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arXiv · 2609.24819

When is a closed-form RGB->S/P ratio adequate? A hyperspectral characterization on natural scenes for mesopic display

Naoyuki Uchida
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Abstract

Mesopic and low-light display transforms require, as their driving signal, a per-pixel scotopic-to-photopic luminance ratio (S/P); the exact spectral S/P is unavailable for ordinary RGB content, so a low-cost closed form that estimates S/P from a linear-RGB triplet is used in its place. Such closed forms exist but have been characterized only on narrowband / LED sources, i.e. spectrally sparse spectra, where a relative error of ~41% has been reported for a three-channel projection. Display content, however, is natural and broadband. We ask whether the same closed form is adequate there, using per-pixel spectral S/P from hyperspectral imagery as ground truth. On a daylight radiance time-series, a six-scalar closed form (three photopic and three scotopic channel weights) reproduces spectral S/P with a median error of ~0.07 that is time-invariant once the RGB input is chromatically adapted to D65; evaluated in un-adapted sRGB the error instead carries a color-temperature tilt across illuminants (~0.19), so adaptation is the enabling step for this use case. The result generalizes to an independent fifty-scene set (pooled median 0.024; 45/50 scenes within a pre-registered 0.10 band), with the few exceedances concentrated in saturated, spectrally-peaky surfaces that approach the narrowband regime (floral close-ups in this set). The scotopic weight vector is shown to be primary-model dependent, but the value used here is corroborated by a primary-free XYZ projection, and the median error stays within the band across all principled coefficient choices. We do not claim observer-validated appearance fidelity or adequacy on narrowband sources; both are out of scope. Both outcomes follow from the same three-channel projection: it is overwhelmed by spectrally sparse inputs and adequate on spectrally smooth ones.

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Naoyuki Uchida. 2026-09-21. When is a closed-form RGB->S/P ratio adequate? A hyperspectral characterization on natural scenes for mesopic display. https://arxiv.org/abs/2609.24819

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