DoG E2=0.15 ·
rg_decay=0.072 · yv_decay=0.014 ·
fovea=90px ·
2026-03-07
What this tests: Scrutinizer's Mode 0 uses a 5-band Difference-of-Gaussians (DoG) decomposition
to approximate how spatial resolution degrades with eccentricity. Each band targets a spatial frequency
(0.25–4 cpd) and is attenuated by an M-scaling sigmoid derived from Rovamo & Virsu (1979).
Higher frequencies are cut at smaller eccentricities — matching the cortical magnification principle
that peripheral neurons pool over larger receptive fields, losing fine detail first.
We validate these predictions against sine-wave grating screenshots processed through Scrutinizer,
and compare the M-scaling cutoff positions against published human contrast sensitivity data.
Each curve shows one DoG frequency band's predicted retention vs eccentricity.
The sigmoid cutoffs create a staircase: 4 cpd dies at ~2°, 2 cpd at ~4°, 1 cpd at ~6°, 0.5 cpd at ~9°.
The residual (0.25 cpd) survives everywhere — coarse structure is always preserved.
Rovamo & Virsu 1979 vs Model
Dashed: human contrast sensitivity from Rovamo & Virsu (1979), showing smooth decay per frequency.
Solid thin: per-band DoG model (step functions — can't reproduce smooth curves by design).
Thick white: composite (frequency-weighted sum across bands) — this is the scored metric.
Composite declines smoothly and correlates well with Rovamo's integrated sensitivity.
Each point compares the same grating with and without Scrutinizer's filter at each ring.
A ratio below 100% means the filter reduced contrast at that frequency and eccentricity.
4 cpd (red) shows the steepest drop — the filter removes fine detail in the periphery, as intended.
0.25 cpd (purple) stays near 100% — coarse structure passes through unchanged.
Frequency vs Avg Cross-Condition Retention
Averaging across all rings: higher spatial frequencies are attenuated more by the filter.
This is the frequency-dependent decay we expect from M-scaling — the filter preferentially
removes detail that would be invisible in peripheral vision anyway.
Tier 1: Must Pass
Observation: Does the filter preserve frequency ordering (higher freq attenuated more)
and monotonic eccentricity decay? Model predictions should hold by construction. Measured grating contrast
should decrease with eccentricity when processed through Scrutinizer. Note: foveal-relative measurements
fail at low frequencies (0.25–0.5 cpd) because the foveal patch is too small for a full grating cycle.
Cross-condition retention is the more robust metric.
PASSRing 1: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=16%, 0.5cpd=100%, 0.25cpd=100%)
PASSRing 2: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=68%, 0.25cpd=100%)
PASSRing 3: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
PASSRing 4: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
PASSRing 5: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
Observation: Do the M-scaling cutoff positions match the expected values from Rovamo & Virsu (1979)?
E2 = 0.15 for the DoG decomposition means band0 (4 cpd) cuts at 0.15 normalized eccentricity,
band1 at 0.45, band2 at 1.05, band3 at 2.25. We also check that chromatic decay respects
the achromatic ≥ BY ≥ RG ordering from castleCSF.
PASSAchromatic >= BY >= RG at ring 3 band3: achrom=0.0%, by=0.0%, rg=0.0%
SKIPRendered vs model — requires per-band model mapping (future)
Tier 3: Stretch
Observation: We compute a frequency-weighted composite (sum of band retentions × freq / total freq)
and correlate it against Rovamo's frequency-averaged sensitivity. Per-band correlations are shown as INFO
— they're meaningless because each band is a step function. The composite captures the model's overall
spatial sensitivity envelope. With E2=0.15, bands 0–1 cut at <3°, so the composite drops fast.