Perceptual Scales Predicted by Fisher Information Metrics
Jonathan Vacher, Pascal Mamassian
TL;DR
The paper addresses how perceptual scales arise when observers evaluate high-dimensional stimuli and develops a framework linking the scale to Fisher information through a univariate transduction function. It derives the key relation $\psi(s) \propto \int_{s_{\text{init}}}^s \sqrt{\mathcal{I}_S(t)} \; dt$ and demonstrates that, under constant internal FI, the perceptual scale captures the information carried by the stimulus about the internal representation. The authors test these predictions with stochastic textures modeled as Gaussian random fields and with naturalistic texture interpolations, showing that the perceptual scale is largely driven by the stimulus power spectrum, though higher-order texture statistics can produce deviations. They introduce the Area Matching Score to quantify perceptual-geometry alignment and discuss implications for measuring perceptual distances and the geometry of images, offering a path toward neurometric validation and richer perceptual metrics.
Abstract
Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the perceptual scale of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured perceptual scale corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the perceptual scale is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of perceptual scale is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.