Characterizing the internal representation of contrast through magnitude estimation.
Cristina Rodríguez-Arribas, Joan López‐Moliner, Daniel Linares · Journal of Vision · 2025
The relationship between physical and perceived magnitude can be modeled through an internal representation that includes a transducer function mapping physical intensity into perceived intensity and noise. However, characterizing this internal representation remains elusive. Discrimination experiments aim to infer this representation by measuring discrimination sensitivity across a range of intensities. However, since sensitivity reflects the slope of the transducer divided by noise, any internal representation where this ratio matches the observed sensitivity pattern is consistent with the data. In contrast, magnitude estimation experiments could, in principle, resolve this ambiguity. The mean of intensity judgments can represent the transducer, while the standard deviation can quantify the noise. This approach to identify the internal representation, however, remains largely unexplored, as magnitude estimation studies have focused on recovering the transducer, neglecting the role of noise. In our study, eleven participants performed a magnitude estimation experiment for contrast perception at low contrast levels. We fitted the responses of each participant to different models of the hypothetical internal representation, combining various functional forms for the transducer and the noise. We found that the best model for all participants included a sigmoidal transducer and a sigmoidal noise. Assuming that magnitude estimation can capture the internal representation, sensitivity, derived as the slope of transducer divided by noise, should align with sensitivity directly obtained from discrimination experiments. To test this, we measured sensitivity in the same participants using a discrimination task and compared it to sensitivity calculated from magnitude estimation. We found that both methods estimated similar sensitivities both consistent with the pedestal effect, a well-known non-linearity observed in discrimination experiments, but never revealed previously with magnitude estimation. Critically, we found that the location of the pedestal effect estimated from both methods correlated across participants. These findings highlight the potential of magnitude estimation to characterize internal representations.