# Perceptual Scales Predicted by Fisher Information Metrics

arXiv: https://arxiv.org/abs/2310.11759 · HTML: https://mlsanity.com/paper/2310.11759/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 51 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Optimal transport for Gaussian mixture models](https://mlsanity.com/paper/1710.07876/) (2017)
- [Texture Interpolation for Probing Visual Perception](https://mlsanity.com/paper/2006.03698/) (2020)
- [On the relation between statistical learning and perceptual distances](https://mlsanity.com/paper/2106.04427/) (2021)
- [Bayesian Modeling of Motion Perception using Dynamical Stochastic Textures](https://mlsanity.com/paper/1611.01390/) (2016)

## Built on by (most cited first, 3 of 3)

- [Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction](https://mlsanity.com/paper/2502.00168/) (2025)
- [Multidimensional Observer Model and Perceptual Dimensions of Human Image Quality Assessment](https://mlsanity.com/paper/2609.38487/) (2026)
- [JLD: Perceptual Distance Through A Jacobian Lens](https://mlsanity.com/paper/2610.05967/) (2026)

## Abstract (arXiv)

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.