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Perceptual Scales Predicted by Fisher Information Metrics
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Measures perceptual scales of spatial frequency, orientation and texture interpolations via difference scaling (MLDS) and tests predictions from a Fisher-information-based probabilistic observer model whose transduction function is tied to the generative model's power spectrum.
Problem
Perceptual scales for fundamental physical variables (spatial frequency, orientation) and for high-dimensional naturalistic textures have not been measured or linked to probabilistic theories of perception; it is unclear how univariate Bayesian observer theories relate to high-dimensional image stat
Approach
Shows that the perceptual scale (transduction function) equals the square root of Fisher information integrated over the stimulus, so predictions can be computed from the generative model (Gaussian random fields, Gaussian VGG-19 feature statistics, pixels, wavelets) and compared with MLDS measurements, using a new Area Matching Score.
Key results
- On Gaussian random field textures, the GRF/power-spectrum prediction gives an average AMS of 0.92 ± 0.69 and matches the logarithmic spatial frequency scale.
- The pixel-only assumption predicts essentially linear behavior and scores near 0, while wavelet and VGG-19 assumptions often overestimate sensitivity (average scores above 1).
- For the conflicting-prediction texture pairs, the GRF assumption predicts late sensitivity but humans show early sensitivity with late saturation; only pair11 under the wavelet assumption scores near ideal.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the GRF (auto-correlation/power spectrum) measurement assumption to predict perceptual scales | Perceptual-scale prediction for naturalistic texture pairs · Early- and late-sensitivity texture pairs | AMS: 0.92 \pm 0.69 | Helped |
| Use the GRF measurement assumption rather than alternative measurement assumptions | Perceptual-scale prediction for naturalistic texture pairs · Conflicting-prediction pairs (pair11 and pair12) | AMS | Hurt |
| Use wavelet measurements to predict the perceptual scale | Perceptual-scale prediction for naturalistic textures · pair11 | AMS: close to 1 | Helped |
| Use single-pixel distribution measurements to predict the perceptual scale | Perceptual-scale prediction for naturalistic textures · Naturalistic texture pairs | AMS: close to 0 | No clear effect |
| Use wavelet or VGG-19 measurements to predict the perceptual scale | Perceptual-scale prediction for naturalistic textures · Naturalistic texture pairs | AMS: above 1 | Hurt |
| Normalize textures along the path to the pair's average power spectrum (ablation) | Naturalistic texture pairs · Additional power-spectrum-normalization experiment | discriminability | Hurt |
| Predict the perceptual scale from the Fisher information of the image power spectrum | Perceptual-scale prediction for Gaussian random field textures · Spatial frequency mode | perceptual scale alignment | Helped |
| Predict the perceptual scale from the Fisher information of the image power spectrum | Perceptual-scale prediction for Gaussian random field textures · Spatial frequency bandwidth | perceptual scale alignment | Hurt |
| Predict the perceptual scale from the Fisher information of the image power spectrum | Perceptual-scale prediction for Gaussian random field textures · Orientation bandwidth | perceptual scale alignment | Helped |
Surprising findings
- Fixing the power spectrum along the interpolation path to the pair average deteriorates discriminability and the power-spectrum prediction no longer explains the measured scale.
- Power-spectrum-normalized textures produced some results that loosely aligned with the original VGG-19-based predictions, which the authors could not explain.
Limitations
- Assumes Gaussianity of feature activations, which is not true for VGG-19 features.
- MLDS limited to a single stimulus dimension and sensitivity not estimated per participant; stimuli chosen without adaptation.
- Predictions for naturalistic textures do not perfectly match measured scales; the theoretical link is not established for non-Gaussian naturalistic textures.
Experimental setup
Datasets: natural textures (VGG-19 texture synthesis)
Benchmarks: human difference scaling experiments (MLDS)
Metrics: Area Matching Score (AMS) bootstrapped 99.5% confidence intervals
Baselines: pixel Gaussian assumption wavelet (steerable pyramid) assumption power spectrum (auto-correlation) assumption
Builds on: Maximum Likelihood Difference Scaling Wei and Stocker optimal observer theory Whittle formula Gaussian random field texture synthesis
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