How does color perception decay in the periphery, and which transfer function best models it for foveated rendering? A proposed evaluation methodology comparing exponential, smoothstep, and dual-sigma Oklab desaturation models.
Andy Edmonds · February 2026 · Motivated by the gap between FOVI's single-sigma RGB decay and Scrutinizer's Oklab pipeline
Foveated rendering systems need to desaturate peripheral content to simulate the rod-dominated periphery. But there's no consensus on the transfer function. Current approaches:
| System | Function | Color Space | Channels |
|---|---|---|---|
| FOVI (mode 6) | $\exp(-e / \sigma)$, single $\sigma$ | RGB luminance | Uniform |
| Scrutinizer (modes 0–1) | smoothstep ramp | Oklab | Uniform (a,b) |
| BubbleView et al. | Gaussian blur | RGB | N/A (blur, not desaturation) |
None of these model the biological reality: the two cone-opponent systems decline at different rates with eccentricity.
Mullen & Kingdom (2002) showed that red-green (L/M) chromatic contrast sensitivity declines much more steeply with eccentricity than achromatic sensitivity — and critically, this loss cannot be fully explained by cortical magnification alone. There is an "extra" post-receptoral loss specific to the red-green system.
Blue-yellow (S-cone) sensitivity declines more gradually. Hansen, Pracejus & Gegenfurtner (2009) measured chromatic discrimination at 5°, 30°, and 50°, finding thresholds ~4.5× foveal at 50° — but with L/M-isolating stimuli degrading faster than S-cone isolating stimuli.
A Feb 2025 bioRxiv preprint reframes the entire question: peripheral desaturation may be a consequence of contrast sensitivity and constancy rather than cone density per se. Higher absolute chromatic contrast is needed to compensate for sensitivity loss in the periphery, and the desaturation percept is what happens when contrast falls below this compensating threshold. This suggests the exponential decay models a contrast sensitivity envelope, not the cone-to-rod transition directly.
The cone density falloff (Curcio et al., 1990) is not exponential — it follows a reciprocal power law: $D(e) = D_0 / (1 + e/r_2)^n$. But for screen-range eccentricities (5–30°), $\exp(-e/\sigma)$ is a tolerable approximation.
The proposed transfer function combines the exponential form (biologically motivated, immediate onset) with Oklab color space (perceptually uniform, opponent channels separated) and dual sigma values (different rates for red-green vs. blue-yellow):
Where lab.y is the Oklab red-green opponent channel, lab.z
is blue-yellow, and $e$ is eccentricity in degrees. The two sigma values
capture the differential decline rates documented by Mullen & Kingdom.
| Channel | Estimated $\sigma$ | Half-saturation | Source |
|---|---|---|---|
| Red-green (lab.y) | $\sigma_{rg} \approx 4$–$8°$ | ~3–6° | Mullen & Kingdom 2002 |
| Blue-yellow (lab.z) | $\sigma_{by} \approx 12$–$25°$ | ~8–17° | Mullen & Kingdom 2002, Hansen 2009 |
| Combined (FOVI default) | $\sigma = 4.0°$ | ~2.8° | FOVI mode 6 (steep/conservative) |
// V4 style_id = 8: Dual-sigma exponential in Oklab
vec3 lab = rgbToOklab(col);
float r_deg = normEcc * fovea_deg;
lab.y *= exp(-r_deg / u_sigma_rg); // red-green: steep
lab.z *= exp(-r_deg / u_sigma_by); // blue-yellow: gradual
col = oklabToRgb(lab);
Six lines of GLSL. The Oklab conversion functions already exist in Scrutinizer's
shader (used by modes 0 and 1). The new uniforms u_sigma_rg and
u_sigma_by slot into the existing config pipeline via
modes.json.
Three experiments, ordered by feasibility. All compare the same three transfer functions: (A) smoothstep in Oklab, (B) single-sigma exponential in RGB, (C) dual-sigma exponential in Oklab.
Present two gaze-contingent foveated images side-by-side. Participant fixates center; one half uses function A, the other uses function C. "Which looks more like real peripheral vision?" Parametrically vary sigma values for both.
Hypothesis: Dual-sigma Oklab will be judged more natural than single-sigma RGB at matched overall desaturation strength, because red elements will fade faster than blue — matching the M/P pathway asymmetry.
2AFC: a color patch at eccentricity $e$ with one desaturation function applied. "Is this red or orange?" Measure threshold elevation as a function of $e$ under each model. Compare resulting threshold curves to Hansen et al. (2009) psychophysics.
Prediction: The model whose threshold curve best fits the Hansen data is the most perceptually accurate. The dual-sigma model should fit better for L/M stimuli, where the extra loss beyond CMF is well-documented.
Foveal reference color patch. Peripheral comparison at 5°, 10°, 20°, 30°. Participant adjusts the sigma parameter until the peripheral patch "looks right" — matching their subjective experience of how color fades in the periphery.
DV: Sigma at point of subjective match. If the exponential form better captures biology, participants will produce more consistent (lower variance) settings with it than the smoothstep.
• Gaze-contingent display with eye tracker (not mouse proxy — saccadic
color judgments confound with foveal sampling)
• Color-calibrated display (sRGB minimum; P3 desirable for wider gamut test
stimuli)
• Separate conditions for L/M-isolating and S-cone-isolating stimuli
• "No desaturation" control condition
• Sufficient eccentricities to distinguish exponential from smoothstep shapes
(the functions diverge most at 5–15°)
Does the functional form of the desaturation transfer function matter to perception? Or is the parameterization (how much desaturation at what eccentricity) more important than the shape of the curve?
If the answer is "form matters" — the dual-sigma exponential in Oklab is a publishable contribution to foveated rendering. If the answer is "only strength matters" — then Scrutinizer's existing smoothstep is fine and the exponential adds complexity without perceptual benefit. Either result is informative.
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Human photoreceptor topography.
Journal of Comparative Neurology, 292(4), 497–523.
Hansen, T., Pracejus, L., & Gegenfurtner, K. R. (2009).
Color perception in the intermediate periphery of the visual field.
Journal of Vision, 9(4):26.
Mullen, K. T., & Kingdom, F. A. A. (2002).
Differential distributions of red–green and blue–yellow cone opponency across the visual field.
Visual Neuroscience, 19(1), 109–118.
Radonjić et al. (2025).
Colour desaturation in the periphery is explained by general mechanisms of contrast sensitivity and constancy.
bioRxiv.
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An estimation and application of the human cortical magnification factor.
Experimental Brain Research, 37(3), 495–510.
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