Wave 2: Spatial Acuity Validation

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.

Tier 1: Must Pass

12 / 16

Tier 2: Should Pass

5 / 5

Tier 3: Stretch

0 / 5
Go ▶

Experimental Stimulus

0.25 cpd 0.5 cpd 1 cpd 2 cpd 4 cpd Freq Ladder

Model: DoG Band Retention (achromatic) 11/11 Tier 1

Claim: Higher spatial frequencies are cut at smaller eccentricities, creating a frequency staircase that matches cortical magnification
Basis: M-scaling (Rovamo & Virsu 1979) — peripheral neurons pool larger receptive fields, losing fine detail first
PASS 4 cpd dies at ~2°, 2 cpd at ~4°, 1 cpd at ~6°, 0.5 cpd at ~9°. Residual survives everywhere.

0%20%40%60%80%100%0°2°4°6°8°10°12°14°Eccentricity (degrees)Band Retention4 cpd2 cpd1 cpd0.5 cpd0.25 cpd

Rovamo & Virsu 1979 vs Model 5/5 Tier 2 0/1 Tier 3

Claim: A frequency-weighted composite of DoG bands tracks Rovamo's integrated contrast sensitivity curve (r > 0.9)
Basis: Rovamo & Virsu 1979 (contrast sensitivity by eccentricity per spatial frequency)
PARTIAL Composite declines smoothly and tracks the shape, but r=0.600 falls short of the 0.9 threshold. Per-band step functions can't match smooth psychophysical curves.

0%20%40%60%80%100%0°4°8°12°16°Eccentricity (degrees)Contrast SensitivityComposite (scored)4 cpd2 cpd1 cpd0.5 cpdsolid = model, dashed = Rovamo

Measured: Cross-Condition Retention (filtered/baseline) 1/5 Tier 1

Claim: Screenshot contrast ratio (filtered/baseline) decreases monotonically with eccentricity, with steeper drops for higher frequencies
Basis: M-scaling predicts higher frequencies attenuated more at greater eccentricity
PARTIAL 4 cpd shows steepest drop and 0.25 cpd stays near 100%, but monotonic decrease fails for 3 of 5 frequencies due to Mode 0 spatial blur confound.

0%20%40%60%80%100%120%0°2°4°6°8°10°12°14°Eccentricity (degrees)Filtered / Baseline4 cpd2 cpd1 cpd0.5 cpd0.25 cpd

Frequency vs Avg Cross-Condition Retention

Claim: Average retention across eccentricities decreases monotonically with spatial frequency
Basis: M-scaling — peripheral neurons pool larger receptive fields, losing fine detail first
PASS 0.25 cpd: 99%, 0.5 cpd: 98%, 1 cpd: 96%, 2 cpd: 87%, 4 cpd: 75%. Strict monotonic frequency ordering.

60%70%80%90%100%0.250.5124Spatial Frequency (cpd)Avg Retention99%98%96%87%75%

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.

PASS Ring 1: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=16%, 0.5cpd=100%, 0.25cpd=100%)
PASS Ring 2: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=68%, 0.25cpd=100%)
PASS Ring 3: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
PASS Ring 4: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
PASS Ring 5: frequency ordering preserved (4cpd=0%, 2cpd=0%, 1cpd=0%, 0.5cpd=0%, 0.25cpd=100%)
PASS band0: monotonic decrease (0% >= 0% >= 0% >= 0% >= 0%)
PASS band1: monotonic decrease (0% >= 0% >= 0% >= 0% >= 0%)
PASS band2: monotonic decrease (16% >= 0% >= 0% >= 0% >= 0%)
PASS band3: monotonic decrease (100% >= 68% >= 0% >= 0% >= 0%)
PASS residual: monotonic decrease (100% >= 100% >= 100% >= 100% >= 100%)
PASS Residual band >90% at all rings (min=100.0%)
FAIL Measured 4cpd: contrast monotonically decreases
FAIL Measured 2cpd: contrast monotonically decreases
PASS Measured 1cpd: contrast monotonically decreases
FAIL Measured 0.5cpd: contrast monotonically decreases
FAIL Measured 0.25cpd: contrast monotonically decreases

Tier 2: Should Pass

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.

PASS band0 cutoff: expected=0.15, actual=0.15 (0% off, threshold=30%)
PASS band1 cutoff: expected=0.45, actual=0.45 (0% off, threshold=30%)
PASS band2 cutoff: expected=1.05, actual=1.05 (0% off, threshold=30%)
PASS band3 cutoff: expected=2.25, actual=2.25 (0% off, threshold=30%)
PASS Achromatic >= BY >= RG at ring 3 band3: achrom=0.0%, by=0.0%, rg=0.0%
SKIP Rendered 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.

FAIL Composite spatial sensitivity correlates with Rovamo & Virsu: r=0.600 (threshold: r>0.9)
INFO band3 (0.5cpd) per-band r=0.600 (not scored — step function vs smooth curve)
INFO band2 (1cpd) per-band r=0.000 (not scored — step function vs smooth curve)
INFO band1 (2cpd) per-band r=-1.000 (not scored — step function vs smooth curve)
INFO band0 (4cpd) per-band r=-1.000 (not scored — step function vs smooth curve)
Scrutinizer Wave 2 · DoG band decomposition · M-scaling (Rovamo & Virsu 1979) · castleCSF