An internal representation of contrast based on magnitude estimation compatible with discrimination

The relationship between physical and perceived magnitude is a longstanding question that remains unsolved. This relationship could be characterized by an internal representation that could be modeled by a function that maps physical intensity into perceived intensity (transducer) and some perceptual variability (noise). This internal representation has been constrained by studies using discrimination tasks, but the challenge is that for a given pattern of discriminability, there are infinite combinations of transducers with noise that are compatible. Recently, Zhou, Duong and Simoncelli (2022) have proposed that magnitude estimation tasks could, not only constraint, but fully specify the internal representation being the transducer the mean estimation response and the noise the standard deviation. Under this proposal, delta (δ), the slope of the transducer at each intensity divided by the noise, should be consistent with the discriminability pattern obtained from discrimination tasks. To test this framework, five participants conducted a discrimination and a magnitude estimation task for contrast. We used contrast because discrimination experiments have shown a nonlinearity at low intensities—the pedestal effect—which should be revealed by δ obtained from magnitude estimation. Our results for the discrimination task replicate the pedestal effect. For magnitude estimation, we found a linear or slightly compressive behavior for the transducer and an expansive behavior for the noise. Notably, δ estimated from magnitude estimation showed a pedestal effect, consistent with the discrimination task. Overall, our findings suggest that magnitude estimation is a valid procedure to characterize the internal responses.