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

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.

Traditional in-camera colorimetric mapping relies on correlated color temperature (CCT)-based interpolation between pre-calibrated transforms optimized for Planckian illuminants such as CIE A and D65. However, modern lighting technologies such as LEDs can deviate substantially from the Planckian locus, exposing the limitations of relying on conventional one-dimensional CCT for illumination characterization. This paper demonstrates that transitioning from 1D CCT (on the Planckian locus) to a 2D chromaticity space (off the Planckian locus) improves colorimetric accuracy across various mapping approaches. In addition, we replace conventional CCT interpolation with a lightweight multi-layer perceptron (MLP) that leverages 2D chromaticity features for robust colorimetric mapping under non-Planckian illuminants. A lightbox-based calibration procedure incorporating representative LED sources is used to train our MLP. Validated across diverse LED lighting, our method reduces angular reproduction error by 22% on average in LED-lit scenes, maintains backward compatibility with traditional illuminants, accommodates multi-illuminant scenes, and supports real-time in-camera deployment with negligible additional computational cost.

Most image colorization systems operate in $Lab$ space by predicting chroma ($ab$) while preserving an input-derived luminance channel ($L$). While effective on standard benchmarks, this fixed-luminance design restricts brightness changes and becomes unreliable when grayscale formation deviates from natural-image luminance, as in historical orthochromatic photography. We propose a luminance-agnostic colorization framework that formulates colorization as full-RGB image editing using a foundation image-editing model. To bridge modern panchromatic and historical orthochromatic conditions, we introduce a mixed grayscale objective that trains the model under both standard luminance grayscale and a red-insensitive grayscale formation. Experiments on COCO, ImageNet, and a multi-instance benchmark show that our method is competitive on standard grayscale inputs and substantially more robust under orthochromatic inputs, with qualitative comparisons and a human study indicating fewer visible color artifacts.