Chroma-gated, differentiable OKLCH interpolation: Continuous Oklab fallback for color-cast reduction

OKLCH -- the cylindrical (lightness, chroma, hue) form of Ottosson's Oklab color space -- is the interpolation space recommended by CSS Color 4 for gradients and color-mix(), and it is now broadly deployed. Its polar parameterization, however, casts color near the neutral axis in two ways: (1) an inter-hue detour between two chromatic endpoints that sweeps through an unintended hue (blue to yellow visibly passing through green), and (2) an off-line bow when one endpoint is achromatic. Existing remedies are uniformly two-valued -- a threshold switch that fires only at an achromatic endpoint -- so they address only (2); on chromatic pairs every one of them reduces to raw OKLCH, leaving the (1) inter-hue cast untreated. We introduce Continuous Oklab fallback (COFb), a one-parameter, differentiable chroma gate $w(C)=C^n/(C^n+σ^n)$ that continuously blends the OKLCH path toward the linear Oklab path as chroma falls. A single gate reduces the (1) cast that the two-valued family leaves untreated and unifies the handling of (1) and (2) without any endpoint test. We characterize a cast-hue trade-off frontier, adopt a default ($n=1$, the rational Michaelis-Menten form; $σ\approx0.19$ for a typical sRGB palette, from a normalization-independent cast-half criterion), and verify the gate's properties symbolically. At the default, COFb halves the inter-hue path detour (mean lateral deviation -49.5%, chroma-weighted hue excursion -35.5%). We also state the method's limits: on (2) alone the two-valued switch remains better, and like any Cartesian blend COFb does not preserve chroma. In deployment, COFb runs entirely in plain Oklab (a,b) to sRGB, so it serves as a fallback that delivers the same cast-reduced gradients where modern CSS color interpolation (color-mix(in oklch) and the like) is unavailable -- older engines, image and video pipelines, or GPU shaders.

Oklch+: A Three-Parameter Extension of Oklab for Improved Color Difference Prediction

Oklab and its cylindrical representation Oklch are widely adopted in interpolation and design workflows as perceptually motivated color spaces, but their color difference prediction accuracy falls short of CIEDE2000. We propose Oklch+, a three-parameter extension of Oklab comprising a power transformation on the L-axis and a Naka-Rushton compression on the C-axis, with Euclidean distance computed in the resulting transformed Oklab coordinates. The Naka-Rushton function is bounded in [0,1], reflecting the saturating nature of chroma sensitivity at high colorimetric values. Evaluated on COMBVD -- 3,813 suprathreshold color difference pairs spanning six independent experimental datasets -- Oklch+ achieves STRESS = 29.09, closely matching CIEDE2000 (29.13; difference = 0.04), using only three parameters optimized against color difference data compared to approximately 17 for CIEDE2000. Cross-validation on a held-out BFD-P D65 subset (2,028 pairs) confirms generalization (STRESS = 26.14), with Oklch+ substantially outperforming Oklab (51.45) and achieving STRESS comparable to CIEDE2000 (24.12) on the held-out set. Improvement over Oklab (47.35) is confirmed across all six COMBVD sub-datasets. Because Oklch+ defines a coordinate system in which Euclidean distance approximates perceptual distance, linear interpolation in the transformed space offers substantially improved perceptual uniformity relative to Oklab. Current evaluation is limited to the sRGB-centered COMBVD dataset; validation in high-chroma regions with empirical observer-rated discrimination data remains future work.