A Fluorescent Material Model for Non-Spectral Editing & Rendering

TL;DR

This work tackles rendering fluorescence in non-spectral engines by introducing an analytic, energy-conserving model that decomposes reduced reradiation into reflectance and normalized fluorescence, enabling real-time editing. Fluorescence is modeled as a Gaussian-based component, allowing analytic integration with Gaussian sensitivity bases and a UV channel, and is supported by a decomposition $P = R + \bar{F}[I - R]$ that preserves energy. A practical, artist-friendly variant uses a single Gaussian for $\bar{F}$ with a lightweight fluorescence palette and transfer matrices to map between XYZU and XYZ spaces, facilitating on-the-fly material editing and spatial variation. The approach is validated with measured materials, demonstrates real-time performance, and points to future extensions including angularly varying fluorescence and inverse design, potentially reducing memory demands while broadening expressivity in both non-spectral and spectral rendering contexts.

Abstract

Fluorescent materials are characterized by a spectral reradiation toward longer wavelengths. Recent work [Fichet et al. 2024] has shown that the rendering of fluorescence in a non-spectral engine is possible through the use of appropriate reduced reradiation matrices. But the approach has limited expressivity, as it requires the storage of one reduced matrix per fluorescent material, and only works with measured fluorescent assets. In this work, we introduce an analytical approach to the editing and rendering of fluorescence in a non-spectral engine. It is based on a decomposition of the reduced reradiation matrix, and an analytically-integrable Gaussian-based model of the fluorescent component. The model reproduces the appearance of fluorescent materials accurately, especially with the addition of a UV basis. Most importantly, it grants variations of fluorescent material parameters in real-time, either for the editing of fluorescent materials, or for the dynamic spatial variation of fluorescence properties across object surfaces. A simplified one-Gaussian fluorescence model even allows for the artist-friendly creation of plausible fluorescent materials from scratch, requiring only a few reflectance colors as input.

Figures (13)

• Figure 1: Model overview. With our decomposition, our model faithfully reproduces a measured reradiation matrix (HERPIPIN) with as low as one Gaussian for the reradiation. Our matrix decomposition works both on full spectral reradiation matrices (Equation \ref{['eqn:normalized-fluo']}) and with reduced matrices (Equation \ref{['eqn:reduced-decomp']}). This ensures energy conservation during the edition without the need to recompute the reduction for all components.
• Figure 2: Fitting of measured materials with our model. Our reradiation rescaling approach not only ensures energy conservation but also better reproduces the shape of the reradiative part for most of the measurements, even when using a single Gaussian.
• Figure 3: Accuracy of our model. We compare the reradiation of standard illuminants on the measured reradiation matrices from Gonzalez and Fairchild Gonzalez00 with the fitting of our model in the spectral domain. We use a different number of Gaussians for the reradiation and six Gaussians for the diagonal. The whiskers bottom and top represent resp. the minimum and the maximum, the box bottom and top represent resp. the first and third quartiles and the central line represent the average $\Delta E^*_{2000}$ distribution.
• Figure 4: Analytical integration of Gaussian-based Fluorescence. We show that we can analytically integrate our 2D model (a) by changing the shape of the integration domain (in red) with a serie of shears (b-c) that produce an axis aligned Gaussian and map the Heaviside to the half plane $\lambda^{\prime\prime}_i > 0$. This later stage enables to integrate separately the dimensions (c). In this Figure, the 2D Gaussian is scaled for visualization purpose and will not spread in the negative domain in practical cases.
• Figure 5: Gaussian basis functions. Our analytical bispectral integration relies on the availability of Gaussian sensitivity functions. We fit the CIE XYZ 2006 $2^\circ$$\bar{x}$ sensitivity function (in red) with a pair of Gaussians, while $\bar{y}$ and $\bar{z}$ only require a single Gaussian. In order to account for reradiation from non-visible to visible light, we provide an additional UV basis (in purple) whose parameters are chosen to best approximate measured materials.

Theorems & Definitions (1)

• proof