figure 1.

(A) Two transparencies rendered with different reflectance, otherwise identical in transmittance ($\alpha$) and luminance range in transparency. (B) Two episcotisters with equal opening $\alpha$ that, when rotated at high speed, will have equal physical transmittance. To an observer, the black one (low $t$) appears more transparent than the white one (high $t$).

Figure 2.

(A) Example set of stimuli and experimental task. The transparency's transmittance ($\alpha$) and luminance when opaque ($t$) were varied in 4 × 9 possible combinations. (B) In Experiment 1, the observer judged which of two transparencies look more transparent. (C) In Experiment 2, the observer judged which of the two cut-outs had higher contrast.

Figure 3.

Perceptual scales obtained by MLCM for perceived transparency (A) and perceived contrast (B) for one observer (O1). Markers indicate scale values; their error bars indicate their 95% confidence intervals. Continuous lines depict the prediction from the space-averaged logarithm of the Michelson contrast ($SAMLG$).

Figure 4.

Perceptual scales obtained by MLCM for perceived transparency (A) and perceived contrast (B) for all observers (O1 to O7, rows). Error bars indicate 95% confidence intervals. Continuous lines depict the prediction from the space-averaged logarithm of the Michelson contrast ($SAMLG$). Dashed red line in O1 illustrates stimuli that would be perceived equally transparent.

Figure 5.

Contrast metrics and their dependency on the transparency's luminance (x-axis) and physical transmittance ($\alpha$). Data plotted on the same format as Figure 4. Each panel shares the x-axis but not the y-axis, as each metric has a different range. See text for metrics formulae.

Figure 6.

Linking assumption between (asymmetric) matching and perceptual scales. (A) Experimental design of an asymmetric matching experiment. The transparent medium of the standard stimulus has one fixed transmittance (${\alpha }_{st}$) and a fixed number of luminances ($t_{st}$). The observer adjusts the luminance of the transparency of the test stimulus ($t_{test}$) for different levels of transmittance (${\alpha }_{test}$) of the test stimulus to match the perceived transparency of the test to that of the standard. (B) Internal scales relating luminance of the transparency (x-axis) and transmittance (panel variable) to perceived transmittance (y-axis). Perceived transmittance is computed as the space-average logarithm of Michelson contrast ($SAMLG$). The top panel shows a case where a perceptual match can be obtained between standard (square) and test (star). The bottom panel shows a case where only a partial match can be obtained (triangle; see text for explanation). (C) Data in a hypothetical matching experiment. The lines are derived as predictions from the scales in B. The dashed line indicates where the match for that ${\alpha }_{test}$ should be if a test stimulus with that luminance would have been included. Since that luminance is beyond the range of possible test luminances, the observer sets the test luminance to $t_{max}$, the maximum luminance (triangle).